MEDICAL    SCHOOL 


Hooper  Foundation 
Accession 


SMITHSONIAN   MISCELLANEOUS   COLLECTIONS 

VOLUME    71,   NUMBER  1 


SMITHSONIAN 

PHYSICAL  TABLES 

REPRINT  OF  SE  VENTH  RE  VISED  EDITION 


PREPARED   BY 


FREDERICK   E.    FOWLE 

AID,  SMITHSONIAN    ASTROPHYSICAL   OBSERVATORY 


(PUBLICATION    2539) 


CITY  OF  WASHINGTON 

PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION 
1921 

3 


78 


ADVERTISEMENT. 

In  connection  with  the  system  of  meteorological  observations  established  by 
the  Smithsonian  Institution  about  1850,  a  series  of  meteorological  tables  was 
compiled  by  Dr.  Arnold  Guyot,  at  the  request  of  Secretary  Henry,  and  the 
first  edition  was  published  in  1852.  Though  primarily  designed  for  meteoro- 
logical observers  reporting  to  the  Smithsonian  Institution,  the  tables  were  so 
widely  used  by  physicists  that  it  seemed  desirable  to  recast  the  work  entirely. 
It  was  decided  to  publish  three  sets  of  tables,  each  representative  of  the  latest 
knowledge  in  its  field,  and  independent  of  one  another,  but  forming  a  homo- 
geneous series.  The  first  of  the  new  series.  Meteorological  Tables,  was 
published  in  1893,  the  second,  Geographical  Tables,  in  1894,  and  the  third, 
Physical  Tables,  in  1896.  In  1909  yet  another  volume  was  added,  so  that  the 
series  now  comprises:  Smithsonian  Meteorological  Tables,  Smithsonian 
Geographical  Tables,  Smithsonian  Physical  Tables,  and  Smithsonian  Mathe- 
matical Tables. 

The  fourteen  years  which  had  elapsed  in  1910  since  the  publication  of  the 
first  edition  of  the  Physical  Tables,  prepared  by  Professor  Thomas  Gray, 
had  brought  such  changes  in  the  material  upon  which  the  tables  must  be 
based  that  it  became  necessary  to  make  a  radical  revision  for  the  fifth  and 
sixth  revised  editions  published  in  1910  and  1914.  The  latter  edition  was  re- 
printed thrice.  For  the  present  seventh  revision  extended  changes  have  been 
made  with  the  inclusion  of  new  data  on  old  and  new  topics. 

CHARLES  D.  WALCOTT, 
Secretary  of  the  Smithsonian  Institution. 
June, 


PREFACE  TO  7™  REVISED  EDITION. 

The  present  edition  of  the  Smithsonian  Physical  Tables  entails  a  considerable 
enlargement.  Besides  the  insertion  of  new  data  in  the  older  tables,  about  170 
new  tables  have  been  added.  The  scope  of  the  tables  has  been  broadened  to 
include  tables  on  astrophysics,  meteorology,  geochemistry,  atomic  and  molecu- 
lar data,  colloids,  photography,  etc.  In  the  earlier  revisions  the  insertion  of 
new  matter  in  a  way  to  avoid  renumbering  the  pages  resulted  in  a  somewhat 
illogical  sequence  of  tables.  This  we  have  tried  to  remedy  in  the  present  edition 
by  radically  rearranging  the  tables;  the  sequence  is  now,  —  mathematical,  me- 
chanical, acoustical,  thermal,  optical,  electrical,  etc. 

Many  suggestions  and  data  have  been  received:  from  the  Bureau  of  Stand- 
ards, —  including  the  revision  of  the  magnetic,  mechanical,  and  X-ray  tables, 
—  from  the  Coast  and  Geodetic  Survey  (magnetic  data),  the  Naval  Observ- 
atory, the  Geophysical  Laboratory,  Department  of  Terrestrial  Magnetism,  etc. ; 
from  Messrs.  Adams  of  the  Mount  Wilson  Observatory,  Adams  of  the  Geo- 
physical Laboratory  (compressibility  tables),  Anderson  (mechanical  tables), 
Bellinger,  Hackh,  Humphreys,  Mees  and  Lovejoy  of  the  Eastman  Kodak  Co. 
(photographic  data),  Miller  (acoustical  data),  Van  Orstrand,  Russell  of  Prince- 
ton (astronomical  tables),  Saunders,  Wherry  and  Lassen  (crystal  indices  of 
refraction),  White,  Worthing  and  Forsythe  and  others  of  the  Nela  Research 
Laboratory,  Zahm  (aeronautical  tables).  To  all  these  and  others  we  are  in- 
debted for  valuable  criticisms  and  data.  We  will  ever  be  grateful  for  further 
criticisms,  the  notification  of  errors,  and  new  data. 

FREDERICK  E.  FOWLE. 

ASTROPHYSICAL  OBSERVATORY, 

SMITHSONIAN  INSTITUTION, 

May,  1919. 


NOTE  TO  REPRINT  OF  ;TH  REVISED  EDITION. 

Opportunity  comes  with  this  reprint  to  insert  in  the  plates  a  number  of  correc- 
tions as  well  as  some  newer  data.  Gratitude  is  especially  due  to  Messrs.  Wherry 
and  Smith  of  the  Bureau  of  Chemistry,  Department  of  Agriculture,  for  sugges- 
tions. 

FREDERICK  E.  FOWLE. 

ASTROPHYSICAL  OBSERVATORY, 
SMITHSONIAN  INSTITUTION, 
March,  1921. 


TABLE   OF  CONTENTS. 

Introduction:    units   of  measurement,   dimensional  and  conversion  formulae, 

standards:      xxiii 

General  discussion,  xxiii;  Fundamental  units,  xxiii;  Derived  units,  xxiv;  Con- 
version factors  and  dimensional  formulae,  xxv;  Dimensional  reason- 
ing, XXV. 

Dimensional  formulae: xxvi 

Geometrical  and  mechanical  units,  xxvi;  Heat  units,  xxviii;  Electric  and  mag- 
netic units,  xxix;  Electrostatic  system,  xxx;  Electromagnetic  system,  xxxi. 

Fundamental  standards: xxxiii 

Standards  of  length,  xxxiv;  Standards  of  mass,.xxxiv;  Standards  of  time, 
xxxiv;  Standards  of  temperature,  xxxiv. 

Numerically  different  systems  of  units: • .    .    .   xxxv 

Proposed  systems  of  units  (table  I),  xxxv;  Gaussian  systems,  xxxv;  Practical 
electromagnetic  system,  xxxvi;  International  electric  units,  xxxvi. 

The  standards  of  the  International  Electric  Units: xxxviii 

Resistance,  xxxviii:  Mercury  standards,  xxxviii;  Secondary  standards,  xxxix; 

Resistance  standards  in  practice,  xxxLx;   Absolute  ohm,  xxxix. 
Current,  xl:    Silver  voltameter,  xl;   Resistance  standards  used  in  current 

measurements,  xli;   Absolute  ampere,  xli. 
Electromotive   force,    xli:    International    volt,    xli;    Weston   normal    cell, 

xli;  Portable  Weston  cell,  xliii;  Absolute  and  semi-absolute  volts,  xliii. 
Quantity  of  electricity,  xliv:   Standards,  xliv. 
Capacity,  xliv. 

Inductance,  xliv:   Inductance  standards,  xliv. 
Power  and  energy,  xlv:  Watt,  xlv;   Standards  and  measurement,  xlv. 

Magnetic  units,  xlv:  Table  II.  —  The  ordinary  and  ampere-turn  units  xlvi. 

TABLE  PAGE 

1.  Spelling  and  abbreviations  of  common  units  of  weight  and  measure  .    .         2 

2.  Fundamental  and  derived  units,  conversion  factors 3 

(a)  Fundamental  units 3 

(b)  Derived  units 3 

3.  Tables  for  converting  U.  S.  weights  and  measures: 

(1)  Customary  to  metric 5 

(2)  Metric  to  customary 6 

4.  Miscellaneous  equivalents  U.  S.  and  metric  weights  and  measures     .    .         7 


Vi  CONTENTS. 

5.  Equivalents  of  metric  and  British  imperial  weights  and  measures: 

(1)  Metric  to  imperial    ..................  8 

(2)  Multiples,  metric  to  imperial      .............  9 

(3)  Imperial  to  metric    ..................  10 

(4)  Multiples,  imperial  to  metric      .............  1  1 

MATHEMATICAL  TABLES 

6.  Derivatives  and  integrals    ....................  12 

7.  Series      ............................  13 

8.  Mathematical  constants      ....................  14 

9.  Reciprocals,  squares,  cubes  and  square  roots  of  natural  numbers  ...  15 

10.  Logarithms,  4-place,  1000-2000     .................  24 

11.  Logarithms,  4-place  .    .    .....................  26 

12.  Antilogarithms,  4-place  ....... 

13.  Antilogarithms,  4-place,  0.9000-1.0000    ..............  30 

14.  Circular  (trigonometric)  functions,  arguments  (°,  ').  .........  32 

15.  "                   "                    "                 "          (radians)  .......  37 

16.  Logarithmic  factorials,  n!,  n  =  i  to  100  ..............  40 

17.  Hyperbolic  functions  .    .    .    .    ..................  41 

18.  Factorials,  i  to  20    ........    ...............  47 

19.  Exponential  functions     ................    .....  48 

20.  Values  of  e*2  and  e~**  and  their  logarithms      ............  54 

21.  "      "  «V_"    e-r  "       "                          ........  ••••.-  55 

22.  "       "  /?*  «  e~v^        «            "             ............  55 

23.  "       "  t*     "    e-'     "      "            "        ,  x  fractional   .......  56 

24.  Least  squares:  probability  integral,  argument  hx      .........  56 

25-                                     "                "     _  "_       */r  .........  57 

26.  values  of  0.6745  \/i/(n  —  i)    ............  57 

27.  "       "  0.6745  Vi/n^^     ...........  58 

28.  "       "  0.8453  Vi/n(n  -  i)  .    .    ..........  58 

29-                                   "       "  0.8453  {i/«V»-  1  1         ...........  58 

30.  formulae    ....................  •  59 

31.  Inverse  probability  integral,  diffusion  integral    ...........  60 

32.  Logarithms  of  gamma  function,  n  between  i  and  2  .........  62 

33.  Values  for  the  first  seven.  zonal  harmonics,  9  =  o°  to  6  =  90°  .    .    .    .  64 

34.  Cylindrical  harmonics,  oth  and  i  st  orders,  x  =  o  to  3.  5,  6-place.    ...  66 
35-                                                                  "       x  =  4  to  15,  4-place  ....  68 
36.    (a)  ist  ten  roots  cylindrical  harmonic  of  zeroth  order  =  o  ......  68 

(b)    "   fifteen  "           "                 "        '«    first        "     =o  ......  68 

Notes,  general  formulae  of  Bessel's  functions     ...........  68 


37. 


Values  f  or  I  *  (i  -  sin2  6  sin2  $)  =*=*(/$;  argument  6;  also  logs   ....  69 

*J  o 

38.  Moments  of  inertia,  radii  of  gyration,  corresponding  weights      ....  70 

39.  International  atomic  weights,  valencies  ..............  71 


CONTENTS.  Vii 

40.  Volume  of  glass  vessel  from  weight  of  its  volume  of  H2O  or  Hg .    ...  72 

41.  Reductions  of  weighings  in  air  to  vacuo 73 

42.  Reductions  of  densities  in  air  to  vacuo 73 

MECHANICAL  PROPERTIES 

43.  Introduction  and  definitions 74 

44.  Ferrous  metals  and  alloys:  Iron  and  iron  alloys 75 

45.  "        "         "       carbon  steels 76 

46.  "  "        "        "       heat  treatments 76 

47.  "  "        "        "       alloy  steels 77 

48.  "       steel  wire,  specification  values 78 

49.  "        "        "          "     .   "     experimental  values 78 

50.  "  "        "        "       semi-steel 78 

51.  steel  wire  rope,  specification  values      ...  79 

52.  "       plow-steel  rope,  "       ....  79 

53.  steel  wire  rope,  experimental  values     ...  79 

54.  Aluminum,  miscellaneous 80 

55.  Aluminum:  (a)  sheet,  experimental  values 80 

(b)       "     specification  values      81 

56.  Aluminum  alloys 81 

57.  Copper:  miscellaneous  experimental  values 82 

58.  rolled,  experimental  values 82 

59.  wire,  specification  values,  hard-drawn 82 

60.  "  "     medium  hard-drawn 83 

61.  "  "     soft  or  annealed 83 

62.  plates 83 

63.  Copper  alloys:  nomenclature 83 

64.  "       copper-zinc  alloys  or  brasses 84 

"       copper-tin         "      "  bronzes 84 

65.  "  "       three  or  more  metals 85 

66.  Miscellaneous  alloys 88 

67.  metals:  tungsten;  zinc;  white  metal      89 

68.  Cement  and  concrete :  (a)  cement 90 

"          "  "         (b)  cement  and  cement  mortars 90 

(c)  concrete      91 

69.  Stone  and  clay  products:  (a)  American  building  stones 92 

"       "      "  "          (b}  Bavarian  building  stones 92 

"        "       "  "          (c)  American  building  bricks 93 

"        "      "  (d)  brick  piers,  terra-cot ta  piers      93 

"          (e)  various  bricks 93 

70.  (a)  Sheet  rubber 94 

(b)  Leather  belting      94 

71.  Manilla  rope 95 

72.  Woods:  hardwoods,  metric  units 96 

73.  "        conifers,  metric  units 97 


viii  CONTENTS. 

74.  Woods:  hardwoods,  English  units 98 

75.  "       conifers,  English  units 99 

76.  Rigidity  Modulus 100 

77.  Variation  of  moduli  of  rigidity  with  the  temperature 100 

78.  Interior  friction,  variation  with  the  temperature 101 

79.  Hardness 101 

80.  Relative  hardness  of  the  elements 101 

81.  Poisson's  ratio 101 

82.  Elastic  moduli  of  crystals,  formulae 102 

83.  "  '         "       "         "       numerical  results 103 

COMPRESSIBILITY  OF  GASES 

84.  Compressibility  of  O,  air,  N,  H,  different  pressures  and  temperatures  .  104 

85.  "               "  ethylene  at          "                          "                             .  104 

86.  Relative  gas  volumes  at  various  pressures,  H,  N,  air,  O,  CC>2     ....  104 

87.  Compressibility  of  carbon  dioxide,  pressure- temperature  variation    .    .  105 

88.  "  gases,  values  of 105 

89.  "  air  and  oxygen  between  1 8°  and  22°  C 105 

90.  Relation  between  pressure,  temperature  and  volume  of  sulphur  dioxide  106 

91.  "              "              "                  "             "         "        "  ammonia  .    .    .  106 

92.  Compressibility  of  liquids 107 

93.  "               "  solids 108 

DENSITIES 

94.  Specific  gravities  corresponding  to  the  Baume  scale 109 

95.  Densities  of  the  solid  and  liquid  elements no 

96.  "  various  woods 112 

97.  "         "        "       solids 113 

98.  "                  "       alloys 114 

99.  natural  and  artificial  minerals 115 

100.  "  molten  tin  and  tin-lead  eutectic 115 

101.  Weight  in  grams  per  square  meter  of  sheet  metal 116 

102.  "  various  common  units  of  sheet  metal 116 

103.  Densities  of  various  liquids 117 

104.  Density  of  air-free  water  between  o°  and  41°  C 118 

105.  Relative  volume  of  water  between  o°  and  40°  C 119 

106.  Density  and  volume  of  water,  — 10°  to  250°  C      120 

107.  "          "         "        "  mercury,  -10°  to  360°  C 121 

108.  Density  of  aqueous  solutions  of  salts,  bases  and  acids 122 

109.  ethyl  alcohol,  temperature  variation 124 

no.                                     methyl  alcohol,  cane-sugar,  sulphuric  acid .    ...  126 

in.                  "  various  gases 127 

112.   Volume  of  gases,  —  values  of  i  +  0.00367  /: 

(a)  for  values  of  t  between  o°  and  10°  C  by  o.  i°  steps     ....  128 

(b)  "       "      ""       "       -90°  and +1990°  C  by  10°  steps      .  129 


CONTENTS.  ix 

(c)  logarithms  for  /  between  -49°  and  399°  C  by  i°  steps      .    .  130 

(d)  +400°  and  1990*0  by  10°  steps    .  132 

113.  Density  of  moist  air:    h/ 7 60,  h  from  i  to  9      133 

114.  "        "      "      "       log  A/y6o,  h  from  80  to  800 133 

115.  "      "       "      0.378^  in  equation  h  =  B  —  0.3786 135 

116.  Maintenance  of  air  at  definite  humidities      135 

117.  Pressure  of  mercury  and  water  columns 136 

BAROMETRIC  TABLES 

1 1 8.  Reduction  of  barometer  to  standard  temperature 137 

119.  gravity,  in.  and  mm,  altitude  term  138 

120.  "  latitude  45°,  o°  to  45°,  mm 139 

"     45°  to  90°,  mm 140 


122.  o°  to  45°,  inches 141 

123.  "     45°  to  90°,  inches 142 

124.  Correction  to  barometer  for  capillarity,  mm  and  inches 143 

125.  Volume  of  mercury  meniscus  in  mm3 .  143 

126.  Barometric  pressure  corresponding  to  the  boiling  point  of  water: 

(a)  metric  scale 144 

(b)  inch  scale 144 

127.  Determination  of  heights  by  the  barometer 145 

ACOUSTICS 

128.  Velocity  of  sound  in  solids 146 

129.  "      "  liquids  and  gases 147 

130.  Musical  scales 148 

131.  "  "        148 

132.  Fundamental  tone,  its  harmonics  and  equal  tempered  scale 149 

133.  Relative  strength  of  the  partials  of  musical  instruments 149 

134.  Characteristics  of  the  vowels 149 

135.  Miscellaneous  sound  data 149 

AERODYNAMICS 

136.  Kinetics  of  bodies  in  resisting  medium,  Stokes  law      150 

137.  Flow  of  gas  through  tubes 150 

138.  Air  pressure,  large  square  normal  planes,  various  speeds 151 

139.  Correction  factor  for  small  square  normal  planes 151 

140.  Effect  of  aspect  ratio 152 

141.  Ratios  of  pressures  on  inclined  and  normal  planes 152 

142.  Skin  friction 152 

143.  Variation  of  air  resistance  with  aspect  and  angle 153 

144.  "  "     shape  and  size 153 

145.  "        "        "      "    and  speed 153 

146.  Friction    . 154 


X  CONTENTS. 

147.  Lubricants 154 

148.  Lubricants  for  cutting  tools 154 

VISCOSITY 

149.  Viscosity  of  fluids  and  solids,  general  considerations 155 

150.  "  water  in  centipoises,  temperature  variation 155 

151.  "  ethyl-alcohol-water  mixtures,  temperature  variation     .    .  155 

152.  and  density  of  sucrose  aqueous  solutions,  temp,  variation    .  156 

153.  "          "         "        "  glycerol       "  "      at  20°  C 156 

154.  "  "  castor  oil,  temperature  variation 156 

155.  "         of  miscellaneous  liquids ^  .  157 

156.  "  organic  liquids 158 

157.  Specific  viscosity  of  solutions,  density  and  temperature  variation    .    .  159 

158.  "  "         "          "         atomic  concentrations,  25°  C 163 

159.  Viscosity  of  gases  and  vapors f 164 

1 60.  "      :  temperature  and  pressure  variation    .  165 

161.  Diffusion  of  an  aqueous  solution  into  pure  water     .........  166 

162.  "  vapors 167 

163.  "  gases  and  vapors 168 

164.  "  metals  into  metals 168 

165.  Solubility  of  inorganic  salts  in  water,  temperature  variation     ....  169 

166.  "          "  a  few  organic  salts  in  water,  temperature  variation      .    .  170 

167.  "  gases  in  water 170 

168.  "  change  of ,  produced  by  uniform  pressure 171 

169.  Absorption  of  gases  by  liquids 172 

170.  Capillarity  and  surface  tension,  water  and  alcohol  in  air '.  173 

171.  "       miscellaneous  liquids  in  air      ....  173 

172.  aqueous  solutions  of  salts 173 

173.  "       liquids-air,  -water,  -mercury    ....  174 

174.  liquids  at  solidifying  point 174 

175.  "       thickness  of  soap  films 174 

VAPOR  PRESSURES 

176.  Vapor  pressures  of  elements 175 

177.  and  rates  of  evaporation,  Mo,  W,  Pt 175 

178.  organic  liquids 176 

179-       "  of  ethyl  alcohol 178 

180.  "  "  methyl  alcohol 178 

181.  «  (a)  carbon  disulphide 179 

(b)  chlorobenzene J79 

(c)  bromobenzene *79 

(d)  aniline 179 

(e)  methyl  salicylate 180 

(/)  bromonaphthalene 180 

(g)  mercury 180 


CONTENTS.  xi 

182.  Vapor  pressure  of  solutions  of  salts  in  water 181 

183.  Pressure  of  saturated  water  vapor  over  ice,  low  temperatures  ....  183 

184.  "     water,  low  temperatures     .    .  183 

185.  "  o°  to  374°  C 183 

186.  Weight  in  g  per  m3  of  saturated  water  vapor 185 

187.  Weight  in  grains  per  ft3  of  saturated  water  vapor 185 

1 88.  Pressure  of  aqueous  vapor  in  atmosphere,  various  altitudes 185 

189.  "         "         "            "      "            "            sea-level 186 

190.  Relative  humidity,  arguments,  vapor  pressure  and  dry  temperature    .  187 

191.  wet  and  dry  thermometers 189 

THERMOMETRY 

192.  Stem  correction  for  thermometers,  centigrade 190 

193.  "                                                      Jena  glass,  o°  to  360°  C 190 

194.  "             "                                           "        "     o°   "     "      " 191 

195.  "  "                          "                "        "     normal,  o°  to  100°  C    .  191 

196.  Gas  and  mercury  thermometers,  formulae 192 

197.  Comparison  of  hydrogen  and  i6UI  thermometers,  o°  to  100°  C  .    .   .    .  192 

198.  "  "          "           "    59111              "            o°  "  100°  C.    ...  192 

199.  "  "          "           "    1 6™    and    59™    thermometers,    -5°    to 
-35°  C 192 

200.  Comparison  of  air  and  i6in  thermometers,  o°  to  300°  C 193 

201.  "            "    "     "      59rn             "             100°  to  200°  C 193 

202.  "  hydrogen  and  various  mercury  thermometers    ....  194 

203.  "  air  and  high  temperature  (59m)  mercury  thermometer  194 

204.  "  H,  toluol,  alcohol,  petrol  ether,  pentane  thermometers  194 

205.  Platinum  resistance  thermometry 195 

206.  Thermodynamic  scale;  temperature  of  ice  point,  Kelvin  scale  ....  195 

207.  Standard  points  for  the  calibration  of  thermometers 195 

208.  Calibration  of  thermo-element,  Pt—Pt-Rh 196 

209.  "           "               "              Cu-constantan 196 

210.  Mechanical  equivalent  of  heat,  summary  to  1900  (Ames) 197 

211.  "                  "          "      "    best  value 197 

212.  Conversion  factors,  work  units 197 

213.  English  and  American  horse  power,  altitude  and  latitude  variation    .  197 

MELTING  AND  BOILING  POINTS 

214.  Melting  points  of  the  chemical  elements ,    .  198 

215.  Boiling  points  of  the  chemical  elements     ....  ....  199 

216.  Melting  points,  effect  of  pressure    ....  200 

217.  Freezing  point  of  water,  effect  of  pressure 200 

218.  Boiling  point,  effect  of  pressure 200 

219.  Inorganic  c.ompounds,  melting  and  boiling  points,  densities 201 


X  CONTENTS. 

2 20.  Organic  compounds,  melting  and  boiling  points,  densities: 203 

(a)  Paraffin  series 203 

(b)  Olefine  series      203 

(c)  Acetylene  series 204 

(d)  Monatomic  alcohols 204 

(e)  Alcoholic  ethers 204 

(/)   Ethyl  ethers 204 

(g)  Miscellaneous 205 

221.  Melting  points  of  various  mixtures  of  metals 206 

222.  "                 "          "           "                    "             "          "            206 

223.  Low-melting-point  alloys 206 

224.  Transformation  and  melting  points,  minerals  and  eutectics 207 

225.  Lowering  of  freezing  points  by  salts  in  solution 208 

226.  Raising  of  boiling  points  by  salts  in  solution 210 

227.  Freezing  mixtures 211 

228.  Critical  temperatures,  pressures,  volumes,  densities  of  gases     ....  212 

THERMAL  CONDUCTIVITY 

229.  Thermal  conductivity  of  metals  and  alloys 213 

230.  insulators,  high  temperatures 214 

231.  various  substances      214 

232.  building  materials 215 

233.  various  insulators 216 

234.  water  and  salt  solutions    ..........  216 

235.  organic  liquids 217 

236.  gases 217 

237.  Diffusivities 217 

EXPANSION  COEFFICIENTS 

238.  Linear  expansion  of  the  elements 218 

239.  "                        "  miscellaneous  substances 219 

240.  Cubical  expansion  of  solids 220 

241.  "  liquids 221 

242.  "  gases 222 

SPECIFIC  HEATS 

243.  Specific  heats  of  elements 223 

244.  Heat  capacities,  true  and  mean  specific  heats,  and  latent  heats  of 

fusion  of  the  metallic  elements,  o°  to  1600°  C 225 

245.  Atomic  heats,  atomic  volumes,  specific  heats  at  50°  K,  elements  226 

246.  Specific  heats  of  various  solids 227 

247.  "      "  water  and  mercury 227 

248.  "      "  various  liquids 228 

249.  "       heat  of  saturated  liquid  ammonia, -50°  to +50°  C  ...  228 

250.  Heat  contents  of  saturated  liquid  ammonia, —50°  to +50°  C    ....  228 


CONTENTS.  Xiil 

251.  Specific  heats  of  minerals  and  rocks 229 

252.  "      (true  and  mean)  of  silicates,  o°  to  1400°  C 229 

253.  of  gases  and  vapors,  also  cp/cv 230 

LATENT  HEATS 

254.  Latent  heats  of  vaporization 231 

255.  formulae 232 

256.  ammonia 232 

257.  "  Latent  heat  of  pressure  variation  "  of  liquid  ammonia 232 

258.  Latent  and  total  heats  of  vaporization  of  elements,  —  theoretical    .    .  233 

259.  Properties  of  saturated  steam 234 

260.  Latent  heats  of  fusion 240 

HEATS  OF  COMBUSTION,  FORMATION,  ETC. 

261.  Heats  of  combustion  of  some  carbon  compounds 241 

262.  "      "  "  miscellaneous  compounds 241 

263.  Heat  values  and  analyses  of  various  fuels:  (a)  coals  and  coke  ....  242 

(b)  peats  and  woods  .    .    .  242 

(c)  liquid  fuels 242 

(d)  gases 242 

264.  Chemical  and  physical  properties  of  explosives 243 

265.  Additional  data  on  explosives " 244 

266.  Ignition  temperatures  of  gaseous  mixtures 244 

267.  Explosive  decomposition,  ignition  temperatures       244 

268.  Flame  temperatures 244 

269.  Thermochemical  data:  heats  of  formation  from  elements 245 

270.  "  "         "      "          "         of  ions 246 

271.  "  "      "  neutralization 246 

272.  "    .  "  dilution  of  sulphuric  acid     .....  246 

RADIATION 

273.  Radiation  formulae  and  constants  for  perfect  (black-body)  radiator  .  247 

274.  in  calories  for  perfect  radiator,  various  temperatures   .    .    .  247 

275.  distribution  in  spectrum  for  various  temperatures    ....  247 

276.  Black-body  spectrum  intensities,  50°  to  20000°  K 248 

277.  Relative  emissive  powers  of  various  bodies  for  total  radiation  ....  249 

278.  Emissivities  of  metals  and  oxides 249 

279.  "  "       "         "         "        249 

280.  Temperature  scale  for  tungsten,  —  color,  black-body  and  true  tem- 

peratures       250 

281.  Color  minus  brightness  temperature  for  carbon 250 

COOLING  BY  RADIATION,  CONDUCTION,  AND  CONVECTION 

282.  Cooling  by  radiation  and  convection:  ordinary  pressures 251 

283.  different  pressures 251 


XIV  CONTENTS. 

284.  Cooling  by  radiation  and  convection:  very  small  pressures 252 

285.  temperature  and  pressure  effect  252 

286.  Conduction  of  heat  across  air  spaces,  ordinary  temperatures    ....  253 

287.  Convection  of  heat  in  air  at  ordinary  temperatures 253 

288.  and  conduction  of  heat  by  gases  at  high  temperatures:     .  254 

(a)  s  as  function  of  a/B     254 

(b)  <j)  in  watts  per  cm.  as/(r°K) 254 

289.  Heat  losses  from  incandescent  filaments: 255 

(a)  Wires  of  platinum  sponge 255 

(b)  "      "  bright  platinum 255 

THE  EYE  AND  RADIATION 

290.  Spectral  variation  of  sensitiveness  as  function  of  intensity  (Lumina- 

tion  intensities  under  various  circumstances) 256 

291.  Threshold  sensibility  as  related  to  field  brightness 256 

292.  Heterochromatic  threshold  sensibility 257 

293.  Contrast  or  photometric  sensibility 257 

294.  Glare  sensibility 257 

295.  Rate  of  adaptation  of  sensibility 257 

296.  Apparent  diameter  of  pupil  and  flux  density  at  retina 258 

297.  Relative  visibility  of  radiation  of  different  wave-lengths 258 

298.  Miscellaneous  eye  data:    physiological;    persistence  of  vision;    sensi- 

bility to  small  differences  of  color;  flicker 258 

PHOTOMETRIC  TABLES 

299.  Photometric  definitions  and  units 259 

300.  standards      260 

301.  Intrinsic  brightness  of  various  light  sources 260 

302.  Visibility  of  white  lights 260 

303.  Brightness,  Crova  wave-length,  mechanical  equivalent  of  light     .    .    .  261 

304.  Luminous  and  total  intensity  and  radiant  luminous  efficiency  of  a 

black-body;  minimum  energy  necessary  for  light  sensation  ...  261 

305.  Color  of  light  emitted  by  various  sources 261 

306.  Efficiency  of  various  electric  lights     262 

PHOTOGRAPHIC  DATA 

307.  Numerical  constants  characteristic  of  a  photographic  plate 263 

308.  Relative  speeds  of  various  photographic  materials 263 

309.  Variation  of  resolving  power  with  plate  and  developer 263 

310.  Photographic  efficiencies  of  various  lights 264 

311.  Relative  intensification  of  various  intensifiers 264 

SPECTRUM  WAVE-LENGTHS 

312.  Wave-lengths  of  the  Fraunhofer  lines 265 

313.  Standards:  Red  cadmium  line,  76  cm,  15°  C,  Angstroms 266 


CONTENTS.  XV 

314.  Standards:  International  secondary  Fe  arc  standards,  Angstroms  .    .  266 

315.  International  secondary  Fe  arc  standards,  Angstroms   .    .  266 

316.  Neon  wave-lengths 266 

317.  International  tertiary  Fe  arc  standards,  Angstroms   .    .    .  267 

318.  Reduction  of  wave-lengths  in  air  to  standard  conditions: 268 

(a)  (d  -  do)/d0  X  1000;  B,  60  to  78  cm,  /,  9°  to  35°  C      ....  268 

(b)  6  =  AoOo-  no')(d-do)/(k 268 

319.  Spectra  of  the  elements 269 

320.  Spectrum  lines  of  the  elements  (Kayser) '270 

321.  Standard  solar  wave-lengths  (Rowland) 272 

322.  Spectrum  series,  general  discussion 275 

323.  "      limits  of  some  of  the  series 276 

324.  "      first  terms  and  vibration  differences 276 

INDICES  OF  REFRACTION 

325.  Indices  of  refraction  of  glass  (American) 277 

326.  Dispersion  of  glasses  of  Table  325 277 

327.  Indices  of  refraction  of  glasses  made  by  Schott  and  Gen,  Jena .    ...  278 

328.  Dispersion  of  Jena  glasses 278 

329.  Changes  of  indices  for  i°  C  change  for  some  Jena  glasses 278 

330.  Index  of  refraction  of  rock-salt  in  air 279 

331.  Change  of  indices  for  i°  C  change  for  rock-salt 279 

332.  Index  of  refraction  of  silvine  (potassium  chloride)  in  air 279 

333.  "      "          "          "  fluorite  in  air 280 

334.  Change  of  indices  for  i°  C  change  for  fluorite 280 

335.  Index  of  refraction  of  iceland  spar  (CaCOs)  in  air 280 

336.  "      "                     "  nitroso-dimethyl-aniline 280 

337.  "      "                     "  quartz  (SiO2) 281 

338.  Indices  of  refraction  for  various  alums 281 

339.  "        "  refraction:  Selected  isotropic  minerals 282 

340.  Miscellaneous  isotropic  solids 283 

341.  Selected  uniaxial  minerals  (positive) 284 

(negative) 284 

342.  Miscellaneous  uniaxial  crystals 285 

343.  Selected  biaxial  minerals  (a)  positive 286 

(b)  negative    ....  287 

344.  Miscellaneous  biaxial  crystals 289 

345.  Liquefied  gases,  oils,  fats,  waxes 289 

346.  Liquids  relative  to  air 290 

347.  Solutions  of  salts  and  acids  relative  to  air  .    .  291 

348.  Gases  and  vapors 292 

349.  Air,  15°  C,  76  cm;  also  corrections  for  reduc- 
ing wave-lengths  and  frequencies  in  air  to  vacuo  (see  Table  318)  .  293 

350.  Media  for  microscopic  determinations  of  refractive  indices:    liquids 

with  ^0(0.589)11)  =  1.74  to  1.87 294 


XVI  CONTENTS. 

351.  Media  for  microscopic  determinations  of  refractive  indices:  resin-like 

substances,  HD (0.589/4)  =  1.88  to  2.10 294 

352.  Media  for  microscopic  determinations  of  refractive  indices:  perma- 

nent standard  resinous  media,  no  =  1.546  to  1.682 294 

353.  Optical  constants  of  metals 295 

354-  "  296 

REFLECTING  POWER 

355.  Reflecting  power  of  metals  (see  Table  359) 296 

356.  Light  reflected  when  incident  light  is  normal  to  transparent  medium  .  297 

357.  •  "•  "     n  is  near  unity  or  equals  i  +  dn,  i  =  o°  to  90°.    .  297 

358.  "  n  =  1.55,  i  =  o°  to  90°,  polarization  percentages.  297 

359.  Reflecting  power  of  metals  (see  Table -3 5 5) 298 

360.  Percentage  diffuse  reflection  from  various  substances 298 

361.  Reflecting  power  of  pigments,  X  =  0.44/4  to  0.70/4 299 

362.  Infra-red  diffuse  reflecting  power  of  dry  pigments 299 

363.  Reflecting  power  of  powders  (white  light) 300 

364.  Variation  of  reflecting  power  of  matt  and  silvered  surfaces  with  angle  300 

365.  Infra-red  reflectivity  of  tungsten,  temperature  variation 300 


TRANSMISSIVE  POWERS 

366.  Transmissibility  of  radiation  by  dyes,  X  =  0.44/4  to  0.70/4 301 

367.  "  Jena  glasses,  0.375  to  3.1/4 302 

368.  "       0.280  to  o.644M  ....  302 

369.  by  Jena  ultra-violet  glasses,  0.280  to  0.397/4   ....  302 

370.  of  radiation  by  glasses  (American)  0.5  to  5.0/4    .    .    .  303 

371.  by  same  glasses  for  various  lights      304 

372.  of  radiation  by  substances  of  Tables  330  to  338 .    .    .  305 

373.  Color  screens  (Landolt) 306 

374.  "  "       (Wood) 306 

375-       "          "       (Jena  glasses) 307 

376.  Transmissibility  of  radiation  by  water,  X  =  0.186/4  to  0.945/4   ....  307 

377.  Transmission  percentages  of  radiation  by  moist  air,  0.75/4  to  20/4  .    .  308 

378.  Long- wave  absorption  by  gases,  23/4  to  314/4 309 

379.  Properties  with  wave-lengths  108=*=  /4: 

(a)  Percentage  reflection 309 

(b)  Percentage  transparency 309 

(c)  Transparency  of  black  absorbers,  2/4  to  108/4      309 

380.  Rotation  of  plane  of  polarized  light  by  solutions 310 

381.  "      "      "         "  "      "  sodium  chlorate  and  quartz    .  310 

382.  Electrical  equivalents 311 


CONTENTS.  xvil 

ELECTROMOTIVE  POWERS 

383.  Data  for  voltaic  cells:  (a)  double-fluid  cells 312 

(b)  single-fluid  cells 313. 

(c)  standard  cells 313 

(d)  secondary  cells 313 

384.  Contact  potential  differences,   solids   with  liquids  and  liquids  with 

liquids  in  air 314 

385.  Contact  potential  differences  between  metals  in  salt  solutions  ....  316 

386.  Thermoelectric  power  of  metals 317 

387.  "       "  alloys 318 

388.  "      against  platinum 319 

389.  of  platinum-rhodium  alloys    .  319 

390.  "      pressure  effect 320 

391.  Peltier  and  Thomson  heats,  pressure  effects      320 

392.  Peltier  effect 321 

393.  "     Fe-constantan,  Ni-Cu,  o°  to  560°  C 321 

394.  "      electromotive  force  in  millivolts 322 

395.  The  tribo-electric  series 322 

ELECTRICAL  RESISTANCE 

396.  Auxiliary  table  for  computing  wire  resistances 322 

397.  Resistivity  of  metals  and  some  alloys,  temperature  coefficients    ...  323 

398.  Resistance  of  metals  under  pressure,  temperature  coefficients  ....  326 

399.  Resistance  of  mercury  and  manganin  under  pressure      326 

400.  Conductivity  and  resistivity  of  miscellaneous  alloys 327 

401.  Conducting  power  of  alloys,  temperature  coefficients      328 

402.  Allowable  carrying  capacity  of  rubber-covered  copper  wires     ....  329 

403.  Resistivities  at  high  and  low  temperatures • 330 

404.  Volume  and  surface  resistivity  of  solid  dielectrics 331 

405.  Variation  of  resistance  of  glass  and  porcelain  with  temperature    ...  332 

(a)  Temperature  coefficients  for  glass,  porcelain  and  quartz  .    .  332 

WIRE  TABLES 

406.  Tabular  comparison  of  wire  gages 333. 

407.  Introduction;  mass  and  volume  resistivity  of  copper  and  aluminum  .  334 

408.  Temperature  coefficients  of  copper 335 

409.  Reduction  to  standard  temperature,  copper      335 

410.  Annealed  copper  wire  table,  English  units,  B.  &  S.  gage 336 

411-                                            "      Metric  units,  B.  &  S.  gage 339 

412.  Hard-drawn  aluminum  wire  table,  English  units,  B.  &  S.  gage     .    .    .  342 

413.  "      Metric  units,  B.  &  S.  gage  ....  343 

414.  Ratio  of  alternating  to  direct  current  resistances  for  copper  wire  .    .  344 

415.  Maximum  diameter  of  wires  for  high-frequency-alternating-to-direct- 

current  ratio  of  i.oi 344 


Xvill  CONTENTS. 

ELECTROLYSIS 

416.  Electrochemical  equivalents 345 

417.  Conductivity  of  a  few  dilute  solutions 346 

418.  Electrochemical  equivalents  and  densities  of  nearly  normal  solutions  346 

419.  Specific  molecular  conductivity  of  solutions      347 

420.  "              "                                                     limiting  values     ....  348 

421.  "              "                                                     temperature  coefficient   .  348 

422.  Equivalent  conductivity  of  salts,  acids,  bases  in  solution 349 

423.  "                                 "  some  additional  salts  in  solution     ....  351 

424.  conductance  of  separate  ions 352 

425.  Hydrolysis  of  ammonium  acetate  and  ionization  of  water 352 

DIELECTRIC  STRENGTH 

426.  Steady  potential  for  spark  in  air,  ball  electrodes      353 

427.  Alternating  potential  for  spark  in  air,  ball  electrodes      353 

428.  Steady  and  alternating  potential  for  longer  sparks  in  air 354 

429.  Effect  of  pressure  of  the  gas  on  the  dielectric  strength 354 

430.  Dielectric  strength  of  various  materials 355 

431.  Potential  in  volts  for  spark  in  kerosene 355 

DIELECTRIC  CONSTANTS 

432.  Specific  inductive  capacity  of  gases,  atmospheric  pressure 356 

433.  Variation  of  dielectric  constant  with  the  temperature  (gases)    ....  356 

434.  "          "                                      "       "    pressure  (gases)  .  357 

435.  Dielectric  constant  of  liquids 357 

436.  "  liquids,  temperature  coefficients 359 

437.  "  liquefied  gases  .    .  359 

438.  "  standard  solutions  for  calibration 360 

439.  "                "         "  solids 360 

440.  "                         "  crystals 361 

WIRELESS  TELEGRAPHY 

441.  Wave-lengths,  frequencies  and  oscillation  constants 362 

442.  Antennae  resistances  for  various  wave-lengths  and  heights 364 

443.  Dielectric  properties  of  non-conductors 364 

MAGNETIC  PROPERTIES 

444.  Definitions  and  general  discussion 365 

445.  Composition  and  magnetic  properties  of  iron  and  steel  (old  data)    .  367 

446.  Magnetic  properties  of  iron  and  steel 368 

447.  Cast  iron  in  intense  fields 368 

448.  Corrections  for  ring  specimens 368 


CONTENTS.  xix 

449.   Magnetic  properties  of  various  types  of  iron  and  steel 369 

450-                                      "  a  specimen  of  very  pure  iron  (0.017  %C)     •    .  369 

451.  "  electrical  sheets 35^ 

452.  "  American  magnet  steel 370 

453.  "  a  ferro-cobalt  alloy 370 

454-                                     "  a  ring  sample  transformer  steel,  weak  field  .  370 

455.  •      "                           :'  iron  in  very  weak  fields 370 

456.  Permeability  of  some  specimens  of  Table  445 37! 

457.  Magnetic  properties  of  soft  iron  at  o°  and  100°  C 371 

458.  "  steel  at  o°  and  100°  C 371 

459.  Magnetism  and  temperature,  critical  temperature      372 

460.  Temperature  variation  for  paramagnetic  substances 372 

461.  effect  on  susceptibility  of  diamagnetic  elements  ....  372 

462.  "  paramagnetic  elements    ...  372 

463.  Magnetic  properties  of  cobalt  at  o°  and  100°  C 373 

464.  "  nickel  "  "      "      "      " 373 

465-                                      "  magnetite 373 

466.  "•  Lowmoor  wrought  iron 373 

467.  "          "  Vicker's  tool  steel 373 

468.  "  Hadfield's  manganese  steel      373 

469.  "  saturation  values  for  steels 373 

470.  Demagnetizing  factors  for  rods 374 

471.  "                  "        "      "      374 

472.  Dissipation  of  energy  in  cyclic  mange tization,  Steinmetz  constant     .  375 

473.  Energy  losses  in  transformer  steels.    . 376 

474.  Magnetic  susceptibility 377 


MAGNETO-OPTIC  ROTATION 

475.  Magneto-optic  rotation,  general  discussion 378 

476.  solids,  Verdet's  constant 379 

477.  liquids,  Verdet's  constant 380 

478.  "        salt  and  acid  water  solutions 381 

479.  "       gases,  Verdet's  constant      382 

480.  Verdet's  and  Kundt's  constants 382 

481.  Values  of  Kerr's  constant 383 

482.  Dispersion  of  Kerr  effect 383 

483-           "          "      "        "      383 

VARIOUS  MAGNETIC  EFFECTS 

484.  Resistance  of  metals,  variation  in  transverse  magnetic  field  (Bi)      .    .  384 

485.  Increase  of  resistance  in  transverse  magnetic  field  (Ni) 384 

486.  Change  of  resistance  of  various  metals  in  magnetic  field 384 

487.  Transverse  galvanomagnetic  and  thermomagnetic  effects 385 

488.  Variation  of  Hall  constant  with  temperature 385 


XX  CONTENTS. 

CATHODE  AND  CANAL  RAYS 

489.  Cathode  and  canal  rays 386 

490.  Speed  of  cathode  rays 386 

491.  Cathodic  sputtering 386 

R6NTGEN    (X-RAYS)    RAYS 

492.  X-rays,  general  properties 387 

493.  Rontgen  secondary  rays 387 

494.  Corpuscular  rays 388 

495.  Intensity  of  X-rays;  ionization 388 

496.  Mass  absorption  coefficients,  \/d 389 

497.  Absorption  coefficients  of  characteristic  radiations  in  gases 389 

498.  X-ray  spectra  and  atomic  numbers 390 

(a)  K-series 390 

(b)  L-series 391 

(c)  M-series      392 

(d)  Tungsten  X-ray  spectrum 392 

499.  X-ray  absorption  spectra  and  atomic  numbers 393 

RADIOACTIVITY 

500.  Relative  phosphorescence  excited  by  radium    . 394 

501.  The  production  of  a  particles  (Helium) 394 

502.  "Heating  effect  of  radium  and  its  emanation      394 

503.  Stopping  powers  of  various  substances  for  a  rays 395 

504.  Absorption  of  ft  rays  by  various  substances      395 

505.  "  7  rays  by  various  substances 395 

506.  Table  of  miscellaneous  properties 396 

507.  Total  number  of  ions  produced  by  the  a,  /3,  and  7  rays 398 

508.  Amount  of  radium  emanation 398 

509.  Vapor  pressure  of  the  radium  emanation  in  cm  of  Hg 398 

510.  References  to  spectra  of  radioactive  substances 398 

MOLECULAR,  ATOMIC  AND  IONIC  DATA 

511.  Molecular  velocities 399 

512.  free  paths,  collision  frequencies  and  diameters 399 

513.  Cross  sections  and  lengths  of  some  organic  molecules 400 

514.  Size  of  diffracting  units  in  crystals 400 

515.  Electrons;  Rutherford  atom;  Bohr  atom;  Magnetic  field  of  atom  .    .  401 

516.  Electron  emission  from  hot  metals 403 

517.  Photo-electric  effect 403 

518.  Ionizing  potentials,  resonance  potentials,  single  line  spectra      ....  403 

519.  Contact  (Volta)  potentials 404 

(a)  Electron  affinity  of  the  elements 404 

(b)  Voltage  of  electrolytic  cells 404 

520.  Ionic  mobilities  and  diffusions,  —  ionic  mobilities 405 

521.  Diffusion  coefficients  4°5 


CONTENTS.  Xxi 

COLLOIDS 

522.  General  properties  of  colloids * 406 

523.  Molecular  weights  of  colloids 406 

524.  Brownian  movement 406 

525.  Adsorption  of  gas  by  finely  divided  particles 407 

526.  Heats  of  adsorption 407 

527.  Molecular  heats  of  adsorption  and  liquefaction 407 

528.  Miscellaneous  constants,  atomic,  molecular,  etc.      ..." 408 

529.  Radiation  wave-length  limits 408 

530.  Periodic  system  of  the  elements  (Mendelejeff) 409 

531.  Atomic  numbers 409 

532.  Periodic  system  of  the  elements  and  radioactive  isotopes  (Hackh)  .    .  410 

ASTRONOMICAL  DATA 

533.  Stellar  spectra  and  related  characteristics 411 

534.  The  Harvard  spectrum  classification 411 

535.  Apex  and  velocity  of  solar  motion  .  ^ 411 

536.  Motion  of  the  stars 412 

537.  Distances  of  the  stars 412 

538.  Brightness  of  the  stars 413 

539.  Masses  and  densities 413 

540.  Miscellaneous  astronomical  data 414 

541.  The  first-magnitude  stars     ...... 415 

542.  Wolf's  observed  sun-spot  numbers,  1750  to  1917 415 

543.  Length  of  degrees  on  the  earth's  surface 416 

544.  Equation  of  time 416 

545.  Planetary  data      " 416 

546.  Numbers  and  equivalent  light  of  the  stars 417 

547.  Albedos 417 

548.  Duration  of  sunshine 417 

549.  The  solar  constant 418 

550.  Solar  spectrum  energy  and  its  transmission  through  the  atmosphere  .  418 

551.  Intensity  of  solar  energy  in  various  sections  of  spectrum 418 

552.  Distribution  of  brightness  (radiation)  over  the  solar  disk 418 

553.  Transmission  of  radiation  through  moist  and  dry  air  (see  Table  376)  .  410 

554.  Brightness  of  sky  at  altitudes  of  1730  m  and  sea-level 419 

555.  Relative  distribution  in  normal  spectrum  of  sun  and  sky  light     .    .    .  419 

556.  Air  masses 419 

557.  Relative  intensity  of  solar  radiation  for  various  months 420 

METEOROLOGICAL  DATA 

558.  Mean  monthly  and  yearly  temperatures  for  representative  stations    .  420 

559.  The  earth's  atmosphere,  variation  with  latitude,  miscellaneous    ...  421 


XXIV  INTRODUCTION. 

possible  of  the  complex  relationships  involving  them.  Further  it  seems  desirable 
that  the  units  should  be  extensive  in  nature.  It  has  been  found  possible  to 
express  all  measurable  physical  quantities  in  terms  of  five  such  units:  ist,  geo- 
metrical considerations  —  length,  surface,  etc.,  — lead  to  the  need  of  a  length; 
2nd,  kinematical  considerations  —  velocity,  acceleration,  etc., — introduce  tune; 
3rd,  mechanics  —  treating  of  masses  instead  of  immaterial  points  —  intro- 
duces matter  with  the  need  of  a  fundamental  unit  of  mass;  4th,  electrical,  and 
5th,  thermal  considerations  require  two  more  such  quantities.  The  discovery 
of  new  classes  of  phenomena  may  require  further  additions. 

As  to  the  first  three  fundamental  quantities,  simplicity  and  good  use  sanction 
the  choice  of  a  length,  L,  a  time  interval,  T,  and  a  mass,  M.  For  the  measure- 
ment of  electrical  quantities,  good  use  has  sanctioned  two  fundamental  quan- 
tities, —  the  dielectric  constant,  K,  the  basis  of  the  "  electrostatic "  system  and 
the  magnetic  permeability,  JJL,  the  basis  of  the  "electromagnetic"  system.  Besides 
these  two  systems  involving  electrical  considerations,  there  is  in  common  use  a 
third  one  called  the  "international"  system  which  will  be  referred  to  later.  For 
the  fifth,  or  thermal  fundamental  unit,  temperature  is  generally  chosen.1 

Derived  Units.  —  Having  selected  the  fundamental  or  basic  units,  —  namely, 
a  measure  of  length,  of  time,  of  mass,  of  permeability  or  of  the  dielectric 
constant,  and  of  temperature,  —  it  remains  to  express  all  other  units  for  physi- 
cal, quantities  in  terms  of  these.  Units  depending  on  powers  greater  than  unity 
of  the  basic  units  are  called  "derived  units."  Thus,  the  unit  volume  is  the  volume 
of  a  cube  having  each  edge  a  unit  of  length.  Suppose  that  the  capacity  of  some 
volume  is  expressed  in  terms  of  the  foot  as  fundamental  unit  and  the  volume 
number  is  wished  when  the  yard  is  taken  as  the  unit.  The  yard  is  three  times 
as  long  as  the  foot  and  therefore  the  volume  of  a  cube  whose  edge  is  a  yard  is 
3X3X3  times  as  great  as  that  whose  edge  is  a  foot.  Thus  the  given  volume 
will  contain  only  1/27  as  many  units  of  volume  when  the  yard  is  the  unit  of 
length  as  it  will  contain  when  the  foot  is  the  unit.  To  transform  from  the  foot 
as  old  unit  to  the  yard  as  new  unit,  the  old  volume  number  must  be  multiplied 
by  1/27,  or  by  the  ratio  of  the  magnitude  of  the  old  to  that  of  the  new  unit  of 
volume.  This  is  the  same  rule  as  already  given,  but  it  is  usually  more  conven- 
ient to  express  the  transformations  in  terms  of  the  fundamental  units  directly. 
In  the  present  case,  since,  with  the  method  of  measurement  here  adopted,  a 
volume  number  is  the  cube  of  a  length-number,  the  ratio  of  two  units  of  volume 
is  the  cube  of  the  ratio  of  the  intrinsic  values  of  the  two  units  of  length.  Hence, 
if  /  is  the  ratio  of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  length,  the 
ratio  of  the  corresponding  units  of  volume  is  I3.  Similarly  the  ratio  of  two  units 
of  area  would  be  /2,  and  so  on  for  other  quantities. 

1  Because  of  its  greater  psychological  and  physical  simplicity,  and  the  desirability  that  the 
unit  chosen  should  have  extensive  magnitude,  it  has  been  proposed  to  choose  as  the  fourth  fun- 
damental quantity,  a  quantity  of  electrical  charge,  e.  The  standard  unit  of  electrical  charge 
would  then  be  the  electronic  charge.  For  thermal  needs,  entropy  has  been  proposed.  While 
not  generally  so  psychologically  easy  to  grasp  as  temperature,  entropy  is  of  fundamental  im- 
portance in  thermodynamics  and  has  extensive  magnitude.  (R.  C.  Tolman,  The  Measurable 
Quantities  of  Physics,  Physical  Review,  9,  p.  237,  1917.) 


INTRODUCTION.  XXV 

Conversion  Factors  and  Dimensional  Formulae.  —  For  the  ratios  of  length, 
mass,  time,  temperature,  dielectric  constant  and  permeability  units  the  small 
bracketed  letters,  [/],  [>],  p],  [0],  [>],  and  [>]  will  be  adopted.  These  symbols 
will  always  represent  simple  numbers,  but  the  magnitude  of  the  number  will 
depend  on  the  relative  magnitudes  of  the  units  the  ratios  of  which  they  repre- 
sent. When  the  values  of  the  numbers  represented  by  these  small  bracketed 
letters  as  well  as  the  powers  of  them  involved  in  any  particular  unit  are  known, 
the  factor  for  the  transformation  is  at  once  obtained.  Thus,  in  the  above  ex- 
ample, the  value  of  /  was  1/3,  and  the  power  involved  in  the  expression  for  volume 
was  3;  hence  the  factor  for  transforming  from  cubic  feet  to  cubic  yards  was  /3 
or  i/33  or  1/27.  These  factors  will  be  called  conversion  factors. 

To  find  the  symbolic  expression  for  the  conversion  factor  for  any  physical 
quantity,  it  is  sufficient  to  determine  the  degree  to  which  the  quantities  length, 
mass,  time,  etc.,  are  involved.  Thus  a  velocity  is  expressed  by  the  ratio  of  the 
number  representing  a  length  to  that  representing  an  interval  of  time,  or  \_L/T~\, 
and  acceleration  by  a  velocity  number  divided  by  an  interval-of-time  number, 
or  [L/r2],  and  so  on,  and  the  corresponding  ratios  of  units  must  therefore  enter 
in  precisely  the  same  degree.  The  factors  would  thus  be  for  the  just  stated  cases, 
\_l/t}  and  p/J2].  Equations  of  the  form  above  given  for  velocity  and  acceleration 
which  show  the  dimensions  of  the  quantity  in  terms  of  the  fundamental  units 
are  called  dimensional  equations.  Thus  [_E~]  =  [ML2  J"~2]  will  be  found  to 
be  the  dimensional  equation  for  energy,  and  [MZ,2r~2]  the  dimensional  formula 
for  it.  These  expressions  will  be  distinguished  from  the  conversion  factors  by 
the  use  of  bracketed  capital  letters. 

In  general,  if  we  have  an  equation  for  a  physical  quantity, 

Q  =  CLaMbTc, 

where  C  is  a  constant  and  L,  M,  T  represent  length,  mass,  and  time  in  terms 
of  one  set  of  units,  and  it  is  desired  to  transform  to  another  set  of  units  in  terms 
of  which  the  length,  mass,  and  time  are  Ln  Mn  Tn  we  have  to  find  the  value  of 
LJ  L,  Mj/M,  Tj/Tj  which,  in  accordance  with  the  convention  adopted  above, 
will  be  /,  m,  t,  or  the  ratios  of  the  magnitudes  of  the  old  to  those  of  the  new  units. 

Thus  Lt  =  LI,  M,  =  Mm,  T,  =  Tt,  and  if  Q,  be  the  new  quantity  number, 

&  =  CLfMfT*, 

=  CLalaMbmbTctc  =  Qlambtc, 

or  the  conversion  factor  is  p°mfr/c],  a  quantity  precisely  of  the  same  form  as  the 
dimension  formula  [_LaMbTc~\. 

Dimensional  equations  are  useful  for  checking  the  validity  of  physical  equa- 
tions. Since  physical  equations  must  be  homogeneous,  each  term  appearing  in 
them  must  be  dimensionally  equivalent.  For  example,  the  distance  moved  by 
a  uniformly  accelerated  body  is  5  =  vrf  +  %at2.  The  corresponding  dimensional 
equation  is  [L]  =  \_(L/T)T]  +  [(L/T2)r2],  each  term  reducing  to  [L]. 

Dimensional  considerations  may  often,  give  insight  into  the  laws  regulating 
physical  phenomena.1  For  instance  Lord  Rayleigh,  in  discussing  the  intensity 

1  See  "On  Physically  Similar  Systems;  Illustrations  of  the  Use  of  Dimensional  Equations." 
E.  Buckingham,  Physical  Review,  (2)  4,  p.  345,  1914. 


XXV111  INTRODUCTION. 


Absolute  Force  of  a  Center  of  Attraction,  or  "  Strength  of  a  Center,"  is  the 
intensity  of  force  at  unit  distance  from  the  center,  and  is  the  force  per  unit  mass 
at  any  point  multiplied  by  the  square  of  the  distance  from  the  center.  The 
dimensional  formula  is  FL2!/-1  or 


Modulus  of  Elasticity  is  the  ratio  of  stress  intensity  to  percentage  strain.  The 
dimensional  of  percentage  strain,  a  length  divided  by  a  length,  is  unity.  Hence 
the  dimensional  formula  of  a  modulus  of  elasticity  is  that  of  stress  intensity 


Work  is  done  by  a  force  when  the  point  of  application  of  the  force,  acting  on 
a  body,  moves  in  the  direction  of  the  force.  It  is  measured  by  the  product  of 
the  force  and  the  displacement.  The  dimensional  formula  is  [_FL]  or  \_M  L2T~'r\. 

Energy.  —  The  work  done  by  the  force  produces  either  a  change  in  the  veloc- 
ity of  the  body  or  a  change  of  its  shape  or  configuration,  or  both.  In  the  first 
case  it  produces  a  change  of  kinetic  energy,  in  the  second,  of  potential  energy. 
The  dimensional  formulae  of  energy  and  work,  representing  quantities  of  the  same 
kind,  are  identical  [ML2r~2]. 

Resilience  is  the  work  done  per  unit  volume  of  a  body  in  distorting  it  to  the 
elastic  limit  or  in  producing  rupture.  The  dimensional  formula  is  [If  L2  r~2L~3] 
or  [ML-lT-2~]. 

'  Power  or  Activity  is  the  time  rate  of  doing  work,  or  if  W  represents  work  and 
P  power,  P  =  dw/dt.  The  dimensional  formula  is  [_WT~l~\  or  \_ML?T-*~],  or  for 
problems  in  gravitation  units  more  conveniently  \_FLT~l~],  where  F  stands  for 
the  force  factor. 

Exs.  —  Find  the  number  of  gram-cms  in  one  ft.-pd.  Here  the  units  of  force  are  the  attrac- 
tion of  the  earth  on  the  pound  and  the  gram  of  matter.  (In  problems  like  this  the  terms  "grams" 
and  "pd."  refer  to  force  and  not  to  mass.)  The  conversion  factor  is  [_JT\,  where/  is  453.59  and 
I  is  30.48.  The.answer  is  453-59  X  30-48  =  13825. 

Find  the  number  of  ft.-poundals  in  1000000  cm-dynes.  Here  m  =  1/453.59,  I  =  I/3°-48, 
/  =  i;  mPr*  =  1/453-59  X  30.48*,  and  loWr2  =  io6/453-59  X  30.48*  =  2.373. 

If  gravity  produces  an  acceleration  of  32.2  ft./sec./sec.,  how  many  watts  are  required  to  make 
one  horse-power?  One  horse-power  is  550  ft.-pds.  per  sec.,  or  550  x  32.2  =  17710  ft.-poundals 
per  second.  One  watt  is  io7  ergs  per  sec.,  that  is,  io7  dyne-cms  per  sec.  The  conversion  factor 
is  [mPt~3^\,  where  m  is  453.59,  I  is  30.48,  and  Ms  i,  and  the  result  has  to  be  divided  by  io7,  the 
number  of  dyne-cms  per  sec.  in  the  watt.  17710  ml2r3/io7  =  17710  x  453.59  X  3o.482/io7 
=  746.3- 

HEAT  UNITS. 

Quantity  of  Heat,  measured  in  dynamical  units,  has  the  same  dimensions  as 
energy  \_M  L?T~2~\.  Ordinary  measurements,  however,  are  made  in  thermal 
units,  that  is,  in  terms  of  the  amount  of  heat  required  to  raise  the  temperature 
of  a  unit  mass  of  water  one  degree  of  temperature  at  some  stated  temperature. 
This  involves  the  unit  of  mass  and  some  unit  of  temperature.  If  we  denote 
temperature  numbers  by  6,  the  dimensional  formula  for  quantity  of  heat,  //, 
will  be  QM0].  Unit  volume  is  sometimes  used  instead  of  unit  mass  in  the  meas- 
urement of  heat,  the  units  being  called  thermometric  units.  The  dimensional 
formula  now  changed  by  the  substitution  of  volume  for  mass  is 


INTRODUCTION. 

Specific  Heat  is  the  relative  amount  of  heat,  compared  with  water  as  standard 
substance,  required  to  raise  unit  mass  of  different  substances  one  degree  in  tem- 
perature and  is  a  simple  number. 

Coefficient  of  Thermal  Expansion  of  a  substance  is  the  ratio  of  the  change  of 
length  per  unit  length  (linear),  or  change  of  volume  per  unit  volume  (voluminal), 
to  the  change  of  temperature.  These  ratios  are  simple  numbers,  and  the  change 
of  temperature  varies  inversely  as  the  magnitude  of  the  unit  of  temperature. 
The  dimensional  formula  is  [0"1]. 

Thermal  Conductivity,  or  Specific  Conductance,  is  the  quantity  of  heat,  H, 
transmitted  per  unit  of  time  per  unit  of  surface  per  unit  of  temperature  gradient. 
The  equation  for  conductivity  is  therefore  K  =  H/L2TQ/L,  and  the  dimen- 
sional formula  \_H/QLT~]  =  \_ML~lT~l~]  in  thermal  units.  In  thermometric 
units  the  formula  becomes  |~Z,2r~1],  which  properly  represents  diffusivity,  and 
in  dynamical  units  [_M  LT-*Qrir\. 

Thermal  Capacity  is  mass  times  the  specific  heat.  The  dimensional  formula 
is 


Latent  Heat  is  the  quantity  of  heat  required  to  change  the  state  of  a  body 
divided  by.  the  quantity  of  matter.     The  dimensional  formula  is  [MQ/M~\  or 
;   in  dynamical  units  it  is  [L2T~2]. 


NOTE.  —  When  0  is  given  the  dimensional  formula  [X2  J1"2^,  the  formulae  in  thermal  and 
dynamical  units  are  identical. 

Joule's  Equivalent,  /,  is  connected  with  the  quantity  of  heat  by  the  equation 
ML2T~2  =  JH  or  JMQ.  The  dimensional  formula  of  /  is  [L2^^-1].  In 
dynamical  units  /  is  a  simple  number. 

Entropy  of  a  body  is  directly  proportional  to  the  quantity  of  heat  it  contains 
and  inversely  proportional  to  its  temperature.  The  dimensional  formula  is 
[MO/0]  or  [Ml  In  dynamical  units  the  formula  is  [ML2!^2©-1]. 

Exs.  —  Find  the  relation  between  the  British  thermal  unit,  the  large  or  kilogram-calorie 
and  the  small  or  gram-calorie,  sometimes  called  the  "therm."  Referring  all  the  units  to  the 
same  temperature  of  the  standard  substance,  the  British  thermal  unit  is  the  amount  of  heat 
required  to  warm  one  pound  of  water  i°  C,  the  large  calorie,  i  kilogram  of  water,  i°  C,  the 
small  calorie  or  therm,  i  gram,  i°  C.  (i)  To  find  the  number  of  kg-cals.  in  one  British  thermal 
unit,  m  =  .45359,  9  =  5/9;  m&  =  .45359  X  5/9  =  .25199.  (2)  To  find  the  number  therms  in  one 
kg-cal.  m  =  1000,  and  0  =  i;  md  =  1000.  (3)  Hence  the  number  of  small  calories  or  therms  in 
one  British  thermal  unit  is  1000  x  .25199  =  251.99. 

ELECTRIC  AND   MAGNETIC  UNITS. 

A  system  of  units  of  electric  and  magnetic  quantities  requires  four  funda- 
mental quantities.  A  system  in  which  length,  mass,  and  time  constitute  three 
of  the  fundamental  quantities  is  known  as  an  "  absolute"  system.  There  are 
two  absolute  systems  of  electric  and  magnetic  units.  One  is  called  the  electro- 
static, in  which  the  fourth  fundamental  quantity  is  the  dielectric  constant,  and 
one  is  called  the  electromagnetic,  in  which  the  fourth  fundamental  quantity  is 
magnetic  permeability.  Besides  these  two  systems  there  will  be  described  a 
third  in  common  use  called  the  "international"  system. 


XXX  INTRODUCTION. 

In  the  electrostatic  system,  unit  quantity  of  electricity,  Q,  is  the  quantity 
which  exerts  unit  mechanical  force  upon  an  equal  quantity  a  unit  distance  from 
it  in  a  vacuum.  From  this  definition  the  dimensions  and  the  units  of  all  the 
other  electric  and  magnetic  quantities  follow  through  the  equations  of  the  mathe- 
matical theory  of  electromagnetism.  The  mechanical  force  between  two  quan- 
tities of  electricity  in  any  medium  is 


where  K  is  the  dielectric  constant,  characteristic  of  the  medium,  and  r  the  dis- 
tance between  the  two  points  at  which  the  quantities  Q  and  Q'  are  located.  A' 
is  the  fourth  quantity  entering  into  dimensional  expressions  in  the  electrostatic 
system.  Since  the  dimensional  formula  for  force  is  [MLT~2],  that  for  Q  is 


The  electromagnetic  system  is  based  upon  the  unit  of  the  magnetic  pole 
strength.  The  dimensions  and  the  units  of  the  other  quantities  are  built  up 
from  this  in  the  same  manner  as  for  the  electrostatic  system.  The  mechanical 
force  between  two  magnetic  poles  in  any  medium  is 

mm' 

*    —  7T  > 

^ 

in  which  /z  is  the  permeability  of  the  medium  and  r  is  the  distance  between  two 
poles  having  the  strengths  m  and  m'  .  p  is  the  fourth  quantity  entering  into 
dimensional  expressions  in  the  electromagnetic  system.  It  follows  that  the 
dimensional  expression  for  magnetic  pole  strength  is  [J^Z^T1"1/**]. 

The  symbols  K  and  JJL  are  sometimes  omitted  in  the  dimensional  formulae  so 
that  only  three  fundamental  quantities  appear.  There  are  a  number  of  objec- 
tions to  this.  Such  formulae  give  no  information  as  to  the  relative  magnitudes 
of  the  units  in  the  two  systems.  The  omission  is  equivalent  to  assuming  some 
relation  between  mechanical  and  electrical  quantities,  or  to  a  mechanical  expla- 
nation of  electricity.  Such  a  relation  or  explanation  is  not  known. 

The  properties  K  and  ju,  are  connected  by  the  equation  i/\/  Kp  =  v,  where  v 
is  the  velocity  of  an  electromagnetic  wave.  For  empty  space  or  for  air,  K  and 
IJL  being  measured  in  the  same  units,  i/^/Kfi  =  c,  where  c  is  the  velocity  of 
light  in  vacuo,  3  x  io10  cm  per  sec.  It  is  sometimes  forgotten  that  the  omission 
of  the  dimensions  of  K  or  JJL  is  merely  conventional.  For  instance,  magnetic 
field  intensity  and  magnetic  induction  apparently  have  the  same  dimensions 
when  jj,  is  omitted.  This  results  in  confusion  and  difficulty  in  understanding  the 
theory  of  magnetism.  The  suppression  of  /z  has  also  led  to  the  use  of  the  "centi- 
meter" as  a  unit  of  capacity  and  of  inductance;  neither  is  physically  the  same 
as  length. 

ELECTROSTATIC  SYSTEM. 

Quantity  of  Electricity  has  the  dimensional  formula  \_M*  L*T~l  KY\,  as  shown 
above. 

Electric  Surface  Density  of  an  electrical  distribution  at  any  point  on  a  surface 
is  measured  by  the  quantity  per  unit  area.  The  dimensional  formula  is  the  ratio 
of  the  formulae  for  quantity  of  electricity  and  for  area  or 


INTRODUCTION.  XX\i 

Electric  Field  Intensity  is  measured  by  the  ratio  of  the  force  on  a  quantity 
of  electricity  at  a  point  to  the  quantity  of  electricity.  The  dimensional 
formula  is  therefore  the  ratio  of  the  formulae  for  force  and  electric  quantity  or 
or 


Electric  Potential  and  Electromotive  Force.  —  Change  of  potential  is  propor- 
tional to  the  work  done  per  unit  of  electricity  in  producing  the  change.  The 
dimensional  formula  is  the  ratio  of  the  formulae  for  work  and  electrical  quantity 
or  MIST-iMiH^K*  or 


Capacity  of  an  Insulated  Conductor  is  proportional  to  the  ratio  of  the  quan- 
tity of  electricity  in  a  charge  to  the  potential  of  the  charge.  The  dimensional 
formula  is  the  ratio  of  the  two  formulae  for  electric  quantity  and  potential  or 
[M*L*T-1K*/M*L*T-1K-*1  or  \_LK], 

Specific  Inductive  Capacity  is  the  ratio  of  the  inductive  capacity  of  the  sub- 
stance to  that  of  a  standard  substance  and  therefore  is  a  number. 

Electric  Current  is  quantity  of  electricity  flowing  past  a  point  per  unit  of 
time.  The  dimensional  formula  is  the  ratio  of  the  formulae  for  electric  quan- 
tity and  for  time  or  {_M*HT-lK*/r\  or  \_M*L*T-*K?]. 

Electrical  Conductivity,  like  the  corresponding  term  for  heat,  is  quantity  per 
unit  area  per  unit  potential  gradient  per  unit  of  time.  The  dimensional  formula 
is  fr&T-iKtVWT-iK-if  or 


Resistivity  is  the  reciprocal  of  conductivity.     The   dimensional  formula  is 


Conductance  of  any  part  of  an  electric  circuit,  not  containing  a  source  of 
electromotive  force,  is  the  ratio  of  the  current  flowing  through  it  to  the  difference 
of  potential  between  its  ends.  The  dimensional  formula  is  the  ratio  of  the  for- 
mulae for  current  and  potential  or  [M*I*T+J&/ii*&T-*&Q  or  [_LT~lfC\. 

Resistance  is  the  reciprocal  of  conductance.     The  dimensional  formula  is 

\_L-IT  K-I~]. 

Exs.  —  Find  the  factor  for  converting  quantity  of  electricity  expressed  in  ft.-grain-sec.  units 
to  the  same  expressed  in  c.g.s.  units.  The  formula  is  [mW*t~lk%~],  in  which  m=  0.0648,. 
/  =  30.48,  /  =  i,  k  =  i;  the  factor  is  0.0648*  X  30.482,  or  42.8. 

Find  the  factor  required  to  convert  electric  potential  from  mm-mg-sec.  units  to  c.g.s.  units. 
The  formula  is  [m*l%t~lk~%~\,  in  which  m  -  o.ooi,  /  =  o.i,  /  =  i,  k  =  i;  the  factor  Js  o.ooii 
X  0.12,  or  o.oi. 

Find  the  factor  required  to  convert  electrostatic  capacity  from  ft.-grain-sec.  and  specific- 
inductive  capacity  6  units  to  c.g.s.  units.  The  formula  is  \_lk~\  in  which  I  =  30.48,  k  =  6;  the 
factor  is  30.48  x  6,  or  182.88. 


ELECTROMAGNETIC  SYSTEM. 

Many  of  the  magnetic  quantities  are  analogues  of  certain  electric  quantities. 
The  dimensions  of  such  quantities  in  the  electromagnetic  system  differ  from 
those  of  the  corresponding  electrostatic  quantities  in  the  electrostatic  system 
only  in  the  substitution  of  permeability  jit  for  K. 


XXxiv  INTRODUCTION. 

ence  standards  are  accurately  compared  copies,  not  necessarily  duplicates,  of 
the  primaries  for  use  in  the  work  of  standardizing  laboratories  and  the  produc- 
tion of  working  standards  for  everyday  use. 

Standard  of  Length.  —  The  primary  standard  of  length  which  now  almost 
universally  serves  as  the  basis  for  physical  measurements  is  the  meter.  It  is 
defined  as  the  distance  between  two  lines  at  o°  C  on  a  platinum-indium  bar 
deposited  at  the  International  Bureau  of  Weights  and  Measures.  This  bar  is 
known  as  the  International  Prototype  Meter,  and  its  length  was  derived  from 
the  "metre  des  Archives,"  which  was  made  by  Borda.  Borda,  Delambre,  Laplace, 
and  others,  acting  as  a  committee  of  the  French  Academy,  recommended  that 
the  standard  unit  of  length  should  be  the  ten-millionth  part  of  the  length,  from 
the  equator  to  the  pole,  of  the  meridian  passing  through  Paris.  In  1795  the 
French  Republic  passed  a  decree  making  this  the  legal  standard  of  length,  and 
an  arc  of  the  meridian  extending  from  Dunkirk  to  Barcelona  was  measured  by 
Delambre  and  Mechain  for  the  purpose  of  realizing  the  standard.  From  the 
results  of  that  measurement  the  meter  bar  was  made  by  Borda.  The  meter  is 
now  denned  as  above  and  not  in  terms  of  the  meridian  length;  hence  subsequent 
measures  of  the  length  of  the  meridian  have  not  affected  the  length  of  the  meter. 

Standard  of  Mass.  —  The  primary  standard  of  mass  now  almost  universally 
used  as  the  basis  for  physical  measurements  is  the  kilogram.  It  is  defined  as 
the  mass  of  a  certain  piece  of  platinum-indium  deposited  at  the  International 
Bureau  of  Weights  and  Measures.  This  standard  is  known  as  the  International 
Prototype  Kilogram.  Its  mass  is  equal  to  that  of  the  older  standard,  the  "  kilo- 
gram des  Archives,"  made  by  Borda  and  intended  to  have  the  same  mass  as  a 
cubic  decimeter  of  distilled  water  at  the  temperature  of  4°  C. 

Copies  of  the  International  Prototype  Meter  and  Kilogram  are  possessed  by 
the  various  governments  and  are  called  National  Prototypes. 

Standard  of  Time.  —  The  unit  of  time  universally  used  is  the  second.  It  is 
the  mean  solar  second,  or  the  864ooth  part  of  the  mean  solar  day.  It  is  founded 
on  the  average  time  required  for  the  earth  to  make  one  rotation  on  its  axis  rela- 
tively to  the  sun  as  a  fixed  point  of  reference. 

Standard  of  Temperature.  —  The  standard  scale  of  temperature  as  adopted 
by  the  International  Committee  of  Weights  and  Measures  (1887)  depends  on 
the  constant-volume  hydrogen  thermometer.  The  hydrogen  is  taken  at  an 
initial  pressure  at  oc  C  of  one  meter  of  mercury,  o°  C,  sea-level  at  latitude  45°. 
The  scale  is  defined  by  designating  the  temperature  of  melting  ice  as  o°  and  of 
condensing  steam  as  100°  under  standard  atmospheric  pressure.  This  is  known 
as  the  Centigrade  scale  (abbreviated  C). 

A  scale  independent  of  the  properties  of  any  particular  substance,  and  called 
the  thermodynamic,  or  absolute  scale,  was  proposed  in  1848  by  Lord  Kelvin. 
In  it  the  temperature  is  proportional  to  the  average  kinetic  energy  per  molecule 
of  a  perfect  gas.  The  temperature  of  melting  ice  is  taken  as  273.13°,  that  of 
the  boiling  point,  373.13°.  The  scale  of  the  hydrogen  thermometer  varies  from 
it  only  in  the  sense  that  the  behavior  of  hydrogen  departs  from  that  of  a  perfect 
gas.  It  is  customary  to  refer  to  this  scale  as  the  Kelvin  scale  (abbreviated  K). 


INTRODUCTION. 


XXXV 


NUMERICALLY  DIFFERENT  SYSTEMS  OF  UNITS. 

The  fundamental  physical  quantities  which  form  the  basis  of  a  system  for 
measurements  have  been  chosen  and  the  fundamental  standards  selected  and 
made.  Custom  has  not  however  generally  used  these  standards  for  the  meas- 
urement of  the  magnitudes  of  quantities  but  rather  multiples  or  submultiples  of 
them.  For  instance,  for  very  small  quantities  the  micron  (JJL)  or  one-millionth 
of  a  meter  is  often  used.  The  following  table  1  gives  some  of  the  systems  pro- 
posed, all  built  upon  the  fundamental  standards  already  described.  The  centi- 
meter-gram-second (cm-g-sec.  or  c.g.s.)  system  proposed  by  Kelvin  is  the  only 

one  generally  accepted. 

TABLE  I. 

PROPOSED  SYSTEMS  OF   UNITS- 


Weber  • 
and 
Gauss 

Kelvin 
c.g.s. 

Moon 
1891 

Giorgi 
MKS 

(Prim. 
Stds.) 

France 
1914 

B.  A. 

Com., 
1863 

Practical 
(B.  A. 
Com., 

1873) 

Strout 
1891 

Length 

mm 

cm 

dm 

m 

m 

m 

io9  cm 

io9  cm 

Mass 

mg 

g 

Kg 

Kg 

I06g 

g 

io-u  g 

io-9g 

Time 

sec. 

sec. 

sec. 

sec. 

sec. 

sec. 

sec. 

sec. 

10 

Further  the  choice  of  a  set  of  fundamental  physical  quantities  to  form  the.  basis 
of  a  system  does  not  necessarily  determine  how  that  system  shall  be  used  in 
measurements.  In  fact,  upon  any  sufficient  set  of  fundamental  quantities,  a 
great  many  different  systems  of  units  may  be  built.  The  electrostatic  and  elec- 
tromagnetic systems  are  really  systems  of  electric  quantities  rather  than  units. 
They  were  based  upon  the  relationships  F  =  QQ' /  Kr2  and  mm'/pr*,  respec- 
tively. Systems  of  units  built  upon  a  chosen  set  of  fundamental  physical  quan- 
tities may  differ  in  two  ways:  (i)  the  units  chosen  for  the  fundamental  quanti- 
ties may  be  different;  (2)  the  defining  equations  by  which  the  system  is  built 
may  be  different. 

The  electrostatic  system  generally  used  is  based  on  the  centimeter,  gram, 
second,  and  dielectric  constant  of  a  vacuum.  Other  systems  have  appeared, 
differing  from  this  in  the  first  way,  —  for  instance  using  the  foot,  grain  and  second 
in  place  of  the  centimeter,  gram  and  second.  A  system  differing  from  it  in  the 
second  way  is  that  of  Heaviside  which  introduces  the  factor  4?r  at  different 
places  than  is  usual  in  the  equations.  There  are  similarly  several  systems  of 
electromagnetic  units  in  use. 

Gaussian  Systems.  — "The  complexity  of  the  interrelations  of  the  units  is 
increased  by  the  fact  that  not  one  of  the  systems  is  used  as  a  whole,  consistently 
for  all  electromagnetic  quantities.  The  'systems'  at  present  used  are  therefore 
combinations  of  certain  of  the  systems  of  units. 

1  Circular  60  of  the  Bureau  of  Standards,  Electric  Units  and  Standards,  1916.  The  subse- 
quent matter  in  this  introduction  is  based  upon  this  circular. 


XXX  VI  INTRODUCTION. 

"Some  writers  l  on  the  theory  of  electricity  prefer  to  use  what  is  called  a  Gaus- 
sian system,  a  combination  of  electrostatic  units  for  purely  electrical  quantities 
and  electromagnetic  units  for  magnetic  quantities.  There  are  two  such  Gaus- 
sian systems  in  vogue,  —  one  a  combination  of  c.g.s.  electrostatic  and  c.g.s  elec- 
tromagnetic systems,  and  the  other  a  combination  of  the  two  corresponding 
Heaviside  systems. 

"When  a  Gaussian  system  is  used,  caution  is  necessary  when  an  equation 
contains  both  electric  and  magnetic  quantities.  A  factor  expressing  the  ratio 
between  the  electrostatic  and  electromagnetic  units  of  one  of  the  quantities 
has  to  be  introduced.  This  factor  is  the  first  or  second  power  of  c,  the  number 
of  electrostatic  units  of  electric  charge  in  one  electromagnetic  unit  of  the  same. 
There  is  sometimes  a  question  as  to  whether  electric  current  is  to  be  expressed 
in  electrostatic  or  electromagnetic  units,  since  it  has  both  electric  and  magnetic 
attributes.  It  is  usually  expressed  in  electrostatic  units  in  the  Gaussian  system." 

It  may  be  observed  from  the  dimensions  of  K  given  in  Table  i  that  [i/  KJJL] 
=  [_L?/T'r\  which  has  the  dimensions  of  a  square  of  a  velocity.  This  velocity 
was  found  experimentally  to  be  equal  to  that  of  light,  when  K  and  JJL  were  ex- 
pressed in  the  same  system  of  units.  Maxwell  proved  theoretically  that  i/\/^M 
is  the  velocity  of  any  electromagnetic  wave.  This  was  subsequently  proved 
experimentally.  When  a  Gaussian  system  is  used,  this  equation  becomes  c/^KfjL 
=  v.  For  the  ether  K  =  i  in  electrostatic  units  and  /i  =  i  in  electromagnetic 
units.  Hence  c  =  v  for  the  ether,  or  the  velocity  of  an  electromagnetic  wave  in 
the  ether  is  equal  to  the  ratio  of  the  c.g.s.  electromagnetic  to  the  c.g.s.  electro- 
static unit  of  electric  charge.  This  constant  c  is  of  primary  importance  in  elec- 
trical theory.  Its  most  probable  value  is  2.9986  x  io10  centimeters  per  second. 

"  Practical "  Electromagnetic  System.  —  This  electromagnetic  system  is 
based  upon  the  units  of  io9  cm,  io~u  gram,  the  sec.  and  jj,  of  the  ether.  It  is 
never  used  as  a  complete  system  of  units  but  is  of  interest  as  the  historical  basis 
of  the  present  International  System.  The  principal  quantities  are  the  resistance 
unit,  the  ohm  =  io9  c.g.s.  units;  the  current  unit,  the  ampere  =  io-1  c.g.s.  units; 
and  the  electromotive  force  unit,  the  volt  =  io8  c.g.s.  units. 

The  International  Electric  Units.  —  The  units  used  in  practical  measurements, 
however,  are  the  "International  Units."  They  were  derived  from  the  "practical " 
system  just  described,  or  as  the  latter  is  sometimes  called,  the  "absolute"  sys- 
tem. These  international  units  are  based  upon  certain  concrete  standards  pres- 
ently to  be  defined  and  described.  With  such  standards  electrical  comparisons 
can  be  more  accurately  and  readily  made  than  could  absolute  measurements  in 
terms  of  the  fundamental  units.  Two  electric  units,  the  international  ohm  and 
the  international  ampere,  were  chosen  and  made  as  nearly  equal  as  possible  to 
the  ohm  and  ampere  of  the  "practical"  or  "absolute"  system. 

1  For  example,  A.  G.  Webster,  "Theory  of  Electricity  and  Magnetism,"  1897;  J.  H.  Jeans, 
"Electricity  and  magnetism,"  1911;  H.  A.  Lorentz,  "The  Theory  of  Electrons,"  1909;  and 
O.  W.  Richardson,  "The  Electron  Theory  of  Matter,"  1914. 


INTRODUCTION.  XXXvii 

This  system  of  units,  sufficiently  near  to  the  "absolute"  system  for  the  pur- 
pose of  electrical  measurements  and  as  a  basis  for  legislation,  was  defined  as 
follows : 

"i.  The  International  Ohm  is  the  resistance  offered  to  an  unvarying  electric 
current  by  a  column  of  mercury  at  the  temperature  of  melting  ice,  14.4521  grams 
in  mass,  of  a  constant  cross-sectional  area  and  of  a  length  of  106.300  centimeters. 
"2.  The  International  Ampere  is  the  unvarying  electric  current  which,  when 
passed  through  a  solution  of  nitrate  of  silver  in  water,  in  accordance  with  speci- 
fication II  attached  to  these  Resolutions,  deposits  silver  at  the  rate  of  o.ooi  11800 
of  a  gram  per  second. 

"3.  The  International  Volt  is  the  electrical  pressure  which,  when  steadily 
applied  to  a  conductor  the  resistance  of  which  is  one  international  ohm'  will  pro- 
.duce  a  current  of  one  international  ampere. 

"4.  The  International  Watt  is  the  energy  expended  per  second  by  an  unvary- 
ing electric  current  of  one  international  ampere  under  the  pressure  of  one  inter- 
national volt." 

In  accordance  with  these  definitions,  a  value  was  established  for  the  electro- 
motive force  of  the  recognized  standard  of  electromotive  force,  the  Weston 
normal  cell,  as  the  result  of  international  cooperative  experiments  in  1910.  The 
value  was  1.0183  international  volts  at  20°  C. 

The  definitions  by  the  1908  International  Conference  supersede  certain  defini- 
tions adopted  by  the  International  Electrical  Congress  at  Chicago  in  1893.    Cer- 
tain of  the  units  retain  their  Chicago  definitions,  however.    They  are  as  follows : 
"Coulomb.     As  a  unit  of  quantity,  the  International  Coulomb,  which  is  the 
quantity  of  electricity  transferred  by  a  current  of  one  international  ampere 
in  one  second. 

"Farad.  As  a  unit  of  capacity,  the  International  Farad,  which  is  the  capacity 
of  a  condenser,  charged  to  be  a  potential  of  one  international  volt  by  one 
international  coulomb  of  electricity. 

"Joule.  As  a  unit  of  work,  the  Joule,  which  is  equal  to  io7  units  of  work  in 
the  c.g.s.  system,  and  which  is  represented  sufficiently  well  for  practical  use 
by  the  energy  expended  in  one  second  by  an  international  ampere  in  an 
international  ohm. 

"  Henry.  As  the  unit  of  induction,  the  Henry,  which  is  the  induction  in  a 
circuit  when  the  electromotive  force  induced  in  this  circuit  is  one  interna- 
tional volt,  while  the  inducing  current  varies  at  the  rate  of  one  ampere  per 
second." 

"The  choice  of  the  ohm  and  ampere  as  fundamental  was  purely  arbitrary. 
These  are  the  two  quantities  directly  measured  in  absolute  electrical  measure- 
ments. The  ohm  and  volt  have  been  urged  as  more  suitable  for  definition  in 
terms  of  arbitrary  standards,  because  the  primary  standard  of  electromotive 
force  (standard  cell)  has  greater  simplicity  than  the  primary  standard  of  current 
(silver  voltameter).  The  standard  cell  is  in  fact  used,  together  with  resistance 
standards,  for  the  actual  maintenance  of  the  units,  rather  than  the  silver  vol- 
tameter and  resistance  standards.  Again,  the  volt  and  ampere  have  some  claim 


XXXV111  INTRODUCTION. 

for   consideration   for   fundamental   definition,  both   being   units   of  quantities 
more  fundamental  in  electrical  theory  than  resistance." 

For  all  practical  purposes  the  "international"  and  the  "practical"  or  "abso- 
lute" units  are  the  same.  Experimental  determination  of  the  ratios  of  the  corres- 
ponding units  in  the  two  systems  have  been  made  and  the  mean  results  are 
given  in  Table  382.  These  ratios  represent  the  accuracy  with  which  it  was  possible 
to  fix  the  values  of  the  international  ohm  and  ampere  at  the  time  they  were 
defined  (London  Conference  of  1908).  It  is  unlikely  that  the  definitions  of  the 
international  units  will  be  changed  in  the  near  future  to  make  the  agreement 
any  closer.  An  act  approved  July  12,  1894,  makes  the  International  units  as 
above  defined  the  legal  units  in  the  United  States  of  America. 

THE  STANDARDS  OF  THE  INTERNATIONAL  ELECTRICAL 

UNITS. 

RESISTANCE 

Resistance.  —  The  definition  of  the  international  ohm  adopted  by  the  London 
Conference  in  1908  is  accepted  practically  everywhere. 

Mercury  Standards.  —  Mercury  standards  conforming  to  the  definition  were 
constructed  in  England,  France,  Germany,  Japan,  Russia  and  the  United  States. 
Their  mean  resistances  agree  to  about  two  parts  in  100,000.  To  attain  this 
accuracy,  elaborate  and  painstaking  experiments  were  necessary.  Tubes  are 
never  quite  uniform  in  cross-section;  the  accurate  measurement  of  the  mass  of 
mercury  filling  the  tube  is  difficult,  partly  because  of  a  surface  film  on  the  walls 
of  the  tube;  the  greatest  refinements  are  necessary  in  determining  the  length  of 
the  tube.  In  the  electrical  comparison  of  the  resistance  with  wire  standards, 
the  largest  source  of  error  is  in  the  filling  of  the  tube.  These  and  other  sources 
of  error  necessitated  a  certain  uniformity  in  the  setting  up  of  mercury  standards 
and  at  the  London  Conference  the  following  specifications  were  drawn  up: 

SPECIFICATION  RELATING  TO  MERCURY  STANDARDS  OF  RESISTANCE. 

The  glass  tubes  used  for  mercury  standards  of  resistance  must  be  made  of  a  glass  such  that 
the  dimensions  may  remain  as  constant  as  possible.  The  tubes  must  be  well  annealed  and  straight. 
The  bore  must  be  as  nearly  as  possible  uniform  and  circular,  and  the  area  of  cross-section  of  the 
bore  must  be  approximately  one  square  millimeter.  The  mercury  must  have  a  resistance  cf 
approximately  one  ohm. 

Each  of  the  tubes  must  be  accurately  calibrated.  The  correction  to  be  applied  to  allow  for 
the  area  of  the  cross-section  of  the  bore  not  being  exactly  the  same  at  all  parts  of  the  tube  must 
not  exceed  5  parts  in  10,000. 

The  mercury  filling  the  tube  must  be  considered  as  bounded  by  plane  surfaces  placed  in 
contact  with  the  ends  of  the  tube. 

The  length  of  the  axis  of  the  tube,  the  mass  of  mercury  the  tube  contains,  and  the  electrical 
resistance  of  the  mercury  are  to  be  determined  at  a  temperature  as  near  to  o°  C  as  possible. 
The  measurements  are  to  be  corrected  to  o°  C. 

For  the  purpose  of  the  electrical  measurements,  end  vessels  carrying  connections  for  the 
current  and  potential  terminals  are  to  be  fitted  on  to  the  tube.  These  end  vessels  are  to  be 
spherical  in  shape  (of  a  diameter  of  approximately  four  centimeters)  and  should  have  cylindrical 
pieces  attached  to  make  connections  with  the  tubes.  The  outside  edge  of  each  end  of  the  tube 


INTRODUCTION.  XXX'ix 

is  to  be  coincident  with  the  inner  surface  of  the  corresponding  end  vessel.  The  leads  which  make 
contact  with  the  mercury  are  to  be  of  thin  platinum  wire  fused  into  glass.  The  point  of  entry 
of  the  current  lead  and  the  end  of  the  tube  are  to  be  at  opposite  ends  of  a  diameter  of  the  bulb; 
the  potential  lead  is  to  be  midway  between  these  two  points.  All  the  leads  must  be  so  thin 
that  no  error  in  the  resistance  is  introduced  through  conduction  of  heat  to  the  mercury.  The 
filling  of  the  tube  with  mercury  for  the  purpose  of  the  resistance  measurements  must  be  carried 
out  under  the  same  conditions  as  the  filling  for  the  determination  of  the  mass. 

The  resistance  which  has  to  be  added  to  the  resistance  of  the  tube  to  allow  for  the  effect  of 
the  end  vessels  is  to  be  calculated  by  the  formula 

0.80    /i       i  \    , 
A  =  -     —    -  +  -i  )  ohm, 
L      r2/ 


where  r\  and  r»  are  the  radii  in  millimeters  of  the  end  sections  of  the  bore  of  the  tube. 

The  mean  of  the  calculated  resistances  of  at  least  five  tubes  shall  be  taken  to  determine  the 
value  of  the  unit  of  resistance. 

For  the  purpose  of  the  comparison  of  resistances  with  a  mercury  tube  the  measurements 
shall  be  made  with  at  least  three  separate  fillings  of  the  tube. 

Secondary  Standards.  —  Secondary  standards,  derived  from  the  mercury 
standards  and  used  to  give  values  to  working  standards,  are  certain  coils  of 
manganin  wire  kept  in  the  national  laboratories.  Their  resistances  are  adjusted 
to  correspond  to  the  unit  or  its  decimal  multiples  or  submultiples.  The  values 
assigned  to  these  coils  are  checked  from  time  to  time  with  the  similar  coils  of 
the  other  countries.  The  value  now  in  use  is  based  on  the  comparison  made 
at  the  U.  S.  Bureau  of  Standards  in  1910  and  may  be  called  the  "1910  ohm." 
Later  measurements  on  various  mercury  standards  checked  the  value  then  used 
within  2  parts  in  100,000.  Thus  the  basis  of  resistance  measurement  is  main- 
tained not  by  the  mercury  standards  of  a  single  laboratory,  but  by  all  the  mer- 
cury standards  of  the  various  national  laboratories;  it  is  furthermore  the  same 
in  all  countries,  except  for  very  slight  outstanding  discrepancies  due  to  the 
errors  of  measurement  and  variations  of  the  standards  with  time. 

Resistance  Standards  in  Practice.  —  In  ordinary  measurements,  working 
standards  of  resistance  are  usually  coils  of  manganin  wire  (approximately  84 
per  cent  Cu  +12  per  cent  Mn  +  4  per  cent  Ni).  They  are  generally  used  in  oil 
which  carries  away  the  heat  developed  by  the  current  and  facilitates  regulation 
and  measurement  of  the  temperature.  The  best  type  is  inclosed  in  a  sealed  case 
for  protection  against  atmospheric  humidity.  Varying  humidity  changes  the 
resistance  of  open  coils  often  to  several  parts  in  10,000  higher  in  summer  than 
in  winter.  While  sealed  i  ohm  and  o.i  ohm  coils  may  remain  constant  to  about 
i  part  in  100,000. 

Absolute  Ohm.  —  The  absolute  measurement  of  resistance  involves  the  pre- 
cise determination  of  a  length  and  a  time  (usually  an  angular  velocity)  in  a 
medium  of  unit  permeability.  Since  the  dimensional  formula  of  resistance  in 
the  electromagnetic  system  is  [Lju/T],  such  an  absolute  measurement  gives  R 
not  in  cm/sec,  but  in  cm  x  ^i/sec.  The  definitions  of  the  ohm,  ampere  and 
volt  by  the  1908  London  conference  tacitly  assume  a  permeability  equal  to 
unity.  The  relation  of  the  international  ohm  to  the  absolute  ohm  has  been 
measured  in  different  ways  involving  revolving  coil,  revolving  disk,  and  alter- 
nate current  methods.  Probably  the  most  accurate  determination  was  made 


Xl  INTRODUCTION. 

in  1913  by  F.  E.  Smith  of  the  National  Physical  Laboratory  of  England,  using 
a  modification  of  the  Lorentz  revolving  disk  method.  His  result  was 

i  international  ohm  =  1.00052  ±  0.00004  absolute  ohms, 

or,  in  other  words,  while  one  international  ohm  is  represented  by  a  mercury 
column  106.300  cm  long  as  specified  above,  one  absolute  ohm  requires  a  similar 
column  106.245  cm  long.  Table  305  of  the  6th  revised  edition  of  these  tables 
contains  data  relative  to  the  various  determinations  of  the  ohm. 

CURRENT. 

The  Silver  Voltameter.  —  The  silver  voltameter  is  a  concrete  means  of  meas- 
uring current  in  accordance  with  the  definition  of  the  international  ampere.  As 
used  for  the  realization  of  the  international  ampere  "it  consists  of  a  platinum 
cathode  in  the  form  of  a  cup  holding  the  silver  nitrate  solution,  a  silver  anode 
partly  or  wholly  immersed  in  the  solution,  and  some  means  to  prevent  anode 
slime  and  particles  of  silver  mechanically  detached  from  the  anode  from  reach- 
ing the  cathode.  As  a  standard  representing  the  international  ampere,  the 
silver  voltameter  includes  also  the  chronometer  used  to  measure  time.  The 
degree  of  purity  and  the  mode  of  preparation  of  the  various  parts  of  the  vol- 
tameter affect  the  mass  of  the  deposit.  There  are  numerous  sources  of  error,  and 
the  suitability  of  the  silver  voltameter  as  a  primary  standard  of  current  has 
been  under  investigation  since  1893.  Differences  of  as  much  as  o.i  per  cent  or 
more  may  be  obtained  by  different  procedures,  the  larger  differences  being 
mainly  due  to  impurities  produced  in  the  electrolyte  (by  filter  paper,  for  instance) . 
Hence,  in  order  that  the  definition  of  current  be  precise,  it  must  be  accompanied 
by  specifications  for  using  the  voltameter." 

The  original  specifications  were  recognized  to  be  inadequate  and  an  inter- 
national committee  on  electrical  units  and  standards  was  appointed  to  com- 
plete the  specifications.  It  was  also  recognized  that  in  practice  standard  cells 
would  replace  secondary  current  standards  so  that  a  value  must  be  fixed  for  the 
electromotive  force  of  the  Weston  normal  cell.  This  was  attempted  in  1910  at 
the  Bureau  of  Standards  by  representatives  of  that  institution  together  with 
one  delegate  each  from  the  Physikalische-Technische  Reichanstalt,  The  National 
Physical  Laboratory  and  the  Laboratoire  Central  d'Electricite.  Voltameters 
from  all  four  institutions  were  put  in  series  under  a  variety  of  experimental  con- 
ditions. Standard  Weston  cells  and  resistance  standards  of  the  four  laboratories 
were  also  intercompared.  From  the  joint  comparison  of  standard  cells  and 
silver  voltameters  particular  values  were  assigned  to  the  standard  cells  from 
each  laboratory.  The  different  countries  thus  have  a  common  basis  of  measure- 
ment maintained  by  the  aid  of  standard  cells  and  resistance  standards  derived 
from  the  international  voltameter  investigation  of  1910. 

It  was  not  found  possible  to  draw  up  satisfactory  and  final  specifications  for 
the  silver  voltameter.  Provisional  specifications  were  submitted  by  the  U.  S. 
Bureau  of  Standards  and  more  complete  specifications  have  been  proposed  in 
correspondence  between  the  national  laboratories  and  members  of  the  inter- 


INTRODUCTION'.  xli 

national  committee  since  1910,  but  no  agreement  upon  final  specifications  has 
yet  been  reached. 

Resistance  Standards  Used  in  Current  Measurements.  —  Precise  measure- 
ments of  currents  require  a  potentiometer,  a  standard  cell  and  a  resistance 
standard.  The  resistance  must  be  so  designed  as  to  carry  the  maximum  current 
without  undue  heating  and  consequent  change  of  resistance.  Accordingly  the 
resistance  metal  must  have  a  small  temperature  resistance  coefficient  and  a 
sufficient  area  in  contact  with  the  air,  oil,  or  other  cooling  fluid.  It  must  have 
a  small  thermal  electromotive  force  against  copper.  Manganin  satisfies  these 
conditions  and  is  usually  used.  The  terminals  of  the  standard  must  have  suffi- 
cient contact  area  so  that  there  shall  be  no  undue  heating  at  contacts.1  It  must 
be  so  designed  that  the  current  distribution  does  not  depend  upon  the  mode  of 
connection  to  the  circuit. 

Absolute  Ampere.  —  The  absolute  ampere  (ro^c.g.s.  electromagnetic  units) 
differs  by  a  negligible  amount  from  the  international  ampere.  Since  the  dimen- 
sional formula  of  the  current  in  the  electromagnetic  system  is  \_IJM  */ Tp,^  which 
is  equivalent  to  \_F*/i^~\,  the  absolute  measurement  of  current  involves  funda- 
mentally the  measurement  of  a  force  in  a  medium  of  unit  permeability.  In  most 
measurements  of  high  precision  an  electrodynamometer  has  been  used  of  the 
form  known  as  a  current  balance.  A  summary  of  the  various  determinations 
will  be  found  in  Table  293  of  the  6th  Revised  Edition  of  these  tables. 

The  best  value  is  probably  the  mean  of  the  determinations  made  at  the  U.  S. 
Bureau  of  Standards,  the  National  Physical  Laboratory  and  at  the  University 
of  Groningen,  which  gives 

i  international  ampere  =  0.99991  absolute  ampere. 

The  separate  values  were  0.99992,  0.99988  and  0.99994,  respectively.  "The 
result  may  also  be  expressed  in  terms  of  the  electrochemical  equivalent  of  silver, 
which,  based  on  the  '1910  mean  voltameter,'  thus  equals  0.00111810  g  per 
absolute  coulomb.  By  the  definition  of  the  international  ampere,  the  value  is 
0.00111800  g  per  international  coulomb." 

ELECTROMOTIVE   FORCE. 

International  Volt.  —  "  The  international  volt  is  derived  from  the  interna- 
tional ohm  and  ampere  by  Ohm's  law.  Its  value  is  maintained  by  the  aid  of  the 
Weston  normal  cell.  The  national  standardizing  laboratories  have  groups  of 
such  cells,  to  which  values  in  terms  of  the  international  ohm  and  ampere  have 
been  assigned  by  international  experiments,  and  thus  form  a  basis  of  reference 
for  the  standardization  of  the  standard  cells  used  in  practical  measurements." 

Weston  Normal  Cell.  —  The  Weston  normal  cell  is  the  standard  used  to 
maintain  the  international  volt  and,  in  conjunction  with  resistance  standards, 
to  maintain  the  international  ampere.  The  cell  is  a  simple  voltaic  combination 

1  See  "Report  to  the  International  Committee  on  Electrical  Units  and  Standards,"  1912,  p. 
199.  For  the  Bureau  of  Standards  investigations  see  Bull.  Bureau  of  Standards,  9,  pp.  209,  493; 
10,  P-  475*  1912-14;  13,  P-  147,  1915;  9,  P-  iSi,  1912:  13,  pp.  447.  479, 


xliv  INTRODUCTION. 

difference  which  exists  between  the  terminals  of  a  resistance  of  one  international 
ohm  when  the  latter  carries  a  current  of  one  absolute  ampere.  The  emf  of  the 
Weston  normal  cell  may  be  taken  as  1.01821  semi-absolute  volts  at  20°  C. 

QUANTITY    OF    ELECTRICITY. 

The  international  unit  of  quantity  of  electricity  is  the  coulomb.  The  faraday 
is  the  quantity  of  electricity  necessary  to  liberate  i  gram  equivalent  in  electroly- 
sis. It  is  equivalent  to  96,500  coulombs.  0 

Standards.  —  There  are  no  standards  of  electric  quantity.  The  silver  voltam- 
eter may  be  used  for  its  measurement  since  under  ideal  conditions  the  mass 
of  metal  deposited  is  proportional  to  the  amount  of  electricity  which  has  flowed. 

CAPACITY. 

The  unit  generally  used  for  capacity  is  the  international  microfarad  or  the 
one-millionth  of  the  international  farad.  Capacities  are  commonly  measured 
by  comparison  with  standard  capacities.  The  values  of  the  standards  are  de- 
termined by  measurement  in  terms  of  resistance  and  time.  The  standard  is 
some  form  of  condenser  consisting  of  two  sets  of  metal  plates  separated  by  a 
dielectric.  The  condenser  should  be  surrounded  by  a  metal  shield  connected  to 
one  set  of  plates  rendering  the  capacity  independent  of  the  surroundings.  An 
ideal  condenser  would  have  a  constant  capacity  under  all  circumstances,  with  zero 
resistance  in  its  leads  and  plates,  and  no  absorption  in  the  dielectric.  Actual 
condensers  vary  with  the  temperature,  atmospheric  pressure,  and  the  voltage, 
frequency,  and  time  of  charge  and  discharge.  A  well-constructed  air  condenser 
with  heavy  metal  plates  and  suitable  insulating  supports  is  practically  free  from 
these  effects  and  is  used  as  a  standard  of  capacity. 

Practically  air  condenser  plates  must  be  separated  by  i  mm  or  more  and  so 
cannot  be  of  great  capacity.  The  more  the  capacity  is  increased  by  approach- 
ing the  plates,  the  less  the  mechanical  stability  and  the  less  constant  the  capac- 
ity. Condensers  of  great  capacity  use  solid  dielectrics,  preferably  mica  sheets 
with  conducting  plates  of  tinfoil.  At  constant  temperature  the  best  mica  con- 
densers are  excellent  standards.  The  dielectric  absorption  is  small  but  not  quite 
zero,  so  that  the  capacity  of  these  standards  with  different  methods  of  measure- 
ment must  be  carefully  determined. 

INDUCTANCE. 

The  henry,  the  unit  of  self-inductance,  is  also  the  unit  of  mutual  inductance. 
The  henry  has  been  known  as  the  " quadrant"  and  the  "secohm."  The  length 
of  a  quadrant  or  quarter  of  the  earth's  circumference  is  approximately  io9  cms. 
and  a  henry  is  io9  cms.  of  inductance.  Secohm  is  a  contraction  of  second  and 
ohm;  the  dimensions  of  inductance  are  [TR]  and  this  unit  is  based  on  the 
second  and  ohm. 

Inductance  Standards.  —  Inductance  standards  are  measured  in  international 
units  in  terms  of  resistance  and  time  or  resistance  and  capacity  by  alternate- 


INTRODUCTION.  xlv 

current  bridge  methods.  Inductances  calculated  from  dimensions  are  in  abso- 
lute electromagnetic  units.  The  ratio  of  the  international  to  the  absolute  henry 
is  the  same  as  the  ratio  of  the  corresponding  ohms. 

Since  inductance  is  measured  in  terms  of  capacity  and  resistance  by  the  bridge 
method  about  as  simply  and  as  conveniently  as  by  comparison  with  standard 
inductances,  it  is  not  necessary  to  maintain  standard  inductances.  They  are 
however  of  value  in  magnetic,  alternating-current,  and  absolute  electrical  meas- 
urements. A  standard  inductance  is  a  circuit  so  wound  that  when  used  in  a 
circuit  it  adds  a  definite  amount  of  inductance.  It  must  have  either  such  a 
form  or  so  great  an  inductance  that  the  mutual  inductance  of  the  rest  of  the 
circuit  upon  it  may  be  negligible.  It  usually  is  a  wire  coil  wound  all  in  the  same 
direction  to  make  self-induction  a  maximum.  A  standard,  the  inductance  of 
which  may  be  calculated  from  its  dimensions,  should  be  a  single  layer  coil  of 
very  simple  geometrical  form.  Standards  of  very  small  inductance,  calculable 
from  their  dimensions,  are  of  some  simple  device,  such  as  a  pair  of  parallel  wires 
or  a  single  turn  of  wire.  With  such  standards  great  care  must  be  used  that  the 
mutual  inductance  upon  them  of  the  leads  and  other  parts  of  the  circuit  is  negli- 
gible. Any  inductance  standard  should  be  separated  by  long  leads  from  the 
measuring  bridge  or  other  apparatus.  It  must  be  wound  so  that  the  distributed 
capacity  between  its  turns  is  negligible;  otherwise  the  apparent  inductance  will 
vary  with  the  frequency. 

POWER    AND   ENERGY. 

Power  and  energy,  although  mechanical  and  not  primarily  electrical  quanti- 
ties, are  measurable  with  greater  precision  by  electrical  methods  than  in  any 
other  way.  The  watt  and  the  electric  units  were  so  chosen  in  terms  of  the  c.g.s. 
units  that  the  product  of  the  current  in  amperes  by  the  electromotive  force  in 
volts  gives  the  power  in  watts  (for  continuous  or  instantaneous  values).  The 
international  watt,  defined  as  "the  energy  expended  per  second  by  an  unvarying 
electric  current  of  one  international  ampere  under  an  electric  pressure  of  one 
international  volt,"  differs  but  little  from  the  absolute  watt. 

Standards  and  Measurements.  —  No  standard  is  maintained  for  power  or 
energy.  Measurements  are  always  made  in  electrical  practice  in  terms  of  some 
of  the  purely  electrical  quantities  represented  by  standards. 

MAGNETIC    UNITS. 

C.G.S.  units  are  generally  used  for  magnetic  quantities.  American  practice 
is  fairly  uniform  in  names  for  these  units:  the  c.g.s.  unit  of  magnetomotive  force 
is  called  the  "gilbert,"  of  reluctance,  the  "oersted,"  following  the  provisional 
definitions  of  the  American  Institute  of  Electrical  Engineers  (1894).  The  c.g.s. 
unit  of  flux  is  called  the  "maxwell"  as  defined  by  the  1900  Paris  conference. 
The  name  "gauss"  is  used  unfortunately  both  for  the  unit  of  induction  (A.I.E.E. 
1894)  and  for  the  unit  of  magnetic  field  intensity  or  magnetizing  force.  "This 
double  usage,  recently  sanctioned  by  engineering  societies,  is  based  upon  the 
mathematical  convenience  of  defining  both  induction  and  magnetizing  force 


xlvi 


INTRODUCTION. 


as  the  force  on  a  unit  magnetic  pole  in  a  narrow  cavity  in  the  material,  the  cavity 
being  in  one  case  perpendicular,  in  the  other  parallel,  to  the  direction  of  the 
magnetization:  this  definition  however  applies  only  in  the  ordinary  electro- 
magnetic units.  There  are  a  number  of  reasons  for  considering  induction  and 
magnetizing  force  as  two  physically  distinct  quantities,  just  as  electromotive 
force  and  current  are  physically  different." 

In  the  United  States  " gauss"  has  been  used  much  more  for  the  c.g.s.  unit  of 
induction  than  for  the  unit  of  magnetizing  force.  The  longer  name  of  "  max- 
well per  cm2"  is  also  sometimes  used  for  this  unit  when  it  is  desired  to  distin- 
guish clearly  between  the  two  quantities.  The  c.g.s.  unit  of  magnetizing  force 
is  usually  called  the  " gilbert  per  cm." 

A  unit  frequently  used  is  the  ampere-turn.  It  is  a  convenient  unit  since  it 
eliminates  47T  in  certain  calculations.  It  is  derived  from  the  "ampere  turn  per 
cm."  The  following  table  shows  the  relations  between  a  system  built  on  the 
ampere- turn  and  the  ordinary  magnetic  units.1 


TABLE  II. 
THE  ORDINARY  AND  THE  AMPERE-TURN   MAGNETIC  UNITS- 


Quantity 

Ordinary 
magnetic 
units 

Ampere-turn 
units. 

Ordinary 
units  in  i 
ampere- 

turn  unit 

i 

Magnetomotive  force 

3F 

Gilbert 

Ampere-turn 

47T/IO 

Magnetizing  force 

H 

Gilbert    per 

Ampere-turn   per 

47T/IO 

cm. 

cm. 

Magnetic  flux 

$ 

Maxwell 

Maxwell 

I 

Magnetic  induction         (  B 

f  Maxwell  per 

f  Maxwell  per  cm.2 

I 

\  cm.2  Gauss 

\  Gauss 

Permeability 

M 

I 

Reluctance 

R 

Oersted 

f  Ampere-turn  per 

47T/IO 

\  Maxwell 

Magnetization  intensity 

J 

Maxwell  per  cm.2 

I/47T 

Magnetic  susceptibility 

K 

I/47T 

Magnetic  pole  strength 

m 

Maxwell 

I/47T 

1  Bellinger,  International  System  of  Electric  and  Magnetic  Units,  Bull.  Bureau  of  Standards, 
13,  p.  599, 


PHYSICAL   TABLES 


2  TABLE  1. 

SPELLING    AND    ABBREVIATIONS   OF   THE   COMMON    UNITS  OF   WEIGHT   AND    MEASURE. 

The  spelling  of  the  metric  units  is  that  adopted  by  the  International  Committee  on  Weights 
and  Measures  and  given  in  the  law  legalizing  the  metric  system  in  the  United  States  (1866). 
The  period  is  omitted  after  the  metric  abbreviations  but  not  after  those  of  the  customary  system. 
The  exponents  "2"  and  "3"  are  used  to  signify  area  and  volume  respectively  in  the  metric  units. 
The  use  of  the  same  abbreviation  for  singular  and  plural  is  recommended.  It  is  also  suggested 
that  only  small  letters  be  used  for  abbreviations  except  in  the  case  of  A.  for  acre,  where  the  use 
of  the  capital  letter  is  general.  The  following  list  is  taken  from  circular  87  of  the  U.  S.  Bureau 
of  Standards. 


Unit. 

Abbreviation. 

Unit. 

Abbreviation. 

acre 

A 

kilogram 

kg 

are 

a 

kiloliter 

kl 

avoirdupois 

av. 

kilometer 

km 

barrel 

bbl. 

link 

li. 

board  foot 

bd.  ft. 

liquid 

liq. 

bushel 

bu. 

•  liter 

1 

carat,  metric 

c 

meter 

m 

centare 

ca 

metric  ton 

t 

centigram 

eg 

micron 

M. 

centiliter 

cl 

mile 

mi. 

centimeter 

cm 

milligram 

mg 

chain 

ch. 

milliliter 

ml 

cubic  centimeter 

cm3 

millimeter 

mm 

cubic  decimeter 

dm3 

millimicron 

mju 

cubic  dekameter 

dkm3 

minim 

min.  or  Tfl, 

cubic  foot 

cu.  ft. 

ounce 

oz. 

cubic  hectometer 

hm3 

ounce,  apothecaries' 

oz.  ap.  or  5 

cubic  inch 

cu.  in. 

ounce,  avoirdupois 

oz.  av. 

cubic  kilometer 

km3 

ounce,  fluid 

fl.  oz. 

cubic  meter 

m3 

ounce,  troy 

oz.  t. 

cubic  mile 

cu.  mi. 

peck 

pk. 

cubic  millimeter 

mm3 

pennyweight 

dwt. 

cubic  yard 
decigram 

cu.  yd. 
dg 

pint 
pound 

pt. 
Ib. 

deciliter 

dl 

pound,  apothecaries' 

Ib.  ap. 

decimeter 

dm 

pound,  avoirdupois 

Ib.  av. 

decistere 

ds 

pound,  troy 

Ib.  t. 

dekagram 

dkg 

quart 

qt. 

dekaliter 

dkl 

rod 

rd. 

dekameter 

dkm 

scruple,  apothecaries' 

s.  ap.  or  9 

dekastere 

dks 

square  centimeter 

cm2 

dram 

dr. 

square  chain 

sq.  ch. 

dram,  apothecaries' 
dram,  avoirdupois 

dr.  ap.  or  5 
dr.  av. 

square  decimeter 
square  dekameter 

dm2 
dkm2 

dram,  fluid 

fl.  dr. 

square  foot 

sq.  ft. 

fathom 

fath. 

square  hectometer 

hm2 

foot 

ft. 

square  inch 

sq.  in. 

firkin 

fir. 

square  kilometer 

km2 

furlong 

fur. 

square  meter 

m2 

gallon 

gal. 

square  mile 

sq.  mi. 

grain 

gr. 

square  millimeter 

mm2 

gram 

g 

square  rod 

sq.  rd. 

hectare 

ha 

square  yard 

sq.  yd. 

hectogram 
hectoliter 

hg 
hi 

stere 
ton 

s 
tn. 

hectometer 

hm 

ton,  metric 

t 

hogshead 

hhd. 

troy 

t. 

hundredweight 

cwt. 

yard 

yd. 

inch 

in. 

SMITHSONIAN  TABLES. 


TABLE  2.  ? 

FUNDAMENTAL   AND   DERIVED   UNITS- 
Conversion  Factors. 

To  change  a  quantity  from  one  system  of  units  to  another:  substitute  in  the  corresponding 
conversion  factor  from  the  following  table  the  ratios  of  the  magnitudes  of  the  old  units  to  the 
new  and  multiply  the  old  quantity  by  the  resulting  number.  For  example:  to  reduce  velocity 
in  miles  per  hour  to  feet  per  second,  the  conversion  factor  is  lrl;  I  =  5280/1,  t=  3600/1,  and 
the  factor  is  5280/3600  or  1.467.  Or  \ve  may  proceed  as  follows:  e.  g.,  to  find  the  equivalent  of 
I  c.g.s.  unit  of  angular  momentum  in  the  pel. ft. m.  unit,  from  the  Table  t  g  cm~/sec.=jc  Ib.  ft.2/rnin, 
where  x  is  the  factor  sought.  Solving,  x=ig/\b.  X  cm'2/ft.'2  X  min./sec.  =  i  X  .002205  X  .001076 
X  6o=.oooi42c;. 

The  dimensional  formulae  lack  one  quality  which  is  needed  for  completeness,  an  indication  of 
their  vector  characteristics;  such  characteristics  distinguish  plane  and  solid  angle,  torque  and 
energy,  illumination  and  brightness. 

(a)   FUNDAMENTAL  UNITS. 

The  fundamental  units  and  conversion  factors  in  the  systems  of  units  most  commonly  used 
are:  Length  [/J;  Mass  \_m~\\  Time  [f\\  Temperature  {B~]\  and  for  the  electrostatic  system, 
Dielectric  Constant  [&];  for  the  electromagnetic  system,  Permeability  [ju].  The  formulae 
will  also  be  given  for  the  International  System  of  electric  and  magnetic  units  based  on  the  units 
length,  resistance  [Y],  current  [f],  and  time. 

(b)   DERIVED  UNITS. 


Name  of  unit. 

(Geometrical  and 
dynamical.  ) 

Conversion 
factor. 

faetof] 

Name  of  units. 
(Heat  and  light.) 

Conversion 
factor. 

lm*lvt*6»] 

r 

X 

y 

2 

X 

. 

y 

z 

Area,  surface  
Volume  .... 

O 
0 
O 

0 

0 
O 

0 
O 
0 

I 
I 

O 

I 
I 
I 

I 

I 
I 

I 
I 

I 

—  I 

2 

3 

0 

0 

-I 

O 

I 

O 

I 
-3 

2 

I 
I 

2 

J 
I 

2 
2 

o 

0 

o 
o 

0 

—  I 
—  I 

—  2 

0 
0 
—  2 

-I 
-I 
—  2 

—  2 
-2 

-3 

-2 

Quantity  of  heat: 
thermal  units  

O 
0 

I 

o 

I 

I 

0 

o 
o 

I 
I 

0 

o 
o 
-I 

o 
3 

2 
0 

—  I 

2 

I 

0 

0 

2 

2 

O 
2 

O 
-2 

-2 

O 
O 
—  2 

0 

—  I 
—  I 

-3 

0 

o 

—  2 

0 

-2 

0 
O 

o 
3 

3 

I 
I 
O 

—  I 

O 
O 

—  I 

0 

I 

0 

I 

0 

1 

I* 
I* 
I* 

I* 
I* 

Angle.  .  .  . 

thermometric  units.  . 
dynamical  units  .... 

Coefficient    of    thermal 
expansion  

Thermal  conductivity: 
thermal  units 

Solid  angle  
Curvature  

Angular  velocity  

Linear  velocity 

Angular  acceleration.  .  .  . 
Linear  acceleration  

Density  
Moment  of  inertia  
Intensity  of  attraction  .  . 

Momentum  

thermometric     units 
or  diffusivity  
dynamical  units  .... 

Thermal  capacity  

Latent  heat: 
thermal  units  
dynamical  units.  .  .  . 

Joule's  equivalent  

Entropy: 
heat  in  thermal  units 
heat     in    dynamical 
units   

Moment  of  momentum.. 
Angular  momentum  .... 

Force 

Moment       of      couple, 
torque  
Work  energy    

Power  activity 

Intensity  of  stress  
Modulus  of  elasticity  — 

Compressibility  

Luminous  intensity.... 
Illumination 

Brightness  

„ 

Visibility           

Viscosity  

I 

— 

—  I 

Luminous  efficiency.  .  .  . 

*  For  these  formulae  the  numbers  in  the  last  column  are  the  exponents  of  F  where  F  refers  to  the  luminous  flux. 
For  definitions  of  these  quantities  see  Table  299,  page  259. 

SMITHSONIAN  TABLES. 


TABLE  2  (continued). 
FUNDAMENTAL  AND   DERIVED    UNITS- 

Conversion  Factors. 
(6)   DERIVED  UNITS. 


NAME  OF  UNIT. 
(Electric  and  magnetic.) 

Sym- 
bol* 

CONVERSION  FACTOR. 

Electrostatic 
system. 

Electromagnetic 
system. 

emu 

International 
system. 

csu 
t 

mzl»t*kv 

m^t1^ 

r*»»W 

X 

y 

z 

• 

X 

y 

2 

V 

.V 

y 

« 

V 

Quantity  of  electricity  
Electric  displacement 

Q 
D 
D 

£ 
V 
E 

C 
K 

I 
7 
P 

g 
R 
m 

m 
3> 
H 

H 
12 
7 

B 

K 

M 

£ 

9R 
91 

f 

f 
I 

0 
O 

o 

i 

o 

0 
0 

o 

I 
i 

I 
f 

1 

I 

o 
o 

* 

0 
0 

o 

f 

-1 
-f 

i 

0 

o 

f 

0 
0 

0 
0 
0 

-2 

-1 
-I 

I 
I 
O 

i 

I 
\ 

O 
O 

o 

i 

-1 

~  2 
2 

-I 

-2 
0 

i 

0 
0 
0 

—  2 
-2 
—  2 

2 

2 
0 

—  I 

_1 
-I 

—  I 

-I 
O 

-i 

C 
C 
C 

i/c 
i/c 

I/C 

c2 
c2 

c 

0 
0 

o 

I 

I 
I 

—  I 
-I 
o 

0 

I 
I 
o 

o 
o 
o 

I 
I 

I 

I 

I 

0 

I 
I 
-I 

I 

I 

o 
o 
o 

I 
o 
o 

0 
0 

I 

I 
I 
o 

o 

0 

o 

I 

o 
o 
o 

I 
I 

o 

-2 
-2 

I 
o 

0 
0 

-I 

0 
0 

—  I 

I 

o 

0 
0 

0 
0 

-I 
-I 

0 

o 

I 

-2 
—  2 

-I 

-I 

-2 

0 
O 
O 

0 
0 

I 
I 
I 

0 

o 
o 

o 

I 
o 

0 

0 

o 

0 

o 

I 

I 
I 

0 

o 
o 
o 

I 
I 
I 

I 
I 
o 

I 
I 
-I 

ot 
ot 

Electric  surface  density  

Electric  field  intensity  
Electric  potential  
Electromotive  force  

Electrostatic  capacity 

Dielectric  constant       .  .  . 

Specific  inductive  capacity. 

Current  .  .  •.  

Electric  conductivity 

Resistivity 

I 

-I 

o 

2 

—  I 

i 

I/C- 

c2 

I/c2 

i/c 

i/c 
i/c 
c 

c 
c 
c 

i/c 

I/C 
I/C 

I/C2 
I/C2 

c 

I/C2 

I/C2 

c3 

# 

Conductance 

Resistance 

-I 

i 

f 
I 

-1 

-2 
-2 

-i 

-i 
-i 
i 

f 

I 
0 

o 
o 

—  2 

—  2 
-2 
-2 

0 
0 

o 

2 
2 
-2 

2 
2 
-2 

-I 
-I 

—  I 
~\ 

~\ 
~\ 
\ 

~\ 

-1 

-I 
—  I 
} 

—  I 

-I 

I 

-f} 

-it 

o 

1 
I 

f 

I 

o 
o 

i 

0 
0 

o 

1 

I 
1 

J 

-1 

I 
1 

-I 
0 

o 

:t 
-I 

I 
I 
-I 

1 
I 

-I 
-I 

—  I 

-I 

—  I 

—  I 
-I 
-I 

-I 

—  I 
—  I 

0 
0 

-I 

0 
0 
0 

-2 

-2 

i 
i 

| 

f 
I 

i 
i 

_! 

I 
I 
—  I 

i| 
il 

Magnetic  pole  strength  
Quantity  of  magnetism 

Magnetic  flux  

Magnetic  field  intensity  . 

Magnetizing  force 

Magnetic  potential 

Magnetomotive  force  

Magnetic  moment  
Intensity  magnetization.  .  .  . 

Magnetic  induction  

Magnetic  susceptibility  
Magnetic  permeability  
Current  density. 

Self-inductance  

Mutual  inductance  

Magnetic  reluctance  

Thermoelectric  power  \  

Peltier  coefficient  J.  .  . 

*  As  adopted  by  American  Institute  of  Electrical  Engineers,  1915. 
t  c  is  the  velocity  of  an  electromagnetic  wave  in  the  ether  =  3  X  io10  approximately. 
J  This  conversion  factor  should  include  [_6~1]. 

SMITHSONIAN  TABLES. 


TABLES. 
TABLES   FOR   CONVERTING   U.   S.  WEIGHTS  AND   MEASURES.* 

(1)  CUSTOMARY   TO    METRIC. 


LINEAR. 

CAPACITY. 

Inches 
to 

Feet  to 

Yards  to 

Miles 
to 

Fluid 
drams  to 
milliliters 

Fluid 
ounces 

Liquid 
quarts  to 

Gallons  to 

millimeters. 

kilometers 

or  cubic 

liters. 

ners. 

centimeters. 

! 

25.4001 

0.304861 

0.914402 

1.60935 

i 

3-70 

29.57 

0.94633 

2 

508001 

0.609601 

1.828804 

3.21869 

2 

7-39 

59.15 

1.89267 

7.57066 

3 

76.2002 

0.914402 

2.743205 

4.82804 

3 

11.09 

88.72 

2.83900 

11.35600 

4 

IOI.6OO2 

I.2I92O2 

3.657607 

6-43739 

4 

14.79 

118.29 

3.78533 

I5-I4i33 

5 

127.0003 

1.524003 

4.572009 

8.04674 

5 

18.48 

147.87 

4-73*67 

18.92666 

6 

152.4003 
177.8004 

1.828804 
2.133604 

5.486411 
6.400813 

9.65608 
11.26543 

6 

7 

22.18 
25.88 

177-44 
207.01 

5.67800 
6-62433 

22.71199 
26.49733 

8 

203.2004 

2.438405 

7.315215 

12.87478 

8 

29-57 

236-58 

7.57066 

30.28266 

9 

228.6005 

2.743205 

8.229616 

14.48412 

9 

33-27 

266.16 

8.51700 

34.06799 

SQUARE.      • 


WEIGHT. 

Square 
inches  to 
square  cen- 
timeters. 

Square  feet 
to  square 
decimeters. 

Square 
yards  to 
square 
meters. 

Acres  to 
hectares. 

Grains  to 
milligrams. 

Avoirdu- 
pois ounces 
to  grams. 

Avoirdu- 
pois pounds 
to  kilo- 
grams. 

Troy 

ounces  to 
grams. 

i 

6.452 

9.290 

0.836 

0.4047 

i 

64.7989 

28.3495 

0-45359 

31.10348 

2 

12.903 

18.581 

1.672 

0.8094 

2 

129.5978 

56-6991 

0.90718 

62.20696 

3 

19-355 

27.87I 

2.508 

1.2141 

3 

194.3968 

85.0486 

1.36078 

93-3  i  °44 

4 

25-807 

37.l6l 

3-345 

1.6187 

4 

259-I957 

113.3981 

I.8I437 

124.41392 

5 

32.258 

46.452 

4.181 

2.0234 

5 

323.9946 

141.7476 

2.26796 

1  55-  5  T  740 

6 

38.710 

55-742 

5.017 

2.4281 

6 

388.7935 

170.0972 

2.72155 

186.62088 

7 
8 
9 

45.161 

5r-6i3 

58.065 

65.032 
74.323 
83-613 

6.689 
7-525 

2.8328 

3-2375 
3.6422 

7 
8 
9 

453-5924 
518-3913 
583-!  903 

198.4467 
226.7962 

255-H57 

3-I75I5 
3.62874 
4.08233 

217.72437 
248.82785 
279-93I33 

CUBIC. 

Cubic 
inches  to 
cubic  cen- 
timeters. 

Cubic  feet 
to  cubic 
meters. 

Cubic 
yards  to 
cubic 
meters. 

Bushels  to 
hectoliters. 

i  Gunter's  chain    =      20.1168      meters. 
i  sq.  statute  mile  =    259.000      hectares. 

i  fathom                  =        1.829        meters. 

r 

16.387 

0.02832 

0.765 

0.35239 

i  nautical  mile       =  1853.25          meters. 

2 

32-774 

0.05663 

1.529 

0.70479 

i  foot                       =        0.304801     meter. 

3 
4 

5 

49.161 

65.549 
81.936 

0.08495 
0.11327 
0.14159 

2.294 
3.0|8 

1.05718 
1.40957 
1.76196 

i  avoir,  pound        =    453.5924277  grams. 
1  5432.35639  grains  =        i.ooo     kilogram. 

6 

98.323 

o.  1  6990 

4.587 

2.11436 

7 

II47IO 

0.19822 

5-352 

2.46675 

i 

131.097 

0.22654 

6.II6 

2.81914 

9 

147.484 

0.25485 

6.881 

3.'7i54 

According  to  an  executive  order  dated  April  15,  1803,  tne  United  States  yard  is  denned  as  3600/3937  meter,  and 
the  avoirdupois  pound  as  1/2.20462  kilogram. 

i  meter  (international  prototype)  —  15^3164.13  times  the  wave-length  of  the  red  Cd.  line.  Benoit,  Fabry  and 
Perot.  C.  R.  144,  1907  differs  only  in  the  decimal  portion  from  the  measure  of  Michelson  and  Benoit  14  years  earlier. 

The  length  of  the  nautical  mile  given  above  and  adopted  by  the  U.  S.  Coast  and  Geodetic  Survey  many  years  ago, 
is  defined  as  that  of  a  minute  of  arc  of  a  great  circle  of  a  sphere  whose  surface  equals  that  of  the  earth  (Clarke's  Sphe- 
roid of  1866). 

*  Quoted  from  sheets  issued  by  the  United  States  Bureau  of  Standards. 

SMITHSONIAN  TABLES. 


TABLE  3  (continual). 
TABLES   FOR   CONVERTING   U.  S.  WEIGHTS   AND   MEASURES. 

(2)   METRIC   TO    CUSTOMARV. 


LINEAR. 

CAPACITY. 

Millili- 

ters  or 

( 

Jenti- 

' 

leca- 

Hecto- 

Meters to 

Meters  to 

Meters  to 

Kilometers 

cubic  cen- 

li 

ters  to 

iters 

liters 

inches. 

feet. 

vards. 

to  miles. 

timeters 

fluid 

to 

to 

to  fluid 

ounces. 

gallons. 

bushels. 

drams. 

i 

39-3700 

3.28083 

1.093611 

0.62137 

, 

0.27 

0.338 

1.0.567 

2.6418 

2.8378 

2 

78.7400 

6.56167 

2.187222 

1.24274 

2 

0-54 

0.676 

2.1134 

5.2836 

3 

IlS.IIOO 

9.84250 

3-280833 

I.864II 

3 

0.8  1 

I 

.014 

3.1701 

7-9253 

8.5135 

4 

157.4800 

J3-I2333 

4-374444 

2.48548   j 

4 

1.  08 

I 

-3S3 

4.2268 

10.5671 

i  I.TSI? 

5 

196.8500 

16.40417 

5.468056 

3.10685 

5 

J-35 

I 

.691 

5.2836 

13.2089 

14.1891  j 

6 

7 

236.2200 
275.5900 

19.68500 
22.96583 

6.561667 
7-655278 

3.72822 

4-34959  i 

6 

7 

1.62 
1.89 

2.029 
2.367 

6-3403 
7-3970 

\\ 

.8507 
.4924 

17.0269 
19.8647 

8 

314.9600 

26.24667 

8.748889 

4.97096 

8 

2.16 

f 

•705 

8.4537 

21 

.1342 

22.7026 

9 

354.3300 

29.52750 

9.842500 

5.59233 

9 

2-43 

3-043 

9-5'°4 

23.7760 

25-5404 

SQUARE. 

|     WEIGHT. 

Square 

Square 

Square 

Milli- 

Kilo- 

Hecto- 

Kilo- 

centimeters 
to  square 

meters  to 
square 

meters  to 
square 

Hectares 
to  acres.    ' 

grams  to 

grams  to 

grams  to 

ounces 

grams  to 
pounds 

inches. 

feet. 

yards. 

grain  . 

avoirdupois. 

avoirdupois. 

i 

2 

0.1550 
0.3100 

-    10.764 
21.528 

1.196 

2.392 

2.471 
4.942 

2 

0.01543 
0.03086 

I  5432.36 
30864.71 

3-5274 
7.0548 

2.20462 
4-40924 

3 

0.4650 

32.292 

3.588 

7-4I3 

3 

0.04630 

46297.07 

10.  ^822 

6.61387 

4 

0.6200 

43-055 

4.784 

9.884 

4 

0.06173 

61729.43 

M 

.1096 

8.81849 

5 

0.7750 

5.980 

12355 

5 

0.07716 

77161.78 

•6370 

1I.O23II 

6 

7 

0.9300 
1.0850 

64.583 

75-347 

7.176 
8-372 

14.826 
17.297 

6 

7 

0-09259 
0.10803 

92594.14 
108026.49 

21.1644 
24.6918 

I3-22773 
15.43236 

8 
9 

1.2400 
1-395° 

86.1  1  1 

96.875 

9-568 
10.764 

19768 
22.239 

8 

9 

0.12346 
0.13889 

123458.85 
138891.21 

28.2192 
31.7466 

17.63698 
19.84160 

CUBIC. 

WEIGHT. 

Cubic 
centimeters 
to  cubic 

Cubic 
decimeters 
to  cubic 

Cubic 
meters  to 
cubic 

Cubic 
meters  to 
cubic 

Quintals  to 
pounds  av. 

Milliers  or 
tonnes  to  pou  ids 

Kilograms 
to  ounces 

inches. 

inches. 

feet. 

yards. 

i 

0.06  10 

61.023 

3S-3M 

1.308 

i 

220.46 

2204.6 

32.1507 

2 

O.I22O 

122.047 

70.269 

2.616    i 

2 

440.92 

4409.2 

64.3015 

3 
4 

0.1831 
0.2441 

183.070 
244.094 

I05943 
141.258 

5^232 

3 

4 

6ft. 

881. 

s's 

6613-9 
8818.5 

96.4522 
128.6030 

5 

0.3051 

305.117 

176.572 

6.540     | 

5 

1102.31 

11023.1 

160.7537 

6 

0.3661 

366.140 

211.887 

7.848 

6 

1322.77 

13227.7 

192.9045 

7 

0.4272 

427.164 

247.201 

9-T56 

7 

1  543- 

24 

1543 

225.0552 

8 

0.4882 

488.187 

282.516 

10.464 

8 

1763.70 

17637.0 

257.2059 

9 

0.5492 

549-210 

3  '7-830 

11.771 

9 

1984- 

1  6 

19841.6 

289.3567 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an  International  Bureau  of  Weights  and 
Measures  has  been  established  near  Paris.  Under  the  direction  of  the  International  Committee,  two  ingots  were 
cast  of  pure  platinum-iridium  in  the  proportion  of  9  parts  of  the  former  to  i  of  the  latter  metal.  From  one  of  these 
a  certain  number  of  kilograms  were  prepared,  from  the  other  a  definite  number  of  meter  bars.  These  standards  of 
weight  and  length  were  intercompared,  without  preference,  and  certain  ones  were  selected  as  International  proto- 
type standards.  The  others  were  distributed  by  lot,  in  September,  1889,  to  the  different  governments,  and  are  called 
National  prototype  standards.  Those  apportioned  to  the  United  States  were  received  in  1890,  and  are  kept  at  the 
Bureau  of  Standards  in  Washington,  I).  C. 

The  metric  svstcm  was  legalized  in  the  United  States  in  1866. 

The  International  Standard  Meter  is  derived  from  the  Metre  des  Archives,  and  its  length  is  defined  by  the 
distance  between  two  lines  at  o°  Centigrade,  on  a  platinum-iridium  bar  deposited  at  the  International  Bureau  of 
Weights  and  Measures. 

The  International  Standard  Kilogram  is  a  mass  of  platinum-iridium  deposited  at  the  same  place,  and  its  weight 
in  vacuo  is  the  same  as  that  of  the  Kilogram  des  Archives. 

The  liter  is  equal  to  the  quantity  of  pure  water  at  4°  C  (760  mm.  Hg.  pressure)  which  weighs  i  kilogram  and  ~ 
1.000027  cu.  dm.  (Trav.  et  Mem.  Bureau  Intern,  des  P.  et  M.  14,  n;io,  Benoit.) 

SMITHSONIAN  TABLES. 


TABLE  4. 

MISCELLANEOUS  EQUIVALENTS  OF   U.  S-   AND   METRIC  WEIGHTS  AND   MEASURES-* 
(For  other  equivalents  than  those  below,  see  Table  3.) 


LINEAR  MEASURES. 

mil  (.001  in.)  =  25.4061  ju 

in.  =  .000015783  mile 

hand  (4  in.)  =  10.16002  cm 

link  (.66  ft.)  =  20.11684  cm 

span. (9  in.)  =  22.86005  cm 

fathom  (6  ft.)  =  1.828804  m 

rod  (25  links)  =  5.029210  m 

chain  (4  rods)  =  20.11684  m 

light  year   (9.5  X  io12  km)  =  5.9  X  io12 

miles 

i  par  sec  (31  X  io12  km)  =  19  X  io12  miles 
•fa  in.  =  .397  mm        ^  in.  =  .794  mm 
&  in.  =  1.588  mm         |  in.  =  3.175  mm 
j  in.    =  6.350  mm         \  in.  =  12.700  mm 
i  Angstrom  unit  =  .oooooooooi  m 
i  micron  (ju)  =  .oooooi  m  =  .00003937  in. 
i  millimicron  (m/x)  =  .00000000 1  m 
i  m  =  4.970960  links  =  1.093611  yds. 
=  .198838  rod  =  .0497096  chain 

SQUARE  MEASURES. 

sq.  link  (62.7264  sq.  in.)  =  404.6873  cm2 
sq.  rod  (625  sq.  links)  =  25.29295  m2 
sq.  chain  (16  sq.  rods)  =  404.6873  m2 
acre  (io  sq.  chains)  =  4046.873  m2 
sq.  mile  (640  acres)  =  2.589998  km2 
km2  =  .3861006  sq.  mile 
m2  =  24.7104  sq.  links  =  10.76387  sq.  ft. 
=  -039537    sq.    rod.  =  .00247104   sq. 
chain 

CUBIC  MEASURES. 

i  board  foot  (144  cu.  in)  =  2359.8  cm3 
i  cord  (128  cu.  ft.)  =  3.625  m3 

CAPACITY  MEASURES. 

i  minim  (TTJ.)  =  .0616102  ml 

i  fl.  dram  (6oTTl)  =  3.69661  ml 

i  fl.  oz.  (8  fl.  dr.)  =  1.80469  cu.  in. 

=  29.5729  ml 
i  gill  (4  fl.  oz.)  =  7. 21875  cu.  in.  =  118.292 

ml 

i  liq.  pt.  (28.875  cu.  in.)  =  .473167  1 
i  liq.  qt.  (57.75  cu.  in.)  =  .946333  1 
i  gallon  (4  qt,  231  cu.  in.)  =  3.785332  1 
i  dry  pt.  (33.6003125  cu.  in.)  =  .550599  1 
i  dry  qt.  (67.200625  cu.  in.)  =  1.101198  1 
i  pk.  (Sdryqt.,  537.605  cu.  in.)  =  8.80958  1 
i  bu.  (4  pk.,  2150.42  cu.  in.)  =  35.2383  1 
i  firkin  (9  gallons)  =  34.06799  1 
i  liter  =  .2641 78. gal.  =  1.05671  liq.  qt. 
=  33.8147  fl.  oz.  =  270.518  fl.  dr. 
i  ml  =  16.2311  minims, 
i  dkl  =  18.620  dry  pt.  =  9.08102  dry  qt. 

=  1.13513  pk.  =  .28378  bu. 


MASS  MEASURES. 
Avoirdupois  weights. 
i  grain  =  .064798918  g 
i  dram  av.  (27.34375  gr.)  =  1.771845  g 
i  oz.  av.  (16  dr.  av.)  =  28.349527  g 
i  pd.  av.  (16  oz.  av.  or  7000  gr.) 

=  I4-S83333  oz.  ap.  (5)  or  oz.  t. 
=  1.2152778   or  7000/5760  pd.  ap 
ort. 

=  453-5924277  g 
i  kg  =  2.204622341  pd.  av. 
i  g    =  15.432356  gr.  =  .5643833  av.  dr. 

=  -03527396  av.  oz. 
i  short  hundred  weight  (100  pds.) 

=  45-359243  kg 
i  long  hundred  weight  (112  pds.) 

,     =  50.802352  kg 
i  short  ton  (2000  pds.) 

=  907.18486  kg 
i  long  ton  (2240  pd.) 
=  1016.04704  kg 

i  metric  ton  =  0.98420640  long  ton 
=  1.1023112  short  tons 


Troy  weights. 

i  pennyweight  (d\vt,  24  gr.)  =  1.555174  g: 
gr.,  oz.,  pd.  are  same  as  apothecary 

Apothecaries1  weights. 
gr.  =  64.798918  mg 
scruple  O,  20  gr.)  =  1.2959784  g 
dram  (3,  3  9)          =  3-8879351  g 
oz.  (5,83)  =  31.103481  g 

pd  (125,  5760  gr.)  =  373.24177  g 
g  =  15.432356  gr.      =  0.771618  3 
=  0.2572059  3       =  .03215074  5 
i  kg  =  32.150742  5     =  2.6792285  pd. 

i  metric  carat  =  200  mg  =  3.0864712  gr. 

U.  S.  \  dollar  should  weigh  12.5  g  and  the 
smaller  silver  coins  in  proportion. 


*  Taken  from  Circular  47  of  the  U.  S.  Bureau  of  Standards,  1915,  which  see  for  more  complete 
tables. 


SMITHSONIAN  TABLES. 


TABLE  5. 


EQUIVALENTS    OF    METRIC    AND   BRITISH   IMPERIAL    WEIGHTS 
AND   MEASURES.* 


(1)  METRIC    TO    IMPERIAL. 


(For  U.S.  Weights  and  Measures,  see  Table  3.) 


LINEAR   MEASURE. 

MEASURE  OF  CAPACITY. 

Im")(mln°       |=      °'°3937    -. 

1  miUer)er  (ml)  ('°01  |    =     °-°6locub-  in- 

I  centimeter  (.01  m.)      =      0.39370     " 
I  decimeter  (.1  m)          =       3-93701 

i  centiliter  (.01  liter)        =  j  ^Q^^II 

(39-370II3  " 

I  METER    (m.)       .      .      .  =  <     3.280843  ft. 

i  deciliter  (.1  liter)  .     .   =     0.176  pint, 
i  LITER  (1,000  cub.    ) 

(    1.09361425  yds. 

centimeters  or  I    >    =     1.75980  pints. 

i  dekameter       \              01614.           " 

cub.  decimeter)       ) 

(10  m.)          }' 

i  dekaliter  (10  liters)     .   =     2.200  gallons. 

h<iSo3r  }•  •  -109.361425  » 

i  hectoliter  (TOO  "   )     .   =     2.75  bushels. 
i  kiloliter  (1,000  "    )     .   =     3.437  quarters. 

:r  >     >  .     .     .=      0.62117  mile. 
(  1,000  m.)     ) 

m(i£ooom.)  J-     '     '=      6-21  37  2  miles. 

APOTHECARIES'   MEASURE. 

i  micron               .     .     .  —      o  ooi  mm. 

i    cubic    centi-  )       C    0.03520  fluid  ounce. 

meter     (I(==S    0.28157  fluid  drachm. 

gram  vv't)       )       (  15.43236  grains  weight. 

i  cub.  millimeter  =  0.01693  minim. 

SQUARE   MEASURE. 

AVOIRDUPOIS   WEIGHT. 

i  sq.  centimeter  .     .     .  =      0.1550  sq.  in. 

i  milligram  (mgr.)    .     .   =  0.01543  grain. 

(100  sq.  centm  )      (  =      I5-5°°  scl-  in< 

i  centigram  (.01  gram.)    =  0.15432 

i  sq.  meter  or  centi-  f  j  10.7639  sq.  ft. 

i  decigram  (.1         "      )   =  1.54324  grains. 

I  GRAM                                         —  I  ^  4^36        " 

eirc  (TOO  so.  dcrn.J  )        /     1.1900  scj.  yds, 
I  ARE  (100  sq.  m.)          =  119.60  sq.  yds. 
i  hectare  (100  ares      1  _ 
or  10,000  sq.  m.)     J  = 

i  dekagram  (10  gram.)    =  5.64383  drams. 
i  hectogram    (100  "     )  =  3-52739  oz. 
C  2.2046223  lb 

I   KILOGRAM  (  I,  OOO"      )    =•?  I  5432.3564 

(          grains. 

i  myriagram  (10  kilog.)    =22.04622  Ibs. 

i  quintal         (TOO    "     )    =  1.96841  cwt. 

i  millier  or  tonne  1           Rot- 

CUBIC   MEASURE. 

(1,000  kilog.)    p 

i  cub.  centimeter          ) 

(c.c.)  (1,000  cubic  >  =    0.0610  cub.  in. 

TROY   WEIGHT. 

millimeters)             ) 

i  cub.  decimeter            ) 
(c.d.)  (1,000  cubic  >  =  61.024       "       " 
centimeters)             ) 

(    0.03215  oz.  Troy. 
I  GRAM      .     .     =  ]    0.64301  pennyweight. 
/  1  5.43236  grains. 

i  CUB.  ME'rER  )               f  35-3148  cub.  ft. 

(1,000  c.d.)  Y            \    1.307954  cub.  yds. 

APOTHECARIES'    WEIGHT. 

(    0.25721  clr?chm. 

i  GRAM      ....=]    0.77162  scruple. 

(  15.43236  grains. 

NOTE.— Tlie  METER  is  the  length,  at  the   temperature  of  o°  C.,  of  the   platinum-iridium   bar  deposited  at  the 
International  Bureau  of  Weights  and  Measures  at  Sevres,  near  Paris,  France. 

The  present  leeal  equivalent  of  the  meter  is  39.370113  inches,  as  above  stated. 

The  KILOGRAM  is  the  mass  of  a  platinum-iridium  weight  deposited  at  the  same  place. 

The  LITER  contains  one  kilogram  weight  of  distilled  water  at  its  maximum  density  (4°  C.),  the  barometer  bein£ 
at  760  millimeters. 

*In  accordance  with  the  schedule  adopted  under  the  Weights  and  Measures  (metric  system)  Act,  1897. 
SMITHSONIAN   TABLES. 


TABLES. 

EQUIVALENTS    OF  METRIC  AND   BRITISH   IMPERIAL  WEIGHTS 
AND  MEASURES. 


(2)     METRIC  TO   IMPERIAL. 


(For  U.S.  Weights  and  Measures,  see  Table  3.) 


LINEAR   MEASURE. 

MEASURE  OF   CAPACITY. 

Millimeters 
to 
inches. 

Meters 
to 
feet. 

Meters 
to 
yards. 

Kilo- 
meters to 
miles. 

I 

2 

3 

4 
5 

Liters 
to 
pints 

Dekaliters 
to 
gallons 

Hectoliters 
to 
busuels. 

Kiloliters 
to 
quarters. 

I 

2 

3 
4 

5 

0.03937011 
0.07874023 
o.i  1811034 
o.i  574804  s 
0.19685056 

3.28084 
6.56169 
9-84253 
I  3-  I  2337 
16.40421 

1.09361 

2.18723 
3.28084 
4-37446 
5.46807 

0.62137 
1.24274 
1.86412 
2.48549  i 
3.1o686i 

1.75980 
3-5I96' 
5-2794I 
7.03921 
8.79902 

2.19975 

4-39951 
6.59926 
8.79902 
10.99877 

2-74969 
549938 
8.24908 
10.99877 
13.74846 

3.43712 

6.87423 

io-3'  135 
13.74846 
17-18558 

6 

I 

9 

0.23622068 

0.27559079 
031496090 

0-35433  '  °2 

19.68506 
22.96590 
26.24674 
29-52758 

6.56169 

7-65530 
8.74891 

9-84253 

3.72823 
4.34960 
4.97097 
5-59235 

6 

8 
9 

10.55882 
12.31862 
14.07842 
15.83823 

13.19852 
15.39828 

17-59803 
19.79778 

16.49815 
19.24785 
21.99754 
24-74723 

20.62269 
24.05981 
27.49692 
30.93404 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
centimeters 
to  square 

inches. 

Square 
meters  to 
square 
feet. 

Square 
meters  to 
square 
yards. 

Hectares 
to  acres. 

Milli- 
grams 
to 
grains. 

Kilograms 
to  grains. 

Kilo- 
grams 
to 
pounds. 

Quintals 
to 
hundred- 
weights. 

I 

2 

3 

4 
5 

0.15500 
0.31000 
0.46500 
O.62OOO 
0.77500 

10.76393 
21.52786 
32.29179 
43-05572 
53-8I965 

1.19599 
2.39198 
3.58798 
478397 
5-97996 

2.4711 
49421 
74132 
9.8842 

1  2-3553 

I 

3 
4 

5 

0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

1  5432.356 
30864.713 
46297.069 
61729.426 
77161.782 

2.20462 
4.40924 
6.61387 
8.81849 
11.0231  I 

1.96841 
3.93683 
5-90524 
7-87365 
9.84206 

6 

8 

9 

0.93000 
1.08500 
I.240OO 
I-3950I 

64.58357 
75-34750 

86  11143 
96.87536 

7-17595 
8.37194 

9-56794 
10.76393 

14.8263 
17.2974 
19.7685 
22.2395 

6 
9 

0.09259 
0.10803 
0.12346 
0.13889 

92594.138 
108026.495 
123458.851 
138891.208 

13.22773 
I5-43236 
17.63698 
19.84160 

11.81048 
I3.77889 
I5-74730 
17.71572 

CUBIC   MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(font.) 

TROY  WEIGHT. 

APOTHE- 
CARIES' 
WEIGHT. 

T 

2 

3 

4 

5 

Cubic 
decimeters 
to  cubic 
inches. 

Cubic             Cubic 
meters  to       meters  to 
cubic               cubic 
feet.                yards. 

Cub.  cen- 
timeters 
to  fluid 
drachms. 

Milliers  or 
tonnes  to 
tons. 

Grams 
to  ounces 
Troy, 

Grams 
to  penny- 
weights. 

Grams 
to 
scruples. 

61.02390 
122.04781 
183.07171 
244.09561 

3°5-II952 

35-3J476 
70.62952 
105.94428 
141.25904 
176.57379 

I-30795 
2.61591 
3.92386 
5.23182 

6-53977 

0.28157 
0.56314 
0.8447  ' 
1.12627 
1.40784 

I 

3 

4 

5 

0.98421 
1.96841 
2.95262 

3-93683 
4.92103 

0.03215 
0.06430 
0.09645 
0.  1  2860 
0.16075 

0.64301 
1.28603 
1.92904 
2.57206 
3.21507 

0.77162 
1.54324 
2-31485 
3.08647 
3.85809 

6 

8 
9 

366.14342 
427.16732 
488.19123 
549-2  T5T  3 

211.88855 
247-20331 
282.51807 
317-83283 

7.84772 
9.15568 
10.46363 
11.77159 

1.68941 
1.97098 

2-25255 
2.53412 

6 

7 
8 

9 

5-90524 
6.88944 

7-87365 
8.85786 

0.19290 
0.22506 
0.25721 
0.28936 

3.85809 
4.5OIIO 
5.I44I2 

5-787I3 

4.62971 
5.40132 
6.17294 
6.94456 

SMITHSONIAN  TABLES. 


IO  TABLE  5. 

EQUIVALENTS  OF  BRITISH    IMPERIAL  AND    METRIC  WEIGHTS 
AND   MEASURES. 


(3)     IMPERIAL   TO    METRIC. 


(For  U.S.  Weights  and  Measures,  see  Table  3.) 


LINEAR  MEASURE. 

MEASURE   OF  CAPACITY. 

(  2  5.400  milli- 
i  inch                          —  i         o«-  or  - 

gill    =  1.42  deciliters. 

{      meters, 
i  foot  (12  in.)     .     .  =       0.30480  meter. 

pint  (4  gills)  .     .     .  =  0.568  liter, 
quart  (2  pints)    .     .  =  1.136     liters. 

I  YARD  (3  ft.)       .      .=          0.9M399      ' 

GALLON  (4  quarts)  ==  4.5459631  " 

i  pole  (5^  yd.)    .     .=        5.0292  meters. 

peck  (  2  galls.)    .     .  =  9.092          " 

i  chain  (22yd.  or  )   _       2O.n68       " 
100  links)         \ 

bushel  (8  galls.)      .  =  3.637  dekaliters, 
quarter  (8  bushels)  =  2.909  hectoliters. 

i  furlong  (220  yd.)  =    201.168 

(     1.6093  kilo- 

i  mile  (1,760  yd.)    -  —  {      meters. 

AVOIRDUPOIS    WEIGHT. 

SQUARE   MEASURE. 

r  grain  .                    -  \  64'8  minU 

6.4516  sq.  cen- 
i  square  inch      .     .     =   =             timeters. 

|      grams. 
Tram   =        1.772  grams. 

(    0.2903  sq.  deci- 

ounce  (16  dr.)  .     .=      28.350 

i  sq.ft.  (144  sq.  in.)    =  =    {        meters. 
{    o  836  1  °6  sq. 

.•oL'M>(.6ozor>             0.45359243  kilogr. 
7,000  grams)      ) 

i  SQ.  YARD  (9  sq.  ft.)  ==    i        meters. 

stone  (  14  Ib.)    .     .  =        6.350 

(    2;.  293   sq.   me- 
i  perch  (3oi  sq.  yd.)  =  j      ^ 

quarter  (28  Ib.)     .  =       12.70 
hundredweight  1        _    \  50.80 

i  rood  (40  perches)     ==       10.117  ares. 
i   i  ACRE  (4840  sq.  yd.)  =         0.40468  hectare. 

i  sq.  mile  (640  acres)  =  |  259.00  hectares. 

(H2lb.)           J        =    j    0.5080  quintal. 
(  1.0160   tonnes 
<    or  10  [6  k'lo- 
i  ton  (aocwt.)  .  ==   I    grams> 

TROY    WEIGHT. 

CUBIC   MEASURE. 

I  cub.  inch  =    16.387  cub.  centimeters. 

i  Troy  OUNCE  (480  J    -31.1035  grams, 
grains  avoir.)      f 

i  cub.  foot  (1728  1        (0.028317  cub  me- 
cub.  in.)             f-          ter,    or     28.317 
(      cub.  decimeters. 

I  i  ptnnvweight  (24  /                            « 

grains)                  ]    ~ 

i  CUB.  YARD  (27  1.^0.76455  cub.  meter, 
cub.  ft.)             J 

NOTE.  —  The  Troy  grain  is  of  the  same  weight  as 
the  Avoirdupois  grain. 

APOTHECARIES'   MEASURE. 

APOTHECARIES'   WEIGHT. 

i  gallon  (8  pints  or  I  _       4.5459631  liters. 
1  60  fluid  ounces)  J 
i  fluid  ounce,  f  3  )           f  28.4123  cubic 
(8  drachms)        f           (      centimeters. 

i  ounce  (8  drachms)    =31.1035  grams, 
i  drachm,  3  i  (  3  scru-  (  _        ggg         « 
pies)                       i 

i   fluid  drachm,  f  3  )              3-55r5  cubic 
(60  minims)          (  ™         centimeters, 
i  minim,  m  (0.91  146  (             0.05919  cubic 

i    scruple     91    (20  I     =           g         « 
grains)                 ) 

tin  weight)       \  —         centimeters. 

NOTE.  —  The  Apothecaries'  ounce  is  of  the  same 
weight  as  the  Troy  ounce.      The    Apothecaries' 

—  The    Apothecaries'  gallon    is  of  the  same 

grain  is  also  of  the  same  weight  as  the  Avoirdupois 

capacity  as  the  Imperial  gallon. 

grain. 

NOTE.  — The  YARD  is  the  length  at  62°  Fahr.,  marked  on  a  bronze  bar  deposited  with  the  Board  of  Trade. 

The  POUND  is  the  weight  of  a  piece  of  platinum  weighed  in  vacuo  at  the  temperature  of  o°  C.,  and  which  is  also 
deposited  with  the  Board  of  Trade. 

The  GALLON  contains  10  Ib.  weight  of  distilled  water  at  the  temperature  of  62°  Fahr.,  the  barometer  being  at 
30  inches. 
SMITHSONIAN  TABLES. 


(4) 


TABLE   5- 

EQUIVALENTS  OF   BRITISH  IMPERIAL   AND    METRIC  WEIGHTS 
AND   MEASURES. 

IMPERIAL  TO   METRIC. 


1  I 


(For  U.S.  Weights  and  Measures,  see  Table  3.) 


1- 

LINEAR   MEASURE. 

MEASURE   OF   CAPACITY. 

Inches 
to 
centimeters. 

Feet 
to 
meters. 

Yards 
to 
meiers. 

Miles 
to  kilo- 
meters. 

Quarts 
to 

liters. 

Gallons 
to 
liters. 

Bushels 
to 
dekaliters. 

Quarters 
to 
hectoliters. 

4 
5 

2-539998 
5.079996 
7.619993 

10.159991 
12.699989 

0.30480 
0.60960 
0.91440 
1.21920 
1.52400 

0.91440 
1.82880 
2.74320 
3.65760 
4.57200 

1.60934 
3.21869 
4.82803 

6-43737 
8.04671 

I 
2 

3 
4 

5 

1.13649 
2.27298 
3-40947 

^ 

4-54596 
9.09193 

I3-63789 

18.18385 
22.72982 

3-63677 
7-27354 
10.91031 
14.54708 
18.18385 

2.90942 

5.81883 
8.72825 
11.63767 
14.54708 

6 

8 
9 

15.239987 
17.7/9984 
20.319982 
22.859980 

1.82880 
2.13360 
2.43840 
2.74320 

5.48640 
6.40080 

7-31519 
8.22959 

9.65606 
11.26540 
12.87474 
1  4.48408 

6 

8 
9 

6.81894 

7-95544 
9.09193 
10.22842 

27.27578 
31.82174 
36.36770 
40.91367 

21  82062 

2545739 
29.09416 

32-73093 

17.45650 
20.36591 

23-27533 
26.18475 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
inches 
to  square 
centimeters. 

Square 
feet 
to  square 
decimeters. 

Square 
yards  to 
square 
meters. 

Acres  to 
hectares. 

Grains 
to  milli- 
grams. 

Ounces  to 
grams. 

Pounds 
to  kilo- 
grams. 

Hundred- 
weights  to 
quintals. 

I 

2 

3 
4 
5 

6-45  1  59 
12.90318 

J9-35477 
25.80636 

32.25794 

9.29029 

18.58058 
27.87086 
37.16115 
46.45144 

0.83613 

1.67225 
2.50838 

3-3445° 
4.18063 

0.40468 
0.80937 
1.21405 
1.61874 
2.02342  . 

2 

3 
4 
5 

64.79892 
129.59784 
'94-39675 
259-  I  9567 
323-99459 

28.34953 
56.69905 
85.04858 
113.39811 
141.74763 

0-45359 
0.90718 
1.36078 
1.81437 
2.26796 

0.50802 
1.01605 
1.52407 
2.03209 
2.54012 

6 

7 
8 

9 

38-70953 
45.16112 
5i.6r27i 
58.06430 

55-74I73 
65.03201 
74.32230 
83.61259 

5.01676 

5.85288 
6.68901 
7-525I3 

2.42811 

2.83279 

3.23748 
3.64216 

6 

8 
9 

388.79351 
453-59243 
5!8.39135 
583.19026 

170.09716 
198.44669 
226.79621 

255-M574 

2.72155 

3.I75I5 
3.62874 
4.08233 

3.04814 
3.556'6 
4.06419 
4.57221 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 

(cont.}. 

TROY  WHKIHT     . 

APOTHE- 
CARIES' 
WEIGHT 

Cubic 

inches 
to  cubic 
centimeters. 

Cubic  feet 
to 
cubic 
meters. 

Cubic 
yards 
to  cubic 
meters. 

Fluid 

drachms 
to  cubic 
centi- 
meters. 

Tons  to 
milliets  or 
tonnes. 

Ounces  to 
grams. 

Penny- 
weights to 
grams. 

Scruples 
to 
grams. 

I 
2 

3 
4 
5 

16.38702 

32-77404 
49.16106 
65.54808 
81.93511 

0.02832 
0.05663 
0.08495 
0.11327 
0.14158 

0.76455 
1.52911 
2.29366 
3.05821 
3.82276 

3-55I53 
7.10307 
10.65460 
14.20613 
I7-75767 

I 

2 

3 
4 

5 

1.01605 
2.03209 
3.048  1  4 
4.06419 
5.08024 

31.10348 
62.20696 
93-3J044 
12441392 
I55-5I740 

I-555I7 

3*1035 
4.66552 

6.22070 
777587 

1.29598 
2.59196 
3.88794 

5-!839i 
6.47989 

6 

I 

9 

98.32213 
114.70915 
131.09617 
147.48319 

0.16990 
0.19822 
0.2265  ^ 
0.25485 

4-58732 
5-35I87 

6.1  1642 
6.88098 

21.30920 
24.86074 
28.41227 
31.96380 

6 

8 
9 

6.09628 
7-11233 
8.12838 

9.14442 

186.62088 

217.72437 
248.82785 
27  9-93  T  33 

9.33I04 
10.88622 
12.44139 
I3-99657 

7.7758/ 
9.07185 
10.36783 
u;66 

SMITHSONIAN  TABLES. 


12 


TABLE  6. 
DERIVATIVES  AND  INTEGRALS/ 


J 

7 

xn+i 

d  arc 

—  d  (IX 

/*«<& 

n+i 

d  «t> 

=  (u%+v^)dx 

fd* 

=  logx 

^ 

A*-*V 

f*<* 

\               »2         / 

e 

dxn 

=  wre71"1  dx 

feaxdx 

=-  eax 

a 

d/(w) 

-^sr^s-* 

fx  c**  dx 

=~(^-i) 

de* 

-e»<fe 

/log  x  dx 

=  x  log  x—x 

deax 

=  a  e°>*  dx 

/n.* 

=  u  v—fv  du 

d  loge  x 

x 

/(a+bx)ndx 

_(a+bx)n+l 

(n+i)b 

dx* 

=  xx  (i+logez) 

d  sin  re 

=  cos  x  dx 

f(a2+x^-l  dx 

=  -  tan-1   -  = 

a              a 

1  sin-1        * 

a            v^^_j_a2 

d  cosx 

=  -sin  x  dx 

f(a1_yZ\-\dX 

=  ^L  log  a+x 

J 

2a        a  —  x 

dtanx 

=  sec2  x  dx 

/(a2  -re2)-*  dx 

.    x                  ,  x 
=  sin"1    -,  or  —cos-1  - 

a                      a 

d  cot  x 

=  —csc2  re  dx 

/x(a2±x2)~*dx 

=  ±(<Z2±X2)* 

dsec  x 

=  tan  re  sec  re  dx 

/sin2  x  dx 

=  —  i  cos  xsin  x+5  x 

d  csc  re 

—  —cot  re  .  scs  re  dx 

/cos2  re  d# 

=  |  sin  x  cos  x+j  re 

d  sin—1  re 

=  (i—  re2)  -*  dx 

/sin  x  cos  x  dx 

=  \  sin2  x 

d  cos-1  re 

=  —  (i—  re2)"*  dx 

/(sin  x  cos  x)"1  dx  =  log  tan  x 

d  tan-1  re 

=  (i+re2)"1  dx 

/tan  x  dx 

=  —log  cos  x 

d  cot-1  re 

=  —  (i+rc2)-1^* 

/tan2  xdx 

=  tan  x—x 

J  sec—1  re 

=  re"1  (x-—  i)-*  dx 

/cot  x  dx 

=  log  sin  x 

d  csc-1  re 

=  —x"1  (x2—  1)~  *  dx 

/cot2  x  dx 

=  —  cot  x—x 

J  sinh  re 

=  cosh  x  dx 

/csc  x  dx 

=  log  tan  ^  x 

d  cosh  re 

=  sinh  x  dx 

/x  sin  x  dx 

=  sin  x—x  cos  x 

d  tanh  re 

=  sech2  x  dx 

fx  cos  x  dx 

=  cosx  +  x  sin  x 

d  coth  x 

=  —csch2  x  dx 

/tanh  xdx 

=  log  cosh  x 

d  sech  x 

=  —sech  x  tanh  dx 

/  coth  x  dx 

=  log  sinh  x 

d  csch  re 

=  —csch  x  .  coth  x  dx 

/sech  x  dx 

=  2  tan-1  cx=gd  u 

d  sinh"1  re 

=  (x2+  1)—  *  dx 

/csch  x  dx 

•=  log  tanh  ~ 

d  cosh"1  x 

=  (x2—  I)"*  dx 

fx  sinh  x  dx 

=  x  cosh  x—  sinh  x 

d  tanh-1  re 

=  (I_JC2)-l  dx 

fx  cosh  x  dx 

=  x  sinh  x—  cosh  x 

d  coth-1  x 

=    (j—^2)-!  </£ 

/sinh2  x  dx 

=  £  (sinh  xcosh  x—x) 

d  sech—1  x 

=  -x-1  (i-x2)-*  dx 

/cosh2  x  dx 

=  i  (sinh  x  cosh  x+x) 

d  csch-1  re 

=  -*-'(*<+.)-. 

/sinh  x  cosh  xdx 

=  1  cosh  (2  x) 

*  See  also  accompanying  table  of  derivatives.     For  example  :  /cos.  x  dx  —  sin.  x  +  constant. 
SMITHSONIAN  TABLES. 


TABLE  7. 
SERIES. 


=  xn  +   2.  jn-i  y  +   ^-J  *n-2  y  +  .  .  . 

»(„-!)...  (n-m+i)  ^n_w 
w ! 

(i  ±  x)»  =  i  ±  »*  4-  Mn~Ia>"  ±  rcfo-i)  (M-2).y2  +  _  _  +  (d 


(»-fcj!  kl 
3'~ 


(»- 

ip  6^5  4- 


f(x+h)  =  f  (x)+hf  (x)  +  k~  /"(*)+...+  ^  /<«>  (*)  +  •  •  •  rayl°series. 

/  /   \        /  /  \   ,    x  f  i  \    ,    x2  *» ,  -  ^n  r  ,n\  Maclaurin's 

/  (x)  =f(o)+  -  )'  (o)  +  -  /"  (o)  +  ...—/  («)  (0)  +  .  .  .  series> 


/        i\  i          i          i          i 

=  hm(  i+-)w=i+  -  -  -f-  -  -  +  --  4  --  .  +... 
V        ;//  i!        2!        3!        4i  T 


=  i  +  x  +  -,  H  --  1  H  --  1  -f-  •  .  . 


ax  =  l+x  ]0ga+  v-  -^  + 


3! 
.r  —  i     ,     i    /x  —  i \ "        i   /x  —  i\3 

i°**=~  +  -2(—)  +-i(v;  +•• 

=  O  -  0  -  M*  -  O2  +  H*  -  O3  -  •  •  • 


l°g  (T  +  *)   =  X  —  $  X2  4-  i  A;3  —  j  .T4  +  .  .  .  . 

•          ==     l     f.ix         .-ix\  —  X*          *5          *7 

~  ~^i(t  ~  3!  +  ?  ~  T"!  4 

cos  .r  =  -  (e'-r  4-  g-»>)  =  i-   —  H 1  —  —   +...  =  i_  versin  .v 


7T  T^                 T             "7           >v5              T             *?             C            A"7 

.    .  i  i  i      '        ^5       **'  v5       0       *^ 

~2"  6         2*4"5"  +  2*4*6'7 

tan~ !  x  =  -   —  cot.—1  #  =  a: #3  H .r5  —  -  a-7  4-  ... 

7T  I                   I                     I 


i   ,  x3        *5         Jc7 

smh  s  =  ~(e*-  e-*)  =x+   -  +  -  +  -,+... 


SMITHSONIAN   TABLES. 


TABLE  7   (continued). 

SERIES. 


I    ,                                               X*           X*           X« 

cosh  x  =  -  (ex  +  «-*)  =  i  H  ,  H  :  +  zi  +  •  •  • 

2  v                                 2!        4!        6! 

,,'<00) 

i              2               17      7 

U2<io 

^^,-.-i£  +  i.  *'.£-!.  a.  I.?*'... 

(*»<!) 

23    245    2467 

-  ^g  2*  +    1   ^   -    ^   ^  +    \   \  I     ~   -  .  .  , 

(,2>I) 

ii          131          i    3  5    i 

COSh-!  x  =  log  2X  _    -   ^   ._    _    .    __     ...    -  -   -   ^   .... 

(*2>I) 

tanh-1  A;  =  x  +  -  .v3  +  -  .v5  +  -  x1  +  •  •  . 

(A'2<I) 

3            5            7 

i              i             61 

cd  A:  =  0  =  x  —  7  *3  H  -v5  —      -~  a;7  +  .  •  • 
6            24           5040  . 

(.v  small) 

IT                           i   sech3.v         i   3  sech  5.v 

2                            23             245 

(.i  large) 

_     d_,  0  _    .    .     i      3         i       5          6l     AT  4. 

r  6  0         24  0         5040 

(•<0 

/"(*)=-  b0  +  b,  cos    f-  b2  cos    -    -  +  .  .  . 

2                                     C                                C 

7T  V                             2  TTX 

+  di  sin  1-  ao  cos  -    -  4- 

.  .  <-<:<.v 

r                        c 

TABLE    8.-  MATHEMATICAL  CONSTANTS, 


e  =  2.71828 

18285 

7T    = 

Numbers. 
3.14159    26536 

Logarithms, 

0.49714   98727 

e-i  =  0.36787 

94412 

7T2    = 

9.86960 

44011 

0.99429 

97454 

M  =  logio'r  =  0.43429 

44819 

I 

7T 

0.31830 

98862 

9.50285 

01273 

(M)~l  =  log,  10  =  2.30258 

50930 

Y/ir  - 

1.77245 

38509 

0.24857 

49363 

logio  logios  =  9-63778 

43113 

2 

0.88622 

69255 

9-94754 

49407 

log]02   =  O.3OIO2 

99957 

I 

0.56418 

95835 

9.75142 

50637 

Ioge2  =  0.69314 

71806 

2 

1.12837 

91671 

0.05245 

5°  593 

logiox  =  M.logea* 

\i= 

1-2533' 

41373 

0.09805 

99385 

\ogRX  =  loge.r.  lo 

gje 

V^= 

0.79788 

45608 

9.90194 

006  1  5 

=  loge#  -j- 

log£B 

7T 

4_ 

0.78539 

81634 

9.89508 

98814 

loge  TT  =  i.i  147- 

98858 

4 

0.44311 

34627 

9.64651 

4945° 

p  =--  0.47693 

62762 

ITT   = 

4.18879 

02048 

0.62208 

86093 

logp  =  9.67846 

03565 

e 

V  2  7T 

1.08443 

755H 

0.03520 

45477 

1 

SMITHSONIAN  TABLES. 


TABLES.  15 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  SQUARE  ROOTS,  OF 

NATURAL   NUMBERS. 


n 

loco.* 

«2 

//«    V" 

n 

1000.^ 

„* 

*» 

i* 

10 

ii 

[00.000 

90.9091 

100 
121 

1000   3.1623 
'331   3-3'66 

65 

66 

15.3846  4225 
15.1515  4356 

274625 
287496 

8.0623 
8.1240 

12 

J3 

83-3333 
76.9231 

144 
169 

1728   3.4641 
2197   3-6056 

67 
68 

14.9254 

14.7059 

4489 
4624 

300763 

3  l  4432 

8.1854 
8.2462 

14 

71.4286 

I96 

2744   3-74I7 

69 

14.4928 

476l 

328509 

8.3066 

15 

66.6667 

225 

3375  i  3-8730 

70 

14.2857   4900 

343000 

8.3666 

16 
17 

62.5000 

58.8235 

256 
289 

4096   4.0000 

4913  :  4.1231 

7i 

72 

14.0845 
13.8889 

5041 
5^4 

3579" 
373248 

8.4261 
8.4853 

18 

55^556 

324 

5832  4.2426 

73   13.6986   5329 

389017 

8.5440 

19 

52-6316 

361 

6859   ;    4-3589 

74   i3-5!35   5476 

405224 

8.6023 

20 

50.0000 

4OO 

8000   i    4.472I 

75   13-3333   5625  !  421875 

8.6603 

21     47.6190    441 

926l       4.5826 

76   13.1579   5776   438976    8.7178 

22    45-4545   4^4 

10648       4.6904 

77   12.9870   5929  i  456533    8.7750 

23    43-4783   529 
24    41.6667   576 

I2I67       47958 
13824       4.8990 

78   12.8205   6084 
79   12.6582   6241 

474552    8.8318 
493039    8.8882 

25    40.0000 

625 

15625       5-0000 

80   12.5000   6400 

512000    8.9443 

26    38.4615 

676 

17576       5.0990 

81 

12.3457  6561 

531441    9.0000 

27    37-0370   729 

19683       5.1962 

82 

12.1951   6724 

551368    9.0554 

28    35.7  i  43  1  784 
29    344828   841 

21952       5.29I5 
24389       5-3852 

83 
84 

12.0482   6889 
11.9048   7056 

571787 
592704 

9.  1  1  04 
9.1652 

30    33-3333   9°° 

27000       54772  I 

85 

11.7647   7225 

614125 

9.2195 

31    32-2581  i  96i 

29791       5-5678 

86 

11.6279  7396 

636056 

9.2736 

32    31.2500  1024 

32768  !   5.6569  I 

87 

11.4943  7569 

658503 

9-3274 

33    3°-303°  Io89 

35937  i  5-7446 

88 

11.3636   7744 

681472 

9.3808 

34    29.4118   1156 

393°4  i  5-83  10 

89 

11.2360 

7921 

704969 

9.4340 

35    28.5714   1225 

42875   5.9161 

90 

ii.ini   8100 

729000 

9.4868 

36    27.7778  ;  1296 

46656   6.0000 

9i 

10.9890 

8281  ' 

753571 

9-5394 

37    27.0270  1369 

50653   6.0828 

92 

10.8696 

8464 

778688 

9-59*7 

38 

26.3158   1444 

54872   6.1644 

93 

10.7527 

8649 

804357 

9-6437 

39    25.6410  1521 

59319   6.2450 

94 

10.6383 

8836 

830584 

9-6954 

40 

25.0000  1600 

64000 

6.3246  ' 

95 

10.5263 

9025 

857375 

9.7468 

4i 

24.3902  ;  1  68  1 

68921 

6.4031 

96 

10.4167 

92l6 

884736 

9.7980 

42 

23.8095 

1764 

74088 

6.4807 

97 

10.3093 

9409 

912673 

9.8489 

43 

23-2558 

1849 

795°7 

6.5574  ; 

98 

10.2041 

9604 

941192 

9.8995 

44 

22.7273 

1936 

85184 

6.6332  ! 

99   10.1010 

9801    970299 

9-9499 

45      22.2222 

2025 

91125 

6.7082 

100  1  r  o.oooo 

I  0000   I  000000 

10.0000 

46    21.7391   2116 

97336 

6.7823  i 

IOF   9.90099   io2or   1030301 

10.0499 

47    2  [.2766  2209 

103823 

6-8557  ! 

102   9.80392   10404   1061208 

10.0995 

48   20.8333  ;  2304 

110592 

6.9282 

103   9.70874   10609   1092727 

10.1489 

49    20.4082  2401 

117649 

7.0000 

104   9-61538   10816  i  1124864 

10.1980 

50 

51 

20.0000 

19.6078 

2500 
2601 

125000 
132651 

7.0711 

7-I4I4  ! 

105   9.52381 
1  06   9-43396 

11025  1157625 
11236  1  191016 

10.2470 
10.2956 

52 

19.2308  2704 

140608   7.2111 

107   9-34579 

11449  i  !  225043 

10.3441 

53 

18.8679  2809 

148877   7.2801 

108   9.25926 

11664   l  2597  I  2 

10.3923 

54 

18.5185 

2916 

157464  1  7-3485 

109   9.1743" 

Il88l 

1295029 

10.4403 

55 

18.1818  3025 

166375   7.4162  ! 

110   :  9.09091 

I2IOO 

1331000 

10.4881 

56 

17-8571  j  3'36 

175616 

7-4833  ! 

III     g.OOOX)! 

I232I   1367631 

•0-5357 

% 

17-5439  !  3249 
17.2414  i  3364 

185193 
195112 

7-5498 
7.6158 

112 

"3 

8.92857 
8.84956 

12544   1404928 
12769  i  1442897 

10.5830 
10.6301 

59 

16.9492 

348i 

205379 

7.6811 

114 

8.77193 

12996   I48I544 

10.6771 

60 

61 

16.6667 
16.3934 

3600 
3721 

216000 
226981 

7.7460 
7.8102 

115   8.69565  13225 
116   8.62069  13456 

1520875 
1560896 

10.7238 
10.7703 

62 

16.1290 

3844 

238328 

7.8740 

117 

8.54701 

13689 

1601613 

10.8167 

63 
64 

i5-8730 
15.6250 

3969 
4096 

250047 
262144 

7-9373 
8.0000 

118 
119 

8.47458 
8.40336 

13924 
I4l6l 

1643032 
1685159 

10.8628 
10.9087 

SMITHSONIAN   TABLES. 


I  6  TABLE  9   (continued). 

VALUES   OF   RECIPROCALS,   SQUARES,   CUBES,   SQUARE    ROOTS, 
OF    NATURAL    NUMBERS. 


H 

1000.^ 

* 

„. 

V- 

n 

1  000.1 

* 

«3 

V" 

120 

121 

8.33333 

8.26446 

14400 
14641 

I728OOO 
1/71561 

'0.9545 
1  1  .0000 

175 

176 

5.71429 
5.68182 

30625 
30976 

5359375 
545'776 

13.2288 
13.2665 

122 

8.19672 

14884 

1815848 

11.0454 

177 

5.64972 

3'329 

5545233 

'3-3041 

I23 

8.13008 

15129 

1860867 

11.0905 

178 

5.61798 

31684 

5639752 

'  3-34  '7 

124 

8.06452 

'5376 

1  906624 

179 

5.58659 

32041 

5735339 

'3-379' 

125 

8.00000 

15625 

'953^5 

11.1803 

180 

5-55556 

32400 

5832000 

13.4164 

126 

7.93651 

15876 

2OOO376 

1  1.2250 

181 

5-52486 

32761 

5929741 

'3-4536 

127 

7.87402 

16129 

2048383 

11.2694 

182 

5-4945' 

33  124 

6028568 

13.4907 

128 
129 

7.81250 
7-75I94 

16384 
16641 

2146689 

'1-3578 

183 
184 

5.46448 
5-43478 

33489 
33856 

6128487 
6229504 

I3-5277 
13-5647 

130 

7.69231 

16900 

2197000 

11.4018 

185 

5-40541 

34225 

633  '62  5 

13.6015 

131 

7-63359 

17161 

2248091 

n-4455 

1  86 

5-37634 

34596 

6434856 

13.6382 

132 

7-57576 
7.51880 

17424 
17689 

2299968 
2352637 

1  1.4891 
11.5326 

187 
1  88 

5-34759 

34969 
35344 

6539203 
6644672 

13.6748 

134 

7.46269 

'7956 

2406104 

II-5758 

189 

5.29101 

35721 

6751269 

'3-7477 

135 

136 
137 

7.40741 

7-35294 
7.29927 

18225 
18496 
18769 

2460375 
25'5456 
2571353 

11.6190 
11.6619 
11.7047 

190 

191 
192 

5.26316 

5-23560 
5-20833 

36100 
36481 
36864 

6859000 
6967871 
7077888 

13.7840 
13.8203 
13-8564 

138 

7.24638 

19044 

2628072 

11  -7473 

!93 

37249 

7189057 

13.8924 

139 

7.19424 

19321 

2685619 

11.7898 

194 

5^5464 

37636 

73OI384 

13.9284 

140 

7.14286 

19600 

2744000 

11.8322 

195 

5.12821 

38025 

74M875 

13.9642 

141 

7.09220 

19881 

2803221 

11.8743 

196 

5.10204 

38416 

7529536 

14.0000 

142 

7.04225 

20164 

2863288 

11.9164 

197 

5.07614 

38809 

7645373 

14-0357 

143 

6.99301 

20449 

2924207 

"•9583 

198 

5-0505' 

39204 

7762392 

14.0712 

144 

6.94444 

20736 

2985984 

I  2.OOOO 

199 

5-02513 

39601 

7880599 

14.1067 

145 

6.89655 

21025 

3048625 

I2.O4I6 

200 

500000 

40000 

8000000 

14.1421 

146 

6.84932 

21316 

3112136 

I  2.0830 

20  1 

4.97512 

40401 

8120601 

14.1774 

147 

6.80272 

21609 

3'76523 

12.1244 

202 

4.95050 

40804 

8242408 

14.2127 

148 
149 

6.75676 
6.71141 

21904 

22201 

3241792 
3307949 

12.1655 
I2.2O66 

203 
204 

4.9261  1 
4.90196 

41209 
41616 

8365427 
8489664 

14.2478 
14.2829 

150 

6.66667 

22500 

3375000 

12.2474 

205 

4.87805 

42025 

8615125 

14.3178 

'5i 

6.62252 

22801 

344295' 

12.2882 

206 

4.85437 

42436 

8741816 

14-3527 

1S2 

6.57895 

23104 

3511808 

12.3288 

207 

4.83092 

42849 

8869743 

'4-3875 

'53 

6-53595 

23409 

358  '577 

12.3693 

208 

4.80769 

43264 

8998912 

14.4222 

"54 

6-4935' 

23716 

3652264 

12.4097 

209 

4.78469 

43681 

9129329 

14.4568 

155 

6.45161 

24025 

3723875 

12.4499 

210 

4.76190 

44100 

9261000 

14.4914 

156 

6.41026 

24336 

3796416 

12.4900 

21  I 

4-73934 

44521 

939393' 

14-5258 

157 

6-36943 

24649 

3869893 

12.5300 

212 

4.71698 

44944 

9528128 

14.5602 

158 

6.32911 

24964 

39443  I2 

I2.5698 

213 

4.69484 

45369 

9663597 

14-5945  ' 

159 

6.28931 

25281 

4019679 

12.6095 

2I4 

4.67290 

45796 

9800344 

14.6287 

160 

6.25000 

25600 

4096000 

12.6491 

215 

4.65116 

46225 

9938375 

14.6629 

161 

6.21118 

25921 

4173281 

12.6886 

216 

4.62963 

46656 

10077696 

14.6969 

162 

6.17284 

26244 

4251528 

12.7279 

217 

4.60829 

47089 

10218313 

14.7309 

163 

6.13497 

26569 

4330747 

12.7671 

218 

4.58716 

47524 

10360232 

14.7648 

164 

6.09756 

26896 

4410944 

1  2.8062 

219 

4.56621 

4796i 

'0503459 

14.7986 

165 

6.06061 

27225 

4492125 

12.8452 

220 

4-54545 

48400 

10648000 

14.8324 

166 

6.02410 

27556 

4574296 

12.8841 

221 

4-52489 

48841 

10793861 

14.8661 

167 

5.98802 

27889 

4657463 

12.9228 

222 

4.50450 

49284 

10941048 

14.8997 

168 

5-95238 

28224 

4741632 

12.9615 

223 

4.48430 

49729 

11089567 

'4-9332 

169 

5.91716 

28561 

4826809 

13.0000 

224 

4.46429 

50176 

11239424 

14.9666 

170 

5.88235 

28900 

4913000 

13.0384 

225 

4-44444 

50625 

11390625 

1  5.0000 

171 

5-84795 

29241 

50002  i  i 

13.0767 

226 

4  42478 

51076 

i  1543176 

'5-0333 

172 

5.81395 

29584 

5088448 

13.1149 

227 

4.40529 

51529 

i  1697083 

1  5.0665 

173 

5-78035 

29929 

5'777'7 

I3-'529 

228 

4.38596 

SI984 

i  1852352 

15.0997 

174 

5-747I3 

30276 

5268024 

13.1909 

229 

4.36681 

52441 

12008989 

'5-'327 

SMITHSONIAN  TABLES. 


TABLE  9  (.continued).  I  7 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE   ROOTS,  OF 

NATURAL    NUMBERS. 


n 

lOOO.jj 

«* 

«3 

v« 

n 

Iooai 

n* 

«3 

V* 

230 

231 

4-34783 
4.32900 

52900 
5336i 

I2I67000 
12326391 

15.1658 
15.1987 

285 

286 

3-50877 
3-49650 

81225 
81796 

23149125 
23393656 

16.8819 

16.9115 

232 

4-3I034 

53824 

12487168 

I5-23I5 

287 

3-48432 

82369 

23639903 

16.9411 

233 

4.29185 

54289 

12649337 

1  5.2643 

288 

3.47222 

82944 

23887872 

16.9706 

234 

4-2735° 

54756 

12812904 

15.2971 

289 

3.46021 

83521 

24U7569 

17.0000 

235 

4-25532 

55225 

12977875 

1  5-3297 

290 

3.44828 

84100 

24389000 

17.0294 

236 

4.23729 

55696 

I3I442S6 

1  5-3623 

291 

3  43643 

84681 

24642171 

17.0587 

237 

4.21941 

56169 

13312053 

15.3948 

292 

3.42466 

85264 

24897088 

17.0880 

238 

4.20168 

56644 

13481272 

15.4272 

293 

3-41297 

85849 

25153757 

17.1172 

239 

4.18410 

57121 

13651919 

I5-4596 

294 

3.40136 

86436 

25412184 

17.1464 

240 

416667 

576oo 

13824000 

I5-49I9 

295 

3.38983 

87025 

25672375 

17.1756 

241 

4.14938 

58081 

1  3997  52  i 

15.5242 

296 

3.37838 

87616 

25934336 

17.2047 

242 

4-13223 

58564 

14172488 

'5-5563 

297 

3.36700 

88209 

26198073 

17.2337 

243 

4-11523 

59049 

14348907 

15-58^5 

298 

3-35570 

88804 

26463592 

17.2627 

244 

4.09836 

59536 

14526784  . 

15.6205 

299 

3-34448 

89401 

26730899 

17.2916 

245 

4.08163 

60025 

14706125 

1  5-6525 

300 

3-33333 

90000 

27000000 

17.3205 

246 

4.06504 

60516 

14886936 

15.6844 

3°r 

3.32226 

90601 

27270901 

17.3494 

247 

4.04858 

61009 

i  5069223 

15.7162 

302 

3.31126 

91204 

275436o8 

17-3781 

248 

4.03226 

61504 

15252992 

15.7480 

3°3 

3-30033 

91809 

27818127 

17.4069 

249 

4.01606 

62001 

15438249 

15-7797 

3°4 

3.28947 

92416 

28094464 

17-4356 

250 

25r 
252 

4.00000 
3.98406 
3.96825 

62500 
63001 
63504 

15625000 
15813251 
16003008 

15.8114 
15.8430 

15-8745 

305 

306 
3°7 

3.27869 
3.26797 
3-25733 

93025 
93636 
94249 

28372625 
28652616 
28934443 

17.4642 
17.4929 
17.5214 

253 

3-95257 

64009 

16194277 

15.9060 

308 

3-24675 

94864 

29218112 

17-5499 

254 

3-93701 

64516 

16387064 

1  5-9374 

309 

3-23625 

95481 

29503629 

17-5784 

255 

3-92I57 

65025 

16581375 

15.9687 

310 

3-22581 

96100 

29791000 

17.6068 

256 

3.90625 

65536 

16777216 

1  6.0000 

3" 

3-21543 

96721 

30080231 

17.6352 

257 

3.89105 

66049 

16974593 

16.0312 

312 

3-20513 

97344 

30371328 

17-6635 

258 

3-87597 

66564 

I7I73512 

16.0624 

3'3 

3.19489 

97969 

30664297 

17.6918 

259 

3.86100 

67081 

17373979 

16.0935 

3'4 

3.18471 

98596 

30959144 

17.7200 

260 

3-84615 

67600 

17576000 

16.1245 

315 

3.17460 

99225 

31255875 

17.7482 

261 

3-83H2 

68121 

i777958i 

'6-1555 

3i6 

3.16456 

99856 

31  554496 

17.7764 

262 

3.81679 

68644 

17984728 

16.1864 

3*7 

3-*5457 

100489 

3l855OI3 

17.8045 

263 

3.80228 

69169 

18191447 

16.2173 

3i8 

3-  14465 

101124 

32157432 

17.8326 

264 

378788 

69696 

18399744 

16.2481 

3*9 

3.13480 

101761 

32461759 

17.8606 

265 

3-77358 

70225 

18609625 

16.2788 

320 

3.12500 

102400 

32768000 

17.8885 

266 

3-75940 

70756 

18821096 

16.3095 

321 

3-IT5  6 

103041 

33076161 

17.9165 

267 

3-74532 

71289 

19034163 

16.3401 

322 

3  I0559 

103684 

33386248 

17.9444 

268 

373'34 

71824 

19248832 

163707 

323 

3-09598 

104329 

33698267 

17.9722 

269 

3-7*747 

72361 

19465109 

16.4012 

324 

3.08642 

104976 

34012224 

18.0000 

270 

370370 

72900 

19683000 

16.4317 

325 

3.07692 

105625 

34328125 

18.0278 

271 

3.69004 

73441 

1990251  i 

16.4621 

326 

3.06748 

106276 

34645976 

18.0555 

272 

3  67647 

73984 

20123648 

16.4924 

327 

3.05810 

106929 

34965783 

18.0831 

273 

3.66300 

74529 

20346417 

16.5227 

328 

3.04878 

107584 

35287552 

18.1108 

274 

3.64964 

75076 

20570824 

16.5529 

329 

3-0395  i 

108241 

35611289 

18.1384 

275 

3.63636 

75625 

20796875 

16.5831 

330 

3.03030 

108900 

3^937000 

18.1659 

276 

3.62319 

76176 

21024576 

16.6132 

331 

3.02115 

109561 

36264601 

18.1934 

277 

3.6101  1 

76729 

21253933 

16.6433 

332 

3.01205 

110224 

36594368 

18.2209 

278 

3-59712 

77284 

21484952 

16.6733 

333 

3.00300 

110889 

36926037 

18.2483 

279 

3-58423 

77841 

21717639 

16.7033 

334 

2.99401 

"'556 

37259704 

18.2757 

280 

3-57M3 

78400 

219152000 

16.7132 

335 

2.98507 

112225 

37595375 

18.3030 

281 

3-55872 

78961 

22188041 

16.7631 

336 

2.97619 

i  i  2896 

37933056 

18.3303 

282 

3.54610 

79524 

22425768 

16.7929 

337 

2.96736 

"3569 

38272753 

,8.3576 

283 

3-53357 

80089 

22665187 

16.8226 

338 

2.95858 

114244 

38614472 

18.3848 

284 

3.52H3 

80656 

22906304 

16.8523 

339 

2.94985 

114921  i 

38958219 

18.4120 

SMITHSONIAN  TABLES. 


18 


TABLE  9    (contin 


VALUES   OF    RECIPROCALS,  SQUARES,  CUBES,  AND    SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

1000.1 

n* 

„ 

tf* 

n 

10004 

+ 

* 

V" 

340 

2.94118 

115600 

39304000 

18.4391 

395 

2.53*65 

156025. 

61629875 

19.8746 

341 

2.93255 

116281 

39651821 

18.4662 

396 

2-52525 

156816 

62099136 

19.8997 

342 

2.92398 

116964 

40001688 

18.4932 

397 

2.51889 

157609 

62570773 

19.9249 

343 

117649 

40353607 

18.5203 

398 

2.51256 

i  58404 

63044792 

19.9499 

344 

2.90698 

118336 

40707584 

18.5472 

399 

2.50627 

159201 

63521199 

19.9750 

345 

2.89855 

119025 

41063625 

18.5742 

400 

2.50000 

160000 

64000000 

20.0000 

346 

2.89017 

119716 

41421736 

18.6011 

401 

2-49377 

160801 

64481201 

2O.O25O 

347 

2.88184 

120409 

41781923 

18.6279 

402 

2.48756 

161604 

64964808 

20.0499 

348 

2.87356 

121104 

42144192 

18.6548 

403 

2.48139 

162409 

65450827 

20.0749 

349 

2.86533 

121801 

42508549 

18.6815 

404 

2.47525 

163216 

65939264 

20.0998 

350 

2.85714 

122500 

42875000 

18.7083 

405 

2.46914 

164025 

66430125 

20.1246 

351 

2.84900 

123201 

43243551 

*8-735o 

406 

2-46305 

164836 

66923416 

20.1494 

352 
353 

2.84091 
2.83286 

123904 
124609 

43614208 
43986977 

18.7617 

18.7883 

407 
408 

2.45700 
2.45098 

165649 
166464 

674>9*43 
679*73*2 

20.1742 
20.1990 

354 

2.82486 

125316 

44361864 

18.8149  | 

409 

2-44499 

167281 

68417929 

20.2237 

355 

2.81690 

126025 

44738875 

18.8414 

410 

2.43902 

168100 

68921000 

20.2485 

356 

2.80899 

126736 

451  18016 

18.8680 

411 

168921 

69426531 

20.2731 

357 

2.80112 

127449 

45499293 

18.8944 

412 

2.42718 

169744 

69934528 

20.2978 

358 

2.79330 

128164 

45882712 

18.9209 

4*3 

2.42131 

170569 

70444997 

20.3224 

359 

2.78552 

128881 

46268279 

18.9473 

4*4 

2.41546 

171396 

70957944 

20.3470 

360 

2.77778 

129600 

46656000 

iS-9737 

415 

2.40964 

172225 

7*473375 

20.37*5 

361 

2.77008 

130321 

4704588  r 

1  9.0000 

416 

2.40385 

173056 

71991296 

20.3961 

362 

2.76243 

131044 

47437928 

19.0263 

4*7 

2.39808 

173889 

7251*713 

20.4206 

363 

2.75482 

131769 

47832147 

19.0526 

418 

2.39234 

174724 

73034632 

20.4450 

364 

2.74725 

132496 

48228544 

19.0788 

419 

2.38663 

73560059 

20.4695 

365 

2-73973 

133225 

48627125 

19.1050 

420 

2.38095 

176400 

74088000 

20-4939 

366 
367 

2.73224 
2.72480 

1  33956 
134689 

49027896 
49430863 

19.1311 
19.1572 

421 
422 

2.37530 
2.36967 

177241 
178084 

74618461 
7515*448 

20.5183 
20.5426 

368 

2.71739 

1  35424 

49836032 

I9'*833 

423 

2.36407 

178929 

75686967 

20.5670 

369 

2.71003 

I36l6l 

50243409 

19.2094 

424 

2.35849 

179776 

76225024 

20.5913 

370 

37  * 

2.70270 
2.69542 

136900 
1  3764  * 

50653000 
51064811 

I9-2354 
19.2614 

425 

426 

2.35294 

2.34742 

180625 
181476 

76765625 

77308776 

20.6155 
20.6398 

372 

2.68817 

138384 

51478848 

19.2873 

427 

2.34192 

182329 

20.6640 

373 

2.68097 

I39I29 

19.3132 

428 

2-33645 

183184 

78402752 

20.6882 

374 

2.67380 

139876 

523*3624 

19-339* 

429 

2.33100 

184041 

789535% 

20.7123 

375 

2.66667 

140625 

52734375 

19.3649 

430 

2.32558 

184900 

79507000 

20.7364 

376 
377 
378 

2.65957 
2.65252 
2.64550 

MI376 
I42I29 
142884 

53*57376 
53582633 
54010152 

19.3907 
19.4165 
19.4422 

43* 
432 
433 

2.32019 
2.31481 
2.30947 

185761 
186624 
187489 

80062991 
80621568 
81182737 

20.7605 
20.7846 
20.8087 

379 

2-63852 

I4364I 

54439939 

19.4679 

434 

2.30415 

188356 

81746504 

20.8327 

380 

38' 

2-63158 
2.62467 

144400 
I45l6l 

54872000 
55306341 

19.4936 
19.5192 

435 

436 

2.29885 
2-29358 

189225 
190096 

82312875 
82881856 

_        -' 

20.8567 
20.8806 

382 
383 

2.61780 
2.61097 

145924 
146689 

55742968 
56181887 

19.5448 
19.5704 

437 
438 

2-28833 
2.28311 

190969 
191844 

83453453 
84027672 

20.9045 
20.9284 

384 

2.60417 

147456 

56623104 

19-5959 

439 

2.27790 

192721 

84604519 

20.9523 

385 

2.59740 

148225 

57066625 

19.6214 

440 

2.27273 

193600 

85184000 

20.9762 

386 

387 

2^58398 

148996 
149769 

575^456 
57960603 

19.6469 
19.6723 

44* 
442 

2.26757 
2.26244 

194481 
195364 

85766121 
86350888 

2I.OOOO 
21.0238 

388 

2-57732 

*  5°544 

58411072 

19.6977 

443 

2-25734 

196249 

86938307 

21.0476 

389 

2.57069 

!5*32i 

58863869 

19.7231 

444 

2.25225 

I97I36 

87528384 

21.0713 

390 

39* 

2.56410 

2-55754 

152100 
152881 

59319000 

59776471 

19.7484 
*9-7737 

445 

446 

2.24719 
2.24215 

198025 
198916 

88121125 
88716536 

2I.O95O 
2I.II87 

392 

2.55102 

153664 

60236288 

19.7990 

447 

2.23714 

199809 

89314623 

21.1424 

393 
394 

2-54453 
2.53807 

154449 
155236 

60698457 
61162984 

19.8242 
19.8494 

448 
449 

2.23214 

2.22717 

200704 
201601 

899*5392 
90518849 

21.  l66o 
21.1896 

SMITHSONIAN  TABLE? 


TABLE  9  (continued).  I 

VALUES   OF    RECIPROCALS,    SQUARES,   CUBES,    AND    SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

looo.i 

»2 

«8 

in 

n 

1000.^ 

«2 

«• 

1* 

450 

2.22222 

202500 

9II25OOO 

21.2132 

505 

1.98020 

255025 

128787625 

22.4722 

451 

2.21729 

203401 

9^3385! 

21.2368 

!  506 

1.97628 

256036 

I295542I6 

22.4944 

452 

2.21239 

204304 

92345408 

21.2603 

;  507 

1.97239 

257049 

130323843 

22.5167 

453 

2.20751 

205209 

92959677 

21.2838 

1  508 

1.96850 

258064 

131096512 

22.5389 

454 

2.2O264 

2o6ll6 

93576664 

21.3073 

5°9 

1.96464 

259081 

131872229 

22.5610 

455 

2.19780 

207025 

94196375 

21.3307 

510 

1.96078 

260100 

I3265IOOO 

22.5832 

456 

2.19298 

207936 

94818816 

21.3542 

511 

i  -95695 

26II2I 

I3343283I 

22.6053 

457 

2.l88l8 

208849 

95443993 

21.3776 

512 

I.953I2 

262144 

I342I7728 

22.6274 

458 

2.18341 

209764 

96071912 

2  1  .4009 

5J3 

1.94932 

263169 

135005097 

22.6495 

459 

2.17865 

2I068I 

96702579 

21.4243 

5H 

1-94553 

264196 

1  35796744 

22.6716 

460 

2.I739I 

2  1  1  6OO 

97336000 

21.4476 

515 

I.94I75 

265225 

136590875 

22.6936 

461 

2.16920 

2I252I 

97972181 

21.4709 

516 

1.93798 

266256 

137388096 

22.7156 

462 

2.16450 

213444 

98611128 

21.4942 

5*7 

1.93424 

267289 

138188413 

22.7376 

463 
464 

2-  1  5983 
2.I55I7 

214369 
215296 

99252847 
99897344 

21.5174 
21.5407 

518 
5r9 

1.93050 
1.92678 

268324 
269361 

138991832 
139798359 

22.7596 
22.7816 

465 

2.15054 

2l6225 

100544625 

21.5639 

520 

1.92308 

27O4OO 

I4O6O8OOO 

22.8035 

466 

2.14592 

217156 

101194696 

21.5870 

|  52i 

1.91939 

27I44I 

141420761 

22.8254 

467 

2.I4I33 

218089 

101847563 

2I.6IO2 

522 

i-9!57i 

272484 

142236648 

22.8473 

468 

2.13675 

219024 

102503232 

21.6333 

523 

1.91205 

273529 

143055667 

22.8692 

469 

2.13220 

219961 

103161709 

21.6564 

524 

1.90840 

274576 

143877824 

22.8910 

470 

2.12766 

220900 

103823000 

21.6795 

525 

1.90476 

275625 

144703125 

22.9129 

4?i 

2.I23I4 

22I84I 

104487111 

21.7025 

526 

1.90114 

276676 

!4553!576 

22.9347 

472 

2.II864 

222784 

105154048 

21.7256 

527 

I-89753 

277729 

146363183 

22.9565 

473 

2.II4I6 

223729 

105823817 

21.7486 

528 

1.89394 

278784 

1  47  197952 

22.9783 

474 

2.10970 

224676 

106496424 

21.7715 

529 

1.89036 

279841 

148035889 

23.0000 

475 

476 

2.10526 
2.10084 

226576 

107171875 
107850176 

21-7945 

2I.8I74  i 

530 

531 

1.88679 
1.88324 

280900 
281961 

148877000 
149721291 

23.0217 
23-0434 

477 
478 

2.09644 
2.09205 

227529 
228484 

I0853!333 
109215352 

21.8403 
21.8632 

S32 
533 

1.87970 
1.87617 

283024 
284089 

150568768 
151419437 

23.0868 

479 

2.08768 

229441 

109902239 

2I.886I 

534 

1.87266 

285156 

152273304 

23.1084 

480 

481 

2-08333 
2.O79OO 

230400 
231361 

110592000 
111284641 

21.9089 
21.9317 

535 

536 

1.86916 
1.86567 

286225 
287296 

I53U0375 
153990656 

23.1301 
23-1517 

482 

2.07469 

232324 

111980168 

21.9545 

537 

1.86220 

288369 

I54854I53 

23-J733 

483 

2.07039 

233289 

112678587 

21.9773 

538 

1.85874 

289444 

155720872 

23.1948 

484 

2.06612 

234256 

ii3379904 

22.0000 

539 

1.85529 

290521 

156590819 

23.2164 

485 

486 

487 

2.06186 
2.05761 
2-05339 

235225 
236196 
237169 

114084125 
114791256 
ii5SOI3°3 

22.0227 
22.0454 
22.0681 

540 

54i 
542 

1.85185 
1.84843 
1.84502 

291600 
292681 
293764 

157464000 
158340421 
i  59220088 

23.2379 
23.2594 
23.2809 

488 

2.04918 

238144 

116214272 

22.0907 

543 

1.84162 

294849 

160103007 

23.3024 

489 

2.04499 

239121 

116930169 

22.1133 

544 

1.83824 

295936 

160989184 

23-3238 

490 

2.04082 

240100 

117649000 

22.1359 

545 

1.83486 

297025 

161878625 

23-3452 

491 

2.03666 

241081 

118370771 

22.1585 

546 

1.83150 

298116 

162771336 

23.3666 

492 

2.03252 

242064 

119095488 

22.l8ll 

547 

1.82815 

299209 

163667323 

23.3880 

493 

2.02840 

243049 

119823157 

22.2036 

548 

1.82482 

300304 

164566592 

23-4094 

494 

2.02429 

244036 

120553784 

22.2261 

549 

1.82149 

3OI4OI 

165469149 

23-4307 

495 

496 

2.O2O2O 
2.Ol6l3 

245025 
246016 

121287375 
122023936 

22.2486 
22.2711 

550 

551 

1.81818 
1.81488 

3O25OO 
303601 

166375000 
167284151 

23.4521 
23-4734 

497 

2.01207 

247009 

122763473 

22.2935 

552 

1.81159 

304704 

168196608 

23-4947 

498 

2.00803 

248004 

123505992 

22.3159 

553 

1.80832 

305809 

169112377 

23.5160 

499 

2.OO4OI 

249001 

124251499 

22.3383 

554 

1.80505 

306916 

170031464 

23-5372 

50O 

2.OOOOO 

25OOOO 

125000000 

22.3607 

555 

i.  80  1  80 

308025 

170953875 

23-5584 

501 

I.99DOI 

25IOOI 

12575^01 

22.3830 

!  556 

1.79856 

309136 

171879616 

23.5797 

502 

1.99203 

252004 

i  26506008 

22.4054 

557 

1-79533 

310249 

172808693 

23.6008 

5°3 

1.98807 

253009 

127263527 

22.4277 

558 

1.79211 

3"364 

173741112 

23.6220 

5°4 

1.98413 

254016 

128024064 

22.4499 

559 

1.78891 

312481 

174676879 

23.6432 

SMITHSONIAN  TABLES. 


2O 


TABLE  9    (continued}. 


VALUES    OF    RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

lOOO.i 

# 

„. 

1* 

i  /; 

IOOO.I 

«• 

* 

V 

560 

1-78571 

313600 

175616000 

23.6643 

615 

1.62602 

378225 

232608375 

24.7992 

561 

1-78253 

176558481 

23.6854 

!  616 

1.62338 

379456 

233744896 

24.8193 

562 

1.77936 

31  5844 

177504328 

23.7065 

|  617 

1.62075 

380689 

234885113 

24.8395 

563 

1.77620 

316969 

178453547 

23.7276 

618 

1.61812 

38*924 

236029032 

24.8596 

564 

1.77305 

318096 

179406144 

23-7487  | 

619 

1-61551 

383*61 

237*76659 

24-8797 

565 

1.76991 

319225 

180362125 

23.7697 

620 

1.61290 

384400 

238328000 

24.8998 

566 

1.76678 

320356 

181321496 

23.7908 

621 

1.61031 

385641 

239483061 

24.9199 

1.76367 

321489 

182284263 

23.8118 

622 

1.60772 

386884 

240641848 

24.9399 

568 

1.76056 

322624 

183250432 

23.8328 

623 

1.60514 

388129 

241804367 

24.9600 

569 

1-75747 

323761 

184220009 

23-8537 

624 

1.60256 

389376 

242970624 

24.9800 

570 

1-75439 

324900 

185193000 

23.8747 

625 

1.60000 

390625 

244140625 

25.0000 

571 

I-75I3I 

326041 

186169411 

23.8956 

626 

1-59744 

39*876 

2453*4376 

25.0200 

572 

1.74825 

327184 

187149248 

23.9165 

627 

1.59490 

393*29 

246491883 

25.0400 

573 

1.74520 

328329 

188132517 

23-9374 

628 

1-59236 

394384 

247673152 

25-0599 

574 

1.74216 

329476 

189119224 

23-9583 

629 

1-58983 

395641 

248858189 

25.0799 

575 

L739I3 

330625 

190109375 

23-9792 

630 

1-58730 

396900 

250047000 

25.0998 

576 

1.73611 

33*776 

191102976 

24.OOOO   : 

63* 

1.58479 

398161 

25*23959* 

25.1197 

577 

i-73310 

332929 

192100033 

24.0208 

632 

1.58228 

399424 

252435968 

25.1396 

578 

1.73010 

334084 

193100552 

24.O4I6 

633 

I-57978 

400689 

253636137 

25-1595 

579 

1.72712 

335241 

194104539 

24.0624 

634 

1.57729 

401956 

254840104 

25.1794 

580 

1.72414 

336400 

195112000 

24.O832 

635 

1.57480 

403225 

256047875 

25.1992 

581 

1.72117 

337561 

196122941 

24.1039 

636 

*-57233 

404496 

257259456 

25.2190 

582 

1.71821 

338724 

*97*37368 

24.1247 

637 

1.56986 

405769 

258474853 

25.2389 

583 
584 

1.71527 
1-71233 

339889 
34*056 

198*55287 
199176704 

24.1454 
24.l66l 

638 
639 

1.56740 
I-56495 

407044 
408321 

2596940/2 
260917119 

25.2587 
25.2784 

585 

1.70940 

342225 

200201625 

24.1868 

640 

1.56250 

409600 

262144000 

25.2982 

586 

1.70648 

343396 

201230056 

24.2074 

641 

1.56006 

410881 

263374721 

25.3180 

587 

1-70358 

344569 

202262003 

24.2281 

642 

1.55763 

412164 

264609288 

25-3377 

588 

1.70068 

345744 

203297472 

24.2487 

643 

4*3449 

265847707 

25-3574 

589 

1.69779 

346921 

204336469 

24.2693 

644 

1.55280 

414736 

267089984 

25-3772 

590 

1.69492 

348100 

205379000 

24.2899 

645 

I-55039 

416025 

268336125 

25-3969 

59  1 

1.69205 

349281 

206425071 

24.3IO5 

646 

1-54799 

4*73*6 

269586136 

25-4*65 

592 

1.68919 

350464 

207474688 

24-33*1 

647 

1.54560 

418609 

270840023 

254362 

593 

1.68634 

35*649 

208527857 

24-35*6 

648 

I-54321 

4*9904 

272097792 

25-4558 

594 

1.68350 

352836 

209584584 

24.3721 

649 

1.54083 

421201 

273359449 

254755 

595 

1.68067 

354025 

210644875 

24.3926 

650 

1.53846 

422500 

274625000 

25.4951 

596 

1.67785 

211708736 

244I3I 

651 

.53610 

423801 

275894451 

25-5*47 

597 

1.67504 

356409 

212776173 

244336 

652 

•53374 

425104 

277167808 

25-5343 

598 

1.67224 

357604 

213847192 

24.4540 

653 

•53*39 

426409 

278445077 

25-5539 

599 

1.66945 

358801 

214921799 

244745 

654 

.52905 

427716 

279726264 

25-5734 

600 

1.66667 

360000 

216000000 

244949 

655 

.52672 

429025 

281011375 

25-5930 

601 

1.66389 

361201 

217081801 

656 

•52439 

430336 

282300416 

25.6125 

602 

1.66113 

362404 

218167208 

24-5357 

657 

•52207 

43*649 

283593393 

25.6320 

603 

1.65837 

363609 

219256227 

24.5561 

658 

.5*976 

432964 

284890312 

25-65*5 

604 

1  -65563 

364816 

220348864 

24-5764 

659 

•5*745 

434281 

286191179 

25.6710 

605 

1.65289 

366025 

221445125 

24-5967 

660 

•5*5*5 

435600 

287496000 

25.6905 

606 

1.65017 

367236 

222545016 

24.6I7I 

66  1 

.51286 

436921 

288804781 

25.7099 

607 

1.64745 

368449 

223648543 

24-6374 

662 

.51057 

438244 

290117528 

25.7294 

608 

1.64474 

369664 

224755712 

24-6577 

663 

.50830 

439569 

291434247 

25-7488 

609 

1.64204 

370881 

225866529 

24.6779 

664 

.50602 

440896 

292754944 

25.7682 

610 

1-63934 

372100 

226981000 

24.6982 

665 

.50376 

442225 

294079625 

25.7876 

611 
612 

1.63666 
I-63399 

37332* 
374544 

228099131 
229220928 

24.7184 
247386 

666 
667 

•50*5° 
.49925 

443S56 
444889 

295408296 
296740963 

25.8070 
25.8263 

613 

1.63132 

375769 

230346397 

247588 

668 

.49701 

446224 

298077632 

25-8457 

614 

1.62866 

376996 

231475544 

247790 

669 

•49477 

44756i 

299418309 

25.8650 

SMITHSONIAN  TABLES. 


TABLE  9    (continued). 


21 


VALUES   OF    RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

lOOO.i 

«2 

«3 

i* 

n 

1  000.1 

»2 

«8 

tf» 

670 

1.49254 

448900 

300763000 

25.8844 

725 

I-3793I 

525625 

381078125 

26.9258 

671 

1.49031 

450241 

3O2III7II 

25.9037 

726 

I-3774I 

527076 

382657176 

26.9444 

672 

1.48810 

45I584 

303464448 

25.9230 

727 

1-37552 

528529 

384240583 

26.9629 

673 

1.48588 

452929 

304821217 

25.9422 

728 

I-37363 

529984 

385828352 

26.9815 

674 

{.48368 

454276 

306182024 

25.9615 

729 

I-37I74 

53I44I 

387420489 

27.0000 

675 

1.48148 

455625 

307546875 

25.9808 

730 

1.36986 

532900 

389017000 

27.0185 

676 

1.47929 

456976 

308915776 

26.OOOO 

731 

1.36799 

53436i 

390617891 

27.0370 

677 

1.47710 

458329 

310288733 

26.OI92 

732 

1.36612 

535824 

392223168 

27-0555 

678 
679 

1-47493 
I-47275 

459684 
461041 

311665752 
313046839 

26.0384 
26.0576 

733 
734 

1.36426 
1.36240 

537289 
538756 

393832837 
395446904 

27.0740 
27.0924 

680 

1.47059 

462400 

314432000 

26.0768 

735 

1.36054 

540225 

397065375 

27.1109 

68  1 

1.46843 

463761 

315821241 

26.0960 

736 

I-35870 

541696 

398688256 

27.1293 

682 

1.46628 

465124 

317214568 

26.1151 

737 

1-35685 

543*69 

400315553 

27.1477 

683 

1.46413 

466489 

318611987 

26.1343 

738 

l-3S5°l 

544644 

401947272 

27.1662 

684 

1.46199 

467856 

320013504 

26.1534 

739 

*-353l8 

546121 

403583419 

27.1846 

685 

1.45985 

469225 

321419125 

26.1725 

740 

i-35'35 

5476oo 

405224000 

27.2029 

686 

1-45773 

470596 

322828856 

26.1916 

74i 

1  -34953 

549081 

40686902  i 

27.2213 

687 

1.45560 

471969 

324242703 

26.2IO7 

742 

i-3477i 

550564 

408518488 

27-2397 

688 

1-45349 

473344 

325660672 

26.2298 

743 

1.34590 

552049 

410172407 

27.2580 

689 

i  -45  J  38 

474721 

327082769 

26.2488 

744 

1.34409 

553536 

411830784 

27.2764 

690 

1.44928 

476100 

328509000 

26.2679 

745 

1.34228 

555025 

413493625 

27-2947 

691 

1.44718 

477481 

329939371 

26.2869 

746 

1.34048 

556516 

415160936 

27.3130 

692 

1.44509 

478864 

331373888 

26.3059 

747 

1.33869 

558009 

416832723 

27-33^3 

693 

1.44300 

480249 

332812557 

26.3249 

748 

1.33690 

559504 

418508992 

27.3496 

694 

1.44092 

481636 

334255384 

26.3439 

749 

J-33511 

561001 

420189749 

27.3679 

695 

696 

1.43885 
1.43678 

483025 
484416 

335702375 
337153536 

26.3629 
26.3818 

750 

75' 

1  -33333 
I-33I56 

562500 
564001 

421875000 
423564751 

27.3861 
27.4044 

697 

1.43472  485809 

338608873   26.4008 

752 

1.32979 

565504 

425259008 

27.4226 

698 

1.43266  ;  487204 

340368392  |  26.4197 

753 

1.32802 

567009 

426957777 

27.4408 

699 

1.43062 

488601 

341532099 

26.4386 

754 

1.32626 

568516 

428661064 

27.4591 

700 

1.42857 

490000 

343OOOOOO 

26.4575 

755 

1.32450 

570025 

430368875 

27-4773 

701 

1.42653 

491401 

344472IOI 

26.4764 

756 

1-32275 

571536 

432081216 

27-4955 

702 

1.42450 

492804 

345948408 

26.4953 

757 

1.32100 

573049 

433798093 

27-5  *  36 

703 

1.42248 

494209 

347428927 

26.5141 

758 

1.31926 

574564 

4355!9512 

27-5318 

704 

1.42045 

495616 

348913664 

26.5330 

759 

1-31752 

576081 

437245479 

27.5500 

705 

1.41844 

497025 

350402625 

26.5518 

760 

I-3I579 

577600 

438976000 

27.5681 

706 

1.41643 

498436 

35I8958I6 

26.5707 

76i 

1.31406 

579121 

440711081 

27.5862 

707 

1.41443 

499849 

353393243 

26.5895 

762 

1.31234  !  580644 

442450728 

27.6043 

708 

1.41243 

501264 

354894912 

26.6083 

763 

1.31062  i  582169 

444194947 

27.6225 

709 

1.41044 

502681 

356400829 

26.6271 

764 

1.30890 

583696 

445943744 

27.6405. 

710 

1.40845 

504100 

3579IIOOO 

26.6458 

765 

1.30719 

585225 

447697125 

27.6586 

711 

712 

1.40647 
1.40449 

505521 
506944 

359425431 
360944128 

26.6646 
26.6833 

766 
767 

1.30548 
1-30378 

586756 
588289 

449455096 
451217663 

27.6767 
27.6948 

713 

1.40252 

508369 

362467097 

26.7O2I 

768 

1.30208 

589824 

452984832 

27.7128 

7H 

1.40056 

509796 

363994344 

26.7208 

769 

1.30039 

591361 

454756609 

27.7308 

715 

1.39860 

511225 

365525875 

26.7395 

770 

1.29870 

592900 

456533000 

27.7489 

716 

1.39665 

512656 

367061696 

26.7582 

771 

1.29702 

594441 

458314011 

27.7669 

717 

1.39470 

514089 

368601813 

26.7769 

772 

1-29534 

595984 

460099648 

27.7849 

718 

1.39276 

5*5524 

370146232 

26.7955 

773 

1.29366 

597529 

461889917 

27.8029 

719 

1.39082 

516961 

371694959 

26.8142 

774 

1.29199 

599076 

463684824 

27.8209 

720 

1.38889 

518400 

373248000 

26.8328 

775 

1.29032 

600625 

465484375 

27.8388 

721 

1.38696 

519841 

374805361 

26.8514 

776 

1.28866 

602176 

467288576 

27.8568 

722 

1.38504 

521284 

376367048 

26.8701 

777 

1.28700 

603729 

469097433 

27.8747 

723 
724 

1  -383  1  3 
1.38122 

522729 
524176 

377933067 
379503424 

26.8887 
26.9072 

778 
779 

1-28535 
1.28370 

605284 
606841 

470910952 
472729139 

27.8927 
27.9106 

SMITHSONIAN  TABLES. 


2  2  TABLE  9  (continued}. 

VALUES   OF   RECIPROCALS,   SQUARES,    CUBES,    AND   SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

«ooo.i    # 

* 

<- 

n 

1  000.  J 

-. 

n* 

v<* 

780 

1.28205  608400 

474552000 

27.9285 

835 

1.19760 

697225 

582182875 

28.8964 

781 

1.28041  609961 

476379541 

27.9464 

!  836 

1.19617 

698896 

584277056 

28.9137 

782 

1.27877  1  611524 

4782II768 

27.9643 

1  837 

1.19474  700569  5^6376253 

28.9310 

783 

1.27714  613089 

480048687 

27.9821 

838 

I'I9332 

702244  588480472 

28.9482 

784 

1.27551  614656 

48l89O3O4    28.OOOO 

839 

1.19190  703921   590589719 

28.9655 

785 

786 

1.27389  616225  483736625  28.0179 
1.27226  617796  485587656  28.0357 

840 

841 

1.19048  705600 
1.18906  707281 

592704000 
594823321 

28.9828 
29.0000 

1.27065  619369  487443403  28.0535 

842 

1.18765  708964 

59694/6S8 

29.0172 

788 

1.26904  620944 

489303872    28.0713 

843 

1.18624  j  710649 

599077107 

29-0345 

789 

1.26743  622521 

49H69069 

28.0891 

844 

1.18483 

712336 

OOI2II584 

29.0517 

790 

791 

1.26582  624100 
1.26422  625681 

493039000 
4949I367I 

28.1069 

28:1247 

845 

846 

1-18343 

1.18203 

714025 
715716 

60335II25 
605495/36 

29.0689 
29.0861 

792 

1.26263  627264 

496793088 

28.1425 

847 

1.18064 

717409 

607645423 

29.1033 

793 

1.26103  628849 

498677257 

28.1603 

848 

1.17925 

719104  609800192 

29.1204 

794 

1.25945  630436 

500566l84    28.1780 

849 

1.17786 

720801  611960049 

29.1376 

795 

1.25786  632025 

502459875    28.1957 

850 

1.17647 

722500 

6I4I25OOO 

29.1548 

|  796 

1.25628  633616 

504358336    28.2135 

851 

1.17509 

724201 

6l6295O5I 

29.1719 

797 

1.25471 

6352O9 

5O626I573    28.2312 

852 

725904 

6l8470208 

29.1890 

798 

I-253I3 

636804 

5OSl69592    28.2489 

853 

1-17233 

727609 

620650477 

29.2062 

799 

1-25156 

638401 

510082399 

28.2666 

854 

1.17096 

729316 

622835864 

29.2233 

800 

1.25000 

64OOOO 

512000000 

28.2843 

855 

1.16959 

731025  625026375 

29.2404 

80  1 

1.24844 

64I60I 

5I392240I     28.3019 

856 

1.16822 

732736  j  627222016   29.2  S7S 

802 

1.24688 

643204 

515849608 

28.3196 

857 

1.  1  6686  I  734449 

629422793 

29.2746 

803 

!-24533 

644809 

5I778l627    28.3373 

858 

1.16550 

736164 

63I6287I2 

29.2916 

804 

1.24378 

646416 

5I97I8464 

28.3549 

859 

1.16414 

73788I 

633839779 

29.3087 

805 

1.24224 

648025 

52I660I25 

28.3725 

860 

1.16279 

739600 

636050000 

29.3258 

806 

1.24069 

649636 

523606616 

28.3901 

861 

1.16144 

741321   638277381 

29.3428 

807 

1.23916 

651249 

525557943 

28.4077 

862 

1.16009 

743044  :  640503928 

808 

1.23762 

652864 

5275I4II2 

28.4253 

863 

1.15875  ;  744769  642735647 

29.3769 

809 

1.23609 

654481 

529475129 

28.4429 

864 

'•15741 

746496 

644972544 

29-3939 

810 

1-23457 

656100 

53I44IOOO 

28.4605 

865 

1.15607 

748225 

647214625 

29.4109 

811 

1.23305 

657721 

5334II73I 

28.4781 

866 

1-15473 

749956  649461896 

29.4279 

812 

I-23I53 

659344 

535387328 

28.4956 

867 

1-15340 

751689  651714363 

29.4449 

813 

1.23001 

537367797 

28.5132 

868 

1.15207 

7534^4 

653972032 

29.4618 

814 

1.22850 

662596 

539353M4 

28.5307 

869 

1.15075 

755161 

656234909 

29.4788 

815 

1.22699 

664225 

541343375 

28.5482 

870 

1.14943 

756900  :  6^8503000 

29.4958 

816 

1.22549  665856 

543338496 

28.5657 

871 

1.14811 

758641 

66O7763I  I 

29.5127 

817 

1.22399 

667489 

5453385J3 

28.5832 

872 

1.14679 

760384 

663054848 

29.5296 

818 

1.22249 

6691  24 

547343432 

28.6007 

873 

1.14548  762129 

665338617 

29.5466 

.819 

I.22IOO 

670761 

549353259 

28.6182 

874 

1.14416 

763876 

667627624 

29-5635 

820 

I.2I95I 

6724OO 

551368000 

28.6356 

875 

1.14286 

765625 

669921875 

29.5804 

821 

1.21803 

674041 

55338766r 

28.6531 

876 

1-14155 

767376 

672221376 

29-5973 

822 
823 

1.21655 
I.2I507 

675684 
677329 

555412248 
557441767 

28.6705 
28.6880 

877 
878 

1.14025 
1-13895 

769129 

770884 

674526133 
676836152 

29.6142 
29.63  1  1 

824 

I.2I359   678976 

559476224 

28.7054 

879 

1.13766 

772641  1  679151439 

29.6479 

825 

826 
827 

I.2I2I2   680625 
I.2I065   682276 

I.2O9I9  :  683929 

561515625  28.7228 
563559976  28.7402 
565609283  28.7576 

880 

88  1 
882 

1.13636 
1-13507 
1-13379 

774400 
776161 
777924 

68I472OOO 
683797841 
686128968 

29.6648 
29.6816 
29.6985 

828 

1.20773 

685584 

567663552  ;  28.7750  | 

883 

1.13250 

779689 

688465387 

29-7153 

829 

I.2O627 

687241 

569722789 

28.7924  1 

884 

1.13122 

781456 

69O8O7IO4 

29.7321 

830 

831 

1.20482 
1.20337 

688900 
690561 

571787000 
573856191 

28.8097 
28.8271 

885 

886 

1.12994 
1.12867 

783225 
784996 

693154125 
695506456 

29.7489 
29.7658 

832 

I.2OI92 

692224 

575930368 

28.8444  ! 

887 

1.12740 

786769 

697864103 

29.7825 

833 

1.20048 

693889 

578009537 

28.8617 

888 

1.12613 

788544 

700227072 

29-7993 

834 

I.I9904 

695556 

580093704 

28.8791 

889 

1.12486 

790321 

702595369 

29.8161 

SMITHSONIAN  TABLES. 


TABLE  9   (continued').  2 

VALUES   OF    RECIPROCALS,  SQUARES,  CUBES,  AND    SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

I  OCX).,; 

n2 

«3 

1* 

n 

1000.4 

«2 

«3 

V* 

890 

891 
892 

.I236O 
.12233 
.12108 

792100 
793881 
795664 

704969000 

707347971 
709732288 

29.8329 
29.8496 
29.8664 

945 

946 

947 

1.05820 
1.05708 
1  -°5597 

893025 
894916 
896809 

843908625 
846590536 
849278123 

30.7409 
30-7571 
30-7734 

893 

.11982 

797449 

7I2I2I957 

29.8831 

948 

1.05485 

898704 

85i97<392 

30.7896 

894 

.11857 

799236 

714516984 

29.8998 

949 

1-05374 

9OO6OI 

854670349 

30.8058 

895 

.11732 

801025 

7I69I7375 

29.9166 

950 

1.05263 

9O25OO 

857375000 

30.8221 

896 

.11607 

802816 

719323136 

29-9333 

951 

1.05152 

904401 

860085351 

30.8383 

897 

.11483 

804609 

721734273 

29.9500 

952 

1.05042 

906304 

862801408 

30-8545 

898 

•II359 

806404 

724150792 

29.9666 

953 

1.04932 

908209 

865523177 

30.8707 

899 

•11235 

808201 

726572699 

29-9833 

954 

1.04822 

9IOIl6 

868250664 

1  30.8869 

900 

.inn 

810000 

729000000 

30.0000 

955 

1.04712 

912025 

870983875 

30.9031 

901 

.10988 

811801 

73I43270I 

30.0167 

956 

i  .04603 

9  13936 

873722816 

30.9192 

902 

.10865 

813604 

733870808 

30-0333 

957 

1.04493 

915849 

876467493 

!  30-9354 

903 
904 

.10742 
.10619 

815409 
817216 

7363M327 
738763264 

3O.O5OO 
30.0666 

958 
959 

1.04384 
1.04275 

917764 
919681 

879217912 
881974079 

1  30.9516 
30.9677 

905 

.10497 

819025 

74I2I7625 

30.0832 

960 

1.04167 

921600 

884736000 

30-9839 

906 

•I0375 

820836 

743677416 

30.0998 

961 

i  .04058 

923521 

887503681 

31.0000 

907 

.10254 

822649 

746142643 

30.1164 

962 

1.03950 

925444 

890277128 

31.0161 

908 

.10132 

824464 

748613312 

3°-  I  330 

963 

1.03842 

927369 

893056347 

31.0322 

909 

.IOOII 

826281 

751089429 

30.1496 

964 

1-03734 

929296 

895841344 

31.0483 

910 

1.09890 

828100 

753571000 

3O.I662 

965 

1.03627 

931225 

898632125 

31.0644 

911 

1.09769 

829921 

756058031 

30.1828 

966 

.03520 

933^6 

901428696 

31.0805 

912 

9i3 

1.09649 
1.09529 

S3I744 
833569 

758550528 
761048497 

30.1993 
30.2159 

967 
968 

•03413 
.03306 

935089 
937024 

904231063 
907039232 

31.0966 
31.1127 

9*4 

1.09409 

835396 

763SSI944 

30.2324 

969 

.03199 

938961 

909-853209 

31.1288 

915 

1.09290 

837225 

766060875 

3O.249O 

970 

•03093 

940900 

912673000 

31.1448 

916 

1.09170 

839056 

768575296 

30-2655  ! 

971 

.02987 

942841 

915498611 

31.1609 

917 

1.09051 

840889 

77I0952I3 

30.2820  | 

972 

.02881 

944784 

918330048 

31.1769 

918 

1.08932 

842724 

773620632 

30.2985  ; 

973 

.02775 

946729 

921167317 

31.1929 

919 

1.08814 

844561 

776I5I559 

30.3150 

974 

.02669 

948676 

924010424 

31.2090 

920 

1.08696 

846400 

778688000 

3°-33I5 

975 

.02564 

950625 

926859375 

31.2250 

921 

1.08578 

848241 

781229961 

30.3480 

976 

.02459 

952576 

929714176 

31.2410 

922 

1.08460 

850084 

783777448 

30-3645 

977 

•02354 

954529 

932574833 

3I-2570 

923 

1.08342 

851929 

786330467 

30.3809 

978 

1.02249 

956484 

935441352 

31.2730 

924 

1.08225 

853776 

788889024 

30-3974  i 

979 

1.02145 

958441 

9383^739 

31.2890 

925 

1.08108 

855625 

79M53I25 

30-4138  i 

980 

1.02041 

960400 

941192000 

31-305° 

926 

1.07991 

857476 

794022776 

30.4302 

981 

•01937 

962361 

944076141 

31.3209 

927 

1.07875 

859329 

796597983 

30.4467 

982 

•01833 

964324 

946966168 

3  *  -3369 

928 

1.07759 

861184 

799178752 

30.4631 

983 

.01729 

966289 

949862087 

3I-3528 

929 

1.07643 

863041 

801765089 

30-4795 

984 

.01626 

968256 

952763904 

31.3688 

930 

1.07527 

864900 

804357000 

30.4959 

985 

•01523 

970225 

955671625 

31-3847 

93  r 

1.07411 

866761 

806954491 

30-5I23 

986 

.01420 

972196 

958585256 

31.4006 

932 

1.07296 

868624 

809557568 

30-5287  ; 

987 

.01317 

974169 

961  504803 

31.4166 

933 

1.07181 

870489 

812166237 

30-5450 

988 

.01215 

976144 

964430272 

3M325 

934 

i  .07066 

872356 

814780504 

30.5614 

989 

I.OIII2 

978121 

967361669 

31.4484 

935 

1.06952 

874225 

817400375 

30-577S 

990 

I.OIOIO 

980100 

970299000 

31-4643 

936 
937 

1.06838 
1.06724 

876096 
877969 

820025856 
822656953 

30-594I 
3O.6IO5 

991 
992 

1.00908 

1.00806 

982081 
984064 

973242271 
976191488 

31.4802 
31.4960 

938 

i.  06610 

879844 

825293672 

30.6268 

993 

1.00705 

986049 

979146657 

3I«5II9 

939 

1.06496 

881721 

827936019 

30-6431 

994 

1  .00604 

988036 

982107784 

3*-5278 

940 

1.06383 

883600 

830584000 

30-6594 

995 

1.00503 

990025 

985074875 

3  i  -5436 

941 

1.06270 

885481 

833237621 

30-6757 

996 

1.00402 

992016 

988047936 

31-5595 

942 
943 

1.06157 
1.06045 

887364 
889249 

835896888 
838561807 

3O.692O 
30.7083 

3 

1.00301 

1.00200 

994009 
996004 

991026973 
994011992 

3*-5753 
3»-59i  * 

944 

1.05932 

891136 

841232384 

30.7246 

999 

I.OOIOO 

998001 

997002999 

31.6070 

SMITHSONIAN  TABLES. 


TABLE  10. 
LOGARITHMS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

100 

oooo 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

003  5 

0039 

0043 

101 

0043 

0048 

0052 

0056 

0060 

0065 

0069 

0073 

0077 

0082 

0086 

102 

0086 

0090 

0095 

0099 

0103 

0107 

Oil  I 

0116 

OI2O 

0124 

0128 

I03 

0128 

0133 

0141 

0145 

0149 

0154 

0158 

Ol62 

0166 

0170 

104 

0170 

0175 

0179 

0183 

0187 

0191 

oi95 

0199 

0204 

0208 

0212 

105 

1  06 

O2I2 
0253 

0216 
0257 

0220 
O26l 

0224 
0265 

0228 
0269 

0233 

0273 

0237 
0278 

0241 
0282 

0245 
0286 

0249 
0290 

0253 
0294 

107 

0294 

0298  0302 

0306 

0310 

03  J4 

0318 

0322 

0326 

033° 

°334 

108 

0334 

0338  0342 

0346 

°35° 

0354 

0358 

0362 

0366 

0370 

0374 

109 

0374 

0378 

0382 

0386 

0390 

0394 

0398 

0402 

0406 

0410 

0414 

110 

0414 

0418 

0422 

0426 

0430 

0434 

0438 

0441 

0445 

0449 

°453 

in 

°453 

0457  0461 

0465 

0469 

0473 

0477 

0481 

0484 

0488 

0492 

112 

0492 

0496  0500 

0504 

0508  0512 

°5T5 

0519 

°523 

0527 

"3 

0531 

0535  0538 

0542 

0546 

°55° 

°554 

0558 

056l 

0565 

0569 

"4 

0569 

0573 

0577 

0580 

0584 

0588 

0592 

0596 

0599 

0603 

0607 

115 

0607 

0611 

0615 

0618 

0622 

0626 

0630 

0633 

0637 

0641 

0645 

116 

0645 

0648 

0652 

0656 

0660 

0663 

0667 

0671 

0674 

0678 

0682 

"7 

0682 

0686 

0689 

0693 

0697 

0700 

0704 

0708 

O7II 

0715 

0719 

118 

"9 

0719 

°755 

0722 
0759 

0726 
0763 

£766 

0734 
0770 

0737 
0774 

0741 
0777 

0745 
0781 

0748 
0785 

0788 

°755 
0792 

120 

0792 

0795 

0799 

0803 

0806 

0810 

0813 

0817 

0821 

0824 

0828 

121 
122 

0828 
0864 

0831 
0867 

0835 
0871 

0839 
0874 

0842 
0878 

0846 
0881 

0849 
0885 

0853  0856 
0888  0892 

0860 
0896 

0864 
0899 

I23 

0899 

0903 

0906 

0910 

0913 

0917 

0920 

0924 

0927   0931 

0934 

124 

0934 

0938 

0941 

0945 

0948 

0952 

0955 

0959 

0962 

0966 

0969 

125 

0969 

0973 

0976 

0980 

0983 

0986 

0990 

0993 

0997 

IOOO 

1004 

126 

1004 

1007 

IOII 

1014 

1017 

IO2I 

1024 

1028 

IO3I 

I035 

1038 

127 

1038 

1041 

1045 

1048 

1052 

IO55 

1059    1062 

1065 

1069 

1072 

128 

1072 

1075 

1079 

1082 

1086 

1089 

1092 

1096 

1099 

1103 

1106 

129 

1106 

1109 

III3 

1116 

1119 

"23 

1126 

1129 

"33 

1136 

"39 

130 

"39 

"43 

1146 

"49 

"53 

1156 

"59 

1163 

1166 

1169 

"73 

131 

"73 

1176 

"79 

1183 

1186 

1189 

"93 

1196 

"99 

1  202 

1206 

132 

1206 

1209 

1212 

1216 

1219 

1222 

1225 

1229 

1232 

1235 

1239 

133 

1239 

1242 

1245 

1248 

1252 

1255 

1258 

1261 

1265 

1268 

1271 

1271 

1274 

I278 

1281 

1284 

1287 

1290 

1294 

1297 

1300 

'303 

135 

1303 

I307 

1310 

I3!3 

1316 

1319 

1323 

1326 

1329 

1332 

1335 

136 

1335 

1339 

1342 

'345 

1348  i  1351 

1358 

1361 

1364 

137 

1367 

1370 

1374 

1377 

1380  1383 

1386 

1389 

1392 

'396 

*399 

138 

1399 

I4O2 

1405 

1408 

1411 

1414 

1418 

1421 

1424 

1427 

143° 

J39 

1430 

1433 

1436 

1440 

1443 

1446 

1449 

M52 

1455 

1461 

140 

1461 

1464 

1467 

I47I 

1474 

1477 

1480 

1483 

1486 

1489 

1492 

141 

1492 

M95 

1498 

I5OI 

1508 

1511 

15*4 

15^7 

1520 

1523 

142 

1523 

1526 

1529   1532 

1535 

1538 

1541 

1544 

1547 

1550 

1553 

X43 

J553 

I  5-56 

1559   1562 

j  565 

1569 

1572 

'I75 

1578 

1581 

1584 

144 

15&4 

I5»7 

1590 

1593 

1599 

1602 

1605 

1608 

1611 

1614 

145 

146 
147 

1614 
1644 
1673 

1617 
1647 
1676 

l620 
1649 
1679 

1623 

1(382 

1626 
!6%5 

i6c;8 

1632 
1661 
1691 

1$ 
1694 

1638 
1667 
1697 

1641 
1670 
1700 

1644 
1673 
1703 

148 

1703 

1706 

1708 

1711 

1714 

1717 

1720 

1723 

1726 

1729 

1732 

149 

1732 

1735 

1738 

1741 

1744 

1746 

1749 

1752 

'755 

/ 

1761 

SMITHSONIAN  TABLES. 


TABLE1O  (continued) 

LOGARITHMS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

150 

1761 

1764 

1767 

1770 

1772 

1775 

1778 

1781 

1784 

1787 

1790 

'51 

1790 

'793 

1796 

1798 

1801 

1804 

1807 

1810 

1813 

1816 

1818 

1S2 
'53 

1818 
1847 

1821 

1850 

1824 
1853 

1827 
1855 

1830 

1858 

1833 
1861 

1836 
1864 

1838 
1867 

1841 
1870 

1844 
1872 

1847 
1875 

154 

1878 

1881 

1884 

1886 

1889 

1892 

1895 

1898 

1901 

1903 

155 

1903 

1906 

1909 

1912 

1915 

1917 

1920 

1923 

1926 

1928 

'93* 

156 

I931 

1934 

J937 

1940 

1942 

1945 

1948 

I951 

1953 

J956 

1959 

1959 

1962 

1967 

1970 

1973 

1976 

1978 

1981 

1984 

1987 

158 

1987 

1989 

1992 

1995 

1998 

2000 

2003 

2006 

2009 

2OII 

2014 

'59 

2014 

2017 

2019 

2O22 

2025 

2028 

2030 

2033 

2036 

2038 

2041 

160 

161 

2041 
2068 

2044 
2071 

2047 
2074 

2049 
2076 

2052 
2079 

2055 
2082 

2057 
2084 

2060 
2087 

2063 
2090 

2066 
2O92 

2068 
2095 

162 

2095 

2098 

2IOI 

2IO3 

2106  2109 

2III 

2114 

2117 

2119 

2122 

163 

2122 

2125 

2127 

2130 

2133 

2135 

2I38 

2140 

2143 

2146 

2148 

164 

2148 

2151 

2154 

2I56 

2159 

2162 

2164 

2167 

2170 

2172 

2175 

165 

2175 

2177 

2180 

2183 

2185 

2188 

2191 

2193 

2196 

2198 

2201 

166 

22OI 

2204 

22O6 

2209 

2212 

2214 

2217 

2219 

2222 

2225 

2227 

167 

2227 

2230 

2232 

2235 

2238 

2240 

2243 

2245 

2248 

2251 

2253 

1  68 

2253 

2256 

2258 

226l 

2263 

2266 

2269 

2271 

2274 

2276      2279 

169 

2279 

2281 

2284 

2287 

2289 

2292 

2294 

2297 

2299 

2302 

2304 

170 

2304 

2307 

2310 

23I2 

2315 

2317 

2320 

2322 

2323 

2327 

2330 

171 

233° 

2333 

2335 

2338 

2340 

2345 

2348 

2353 

2355 

172 

2355 

2358 

2360 

2363 

2365 

2368 

2370 

2373 

2375 

2378 

2380 

173 

238Q 

2383 

2385 

2388 

2390 

2393 

2395 

2398 

2400 

2403 

2405 

174 

2405 

2408 

2410 

2413 

2415 

2418 

2420 

2423 

2425 

2428 

2430 

175 

176 

2430 

2455 

2433 

2458 

2435 
2460 

2438 
2463 

2440 
2465 

2443 
2467 

2445 
2470 

2448 
2472 

2450 
2475 

2453 
2477 

2455 
2480 

177 

2480 

2482 

2485 

2487 

2490 

2492 

2494 

2497 

2499 

2502 

2504 

178 

2504 

2507 

2509 

25I2 

25M 

2516 

2519 

2521 

2524 

2526 

2529 

179 

2529 

253r 

2533 

2536 

2538 

2541 

2543 

2545 

2548 

2550 

2553 

180 

2553 

2555 

2558 

256O 

2562 

2565 

2567 

2570 

2572 

2574 

2577 

181 

2577 

2579 

2582 

2584 

2586 

2589 

2591 

2594 

2596 

2598 

26OI 

182 

2601 

2603 

2605 

2608 

26lO 

2613 

2615 

2617 

262O 

2622 

2625 

183 
184 

2625 
2648 

2627 
2651 

2629 
2653 

2632 
2655 

2634 
2658 

2636 
2660 

266? 

2641 
2665 

2643 

2646 
2669 

2648 
2672 

185 

2672 

2674 

2676 

2679 

268l 

2683 

2686 

2688 

2690 

2693 

2695 

186 

2695 

2697 

2700 

2702 

2704 

2707 

2709 

2711 

2714 

2716 

2718 

187 

2718 

2721 

2723 

2725 

2728 

2730 

2732 

2735 

2737 

2739 

2742 

1  88 
189 

2742 
2765 

2744 
2767 

2746 
2769 

2749 

2772 

2751 
2774 

2753 
2776 

2755 
2778 

2758 
2781 

2760 
2783 

2762 
2785 

fsl 

190 

•2788 

2790 

2792 

2794 

2797 

2799 

2801 

2804 

2806 

2808 

28lO 

191 

28lO 

2813 

28l5 

2817 

2819 

2822 

2824 

2826 

2828 

2831 

2833 

192 

2833 
2856 

2835 
2858 

2838 
2860 

2840 
2862 

2842 
2865 

2844 
2867 

2847 
2869 

2849 
2871 

2851 
2874 

2853 
2876 

2856 
2878 

194 

^2878 

2880 

2882 

2885 

2887 

2889 

2891 

2894 

2896 

2898 

2900 

195 

29OO 

2903 

2905 

2907 

2009 

2911 

2914 

2916 

2918 

2920 

2923 

196 

2923 

2925 

2927 

2929 

2931 

2934 

2936 

2938 

2940 

2942 

2945 

2945 

2947 

2949 

29S1 

2953 

2956 

29<;8 

2960 

2962   2964 

2967 

198 

2967     2969 

2971 

2973 

2975 

2978 

2980 

2982 

2984   2986 

2989 

199 

2989     2991 

2993 

2995 

2997 

2999 

3OO2 

3004 

3006 

3008 

3010 

SMITHSONIAN  TABLES. 


26 


TABLE  11. 
LOGARITHMS. 


N 

0123      456      789 

P.I 

> 

•L^w          TV       */       U          /       O       *7 

1 

2 

3 

4 

5 

10 

0000    0043  0086  0128    0170  0212  0253    0294  0334  0374 

4 

8 

12 

17 

21 

ii 

0414   0453  °492  O53£   0569  0607  0645   0682  0719  0755 

4 

8 

II 

15 

*9 

12 

0792   0828  0864  0899   0934  0969  1004   '038  1072  1  1  06 

3 

7 

10 

14 

J7 

13 

1139   1173  1206  1239   1271  1303  1335   1367  1399  1430 

3 

6 

IO 

*3 

16 

14 

1461    1492  1523  1553   1584  1614  1644   1673  '703  173* 

3 

6 

9 

12 

15 

15 

1761    1790  1818  1847   *875  1903  1931   1959  1987  2014 

3 

6 

8 

II 

M 

16 

2041     2068   2095   2122     2148   2175   2201     2227   2253   2279 

3 

5 

8 

II 

13 

17 
18 

23°4   2330  2355  2380   2405  2430  2455   2480  2504  2529 
2553   2377  2601  2625   2648  2672  2695   27i8  2742  2765 

2 

2 

5 
5 

7 
7 

10 

9 

12 
12 

19 

2788   2810  2833  2856   2878  2900  2923   2945  2967  2989 

2 

4 

7 

9 

II 

20 

3010   3032  3054  3075   3096  3118  3139   3160  3181  3201 

2 

4 

6 

8 

II 

21 

3222   3243  3263  3284   3304  3324  3345   3365  3385  3404 

2 

4 

6 

8 

IO 

22 
23 

3424   3444  3464  3483   3502  3522  3541    3560  3579  3598 
3617   3636  3655  3674   3692  3711  3729   3747  3766  3784 

2 

2 

4 
4 

6 

5 

8 
7 

10 

9 

24 

3802   3820  3838  3856   3874  3892  3909   3927  3945  3962 

2 

4 

5 

7 

9 

25 

3979   3997  4014  4031   4048  4065  4082   4099  4116  4133 

2 

3 

5 

7 

9 

26 

4150   4166  4183  4200   4216  4232  4249   4265  4281  4298 

2 

3 

5 

7 

8 

2£ 

43  i  4   433°  4346  4362   4378  4393  4409   44  2  5  444°  4456 

2 

3 

5 

6 

8 

28 

4472   4487  45°2  45  J  8   4533  4548  4564   4579  4594  4609 

2 

3 

5 

6 

8 

29 

4624   4639  4654  4669   4683  4698  4713   4728  4742  4757 

I 

3 

4 

6 

7 

30 

4771   4786  4800  4814   4829  4843  4857   4871  4886  4900 

3 

4 

6 

7 

3« 

4914   4928  4942  4955   4969  4983  4997   5011  5024  5038 

3 

4 

6 

7 

32 

5°5J   5°65  5°79  5°92   5I05  5"9  S132   5*45  5J59  5J72 

3 

4 

5 

7 

33 
34 

5l85   5!98  5211  5224   5237  525°  5263   5276  5289  53°2- 
5315   5328  5340  5353   5366  5378  539i   5403  54i6  5428 

3 

3 

4 
4 

5 
5 

6 
6 

35 

544i   5453  5465  5478   549°  5502  5514   5527  5539  5551 

2 

4 

5 

6 

36 

5563   5575  5587  5599   56"  5623  5^35   564?  5658  5670 

2 

4 

5 

6 

37 

5682   5694  5705  5717   5729  5740  5752   5763  5775  5786 

2 

3 

5 

6 

38 

5798   5809  5821  5832   5843  5855  5866   5877  5888  5899 

2 

3 

5 

6 

-39 

5911   5522.  5933  5944   5955  5966  5977   5988  5999  6010 

2 

3 

4 

6 

40 

6021   6031  6042  6053   6064  6075  6o85   6096  6107  6117 

2  ' 

3 

4 

5 

4i 

6128   6138  6149  6160   6170  6180  6r9i   6201  6212  6222 

2 

3 

4 

5 

42 
43 
44 

6232   6243  6253  6263   6274  6284  6294   6304  6314  6325 
6335   6345  6355  6365   6375  6385  6395   6405  6415  6425 
6435   6444  6454  6464   6474  6484  6493   6503  6513  6522 

2 
2 
2 

3 
3 
3 

4 
4 
4 

5 
5 
5 

45 

46 

6532   6542  6551  6561   6571  6580  6590   6599  6609  6618 
6628   6637  6646  6656   6665  6675  6684   6693  6702  6712 

2 
2 

3 
3 

4 
4 

5 
5 

47 

6721   6730  6739  6749   6758  6767  6776   6785  6794  6803 

2 

3 

4 

5 

48 

6812   6821  6830  6839   6848  6857  6866   6875  6884  6893 

2 

3 

4 

4 

49 

6902   6911  6920  6928   6937  6946  6955   6964  6972  6981 

2 

3 

4 

4 

50 

6990   6998  7007  7016   7024  7033  7042   7050  7059  7067 

2 

3 

3 

4 

51 

7076   7084  7093  7101   7110  7118  7126   7135  7143  7152 

2 

3 

3 

4 

52 

7160   7168  7177  7185   7193  7202  7210   7218  7226  7235 

2 

2 

3 

4 

53 

7243   7251  7259  7267   7275  7284  7292   73°°  73°8  73l6 

2 

2 

3 

4 

54 

7324   7332  7340  7348   7356  7364  7372   7380  7388  7396 

2 

2 

3 

4 

SMITHSONIAN  TABLES. 


TABLE    11    (continued}. 

LOGARITHMS. 


0-ioq       456       7     R     9 

] 

=>.  P 

• 

J.         A         O             YWW              /          O         *7 

1 

2 

3 

4 

5 

55 

7404   7412  7419  7427   7435  7443  7451   7459  7466  7474 

2 

2 

3 

4 

56 

7482   7490  7497  75°5   75'3  752°  7528   7536  7543  7551 

2 

2 

3 

4 

57 

7559   7566  7574  75§2   7589  7597  7604   7612  7619  7627 

2 

2 

3 

4 

58 

7634   7642  7649  7657   7664  7672  7679   7686  7694  7701 

I 

2 

3 

4 

59 

7709   7716  7723  7731   7738  7745  7752   7760  7767  7774 

I 

2 

3 

4 

60 

7782   7789  7796  7803   7810  7818  7825   7832  7839  7846 

2 

3 

4 

61 

7853   7860  7868  7875   7882  7889  7896   7903  79io  7917 

2 

3 

4 

62 

7924   793  i  793s  7945   7952  7959  7966   7973  798o  7987 

2 

3 

3 

63 

7993   8000  8007  8014   8021  8028  8035   8041  8048  8055 

2 

3 

3 

64 

8062   8069  8075  8082   8089  8096  8102   8109  8116  8122 

2 

3 

3 

65 

8129   8136  8142  8149   8156  8162  8169   8176  8182  8189 

2 

3 

3 

66 

8195   8202  8209  8215   8222  8228  8235   8241  8248  8254 

2 

3 

3 

67 

8261   8267  8274  8280   8287  8293  8299   8306  8312  8319 

2 

3 

3 

68 
69 

8325   8331  8338  8344   8351  8357  8363   8370  8376  8382 
8388   8395  8401  8407   8414  8420  8426   8432  8439  8445 

2 

2 

3 
3 

3 
3 

70 

8451   8457  8463  8470   8476  8482  8488   8494  8500  8506 

2 

2 

3 

7i 

8513   8519  8525  8531   8537  8543  8549   8555  8561  8567 

2 

2 

3 

72 

8573   8579  8585  8591   8597  8603  8609   8615  8621  8627 

2 

2 

3 

73 

8633   8639  8645  8651   8657  8663  8669   8675  8681  8686 

2 

2 

3 

74 

8692   8698  8704  8710   8716  8722  8727   8733  8739  8745 

2 

2 

3 

75 

8751   8756  8762  8768   8774  8779  8785   8791  8797  8802 

2 

2 

3 

76 

8808   8814  8820  8825   8831  8837  8842   8848  8854  8859 

2 

2 

3 

77 

8865   8871  8876  8882   8887  8893  8899   8904  8910  8915 

2 

2 

3 

78 

8921   8927  8932  8938   8943  8949  8954   8960  8965  8971 

2 

2 

3 

79 

8976   8982  8987  8993   8998  9004  9009   9015  9020  9025 

2 

2 

3 

80 

9031   9036  9042  9047   9053  9058  9063   9069  9074  9079 

2 

2 

3 

81 

9085   .9090  9096  9101   9106  9112  9117   9122  9128  9133 

2 

2 

3 

82 

9138   '9143  9149  9154   9159  9165  9170   9175  9180  9186 

2 

2 

3 

83 

9191   9196  9201  9206   9212  9217  9222   9227  9232  9238 

2" 

2 

3 

84 

9243   9248  9253  9258   9263  9269  9274   9279  9284  9289 

2 

2 

3 

85 

9294   9299  9304  9309   9315  9320  9325   9330  9335  9340 

2 

2 

3 

86 

9345   935°  9355  936o   9365  9370  9375   938o  9385  939° 

2 

2 

3 

87 

9395   9400  9405  9410   9415  9420  9425   9430  9435  9440 

0 

2 

2 

88 

9445   9450  9455  9460   9465  9469  9474   9479  9484  9489 

o 

2 

2 

89 

9494   9499  9504  9509   9513  9518  9523   9528  9533  9538 

o 

2 

2 

.90 

9542   9547  9552  9557   9562  9566  9571   9576  9581  9586 

0 

2 

2 

'91 

9590   9595  9600  9605   9609  9614  9619   9624  9628  9633 

o 

2 

2 

92 

.9638   9643  9647  9652   9657  9661  9666   9671  9675  9680 

o 

2 

2 

93 

9685   9689  9694  9699   9703  9708  9713   9717  9722  9727 

o 

2 

2 

94 

9731   9736  974i  9745   975°  9754  9759   9763  9768  9773 

0 

2 

2 

95 

9777   9782  9786  9791   9795  9800  9805   9809  9814  9818 

o 

2 

2 

96 

9823   9827  9832  9836   9841  9845  9850   9854  9859  9863 

o 

2 

2 

97 

9868   9872  9877  9881   9886  9890  9894   9899  9903  9908 

0 

2 

2 

98 

9912   9917  9921  9926   9930  9934  9939   9943  9948  9952 

0 

2 

2 

99 

9956   9961  9965  9969   9974  9978  9983   9987  9991  9996 

o 

2 

2 

SMITHSONIAN  TABLES. 


28 


TABLE  12. 
ANTILOGARITHMS. 


01    2    3      456      789 

] 

3.  p 

^       A       O          Y«/9          fO«7 

1 

2 

3 

4 

5 

.00 

IOOO     IOO2   IOO5   IOO7     IOO9  IOI2   IOI4     IOl6  IOI9  IO2I 

o 

0 

i 

.01 

1023     1026   1028   1030     1033   1035   1038     1040   1042   1045 

o 

o 

i 

.02 

1047    I05°  I052  I054   I057  I059  Io62    Io()4  Io67  Io69 

0 

o 

i 

•°3 

1072   1074  1076  1079   1081  1084  1086   1089  1091  1094 

0 

0 

i 

.04 

1096   1099  1102  1104   1107  1109  iii2   1114  1117  1119 

o 

I 

i 

.05 

1122     1125   1127   1130     1132   1135   1138     1140   1143   I1[46 

0 

.06 

1148   1151  1153  1156   1159  1161  1164   1167  tl&)  1172 

o 

.07 

1175    1178  1180  1183    1186  1189  1191    1194  1197  1199 

o 

.08 

1202     1205   1208   I2II     1213   I2l6   1219     1222   1225   I227 

0 

.09 

1230     1233   1236   1239     1242   1245   1247     1250   1253   1256 

o 

.10 

1259     1262   1265   1268     1271   1274   1276     1279   1282   1285 

o 

i 

.11 

1288     1291   1294   1297     1300   1303   1306     1309   1312   1315 

o 

2 

.12 

1318     1321   1324   1327     1330   1334   1337     1340   1343   1346 

o 

2 

•13 

1349   '352  *355  i358   !361  T365  1368   1371  1374  '377 

o 

2 

.14 

1380   1384  1387  1390   1393  1396  1400   1403  1406  1409 

o 

2 

.15 

.16 

1413   1416  1419  1422   1426  1429  1432   1435  1439  1442 
1445   J449  J452  J455   J459  1462  1466   1469  1472  1476 

o 
o 

2 

2 

•17 

1479   J483  T486  1489   1493  X496  1500   1503  1507  1510 

o 

2 

.18 

i5'4   I5J7  i521  J524   i528  I531  J535   J538  i542  1545 

0 

2 

.19 

J549   J552  !556  Z56°   J563  Z567  1570   1574  J578  1581 

o 

2 

.20 

^85   1589  I592  1596   1600  1603  1607   1611  1614  1618 

0 

j 

2 

.21 

1622   1626  1629  1633   1637  1641  1644   1648  1652  1656 

0 

2 

2 

.22 

1660   1663  1667  1671    1675  J^79  J683   1687  1690  1694 

o 

2 

2 

•23 

1698   1702  1706  1710   1714  1718  1722   1726  1730  1734 

o 

2 

2 

.24 

1738   1742  1746  1750   1754  1758  1762   1766  1770  1774 

o 

2 

2 

.25 

1778   1782  1786  1791    1795  T799  l803   1807  1811  1816 

o 

2 

2 

.26 

1820   1824  1828  1832   1837  1841  1845   l849  1854  1858 

o  . 

2 

2 

.27 

1862   1866  1871  1875   l879  1884  1888   1892  1897  1901 

o 

2 

2 

.28 

1905   1910  1914  1919   1923  1928  1932   1936  1941  1945 

0 

2 

2 

.29 

J95°   J954  J959  T963   1968.1972  1977   1982  1986  1991 

o 

2 

2 

.30 

1995   2000  2004  2009   2014  2018  2023   2028  2032  2037 

0 

I 

2 

2 

•31 

2042   2046  2051  2056   2061  2065  2070   2075  2080  2084 

o 

I 

2 

2 

•32 

2089   2094  2099  2104   2109  2113  2118   2123  2128  2133 

o 

I 

2 

2 

•33 

2138   2143  2148  2153   2158  2163  2168   2173  2178  2183 

o 

I 

2 

2 

•34 

2188   2193  2198  2203   2208  2213  2218   2223  2228  2234 

I 

I 

2 

2 

3 

.35 

2239   2244  2249  2254   2259  2265  2270   227?  2280  2286 

I 

2 

2 

3 

•36 

2291   2296  2301  2307   2312  2317  2323   2328  2333  2339 

I 

2 

2 

3 

•37 

2344   2350  2355  2360   2366  2371  2377    2382  2388  2393 

2 

2 

3 

•38 

2399   2404  2410  2415   2421  2427  2432   2438  2443  2449 

2 

2 

3 

•39 

2455   2460  2466  2472   2477  2483  2489   2495  25°°  25°6 

2 

2 

3 

.40 

.41 

2512   2518  2523  2529   2535  2541  2547   2553  2559  2564 
257°   2576  2582  2588   2594  2600  2606   2612  2618  2624 

2 
2 

2 
2 

3 
3 

.42 

2630   2636  2642  2649   2655  2661  2667   2673  2679  2685 

2 

2 

1 

•43 

2692   2698  2704  2710   2716  2723  2729   2735  2742  2748 

2 

3 

3 

•44 

2754   2761  2767  2773   2780  2786  2793   2799  2805  2812 

2 

3 

3 

.45 

2818  .  2825  2831  2838   2844  2851  2858   2864  2871  2877 

2 

3 

3 

.46 

2884   2891  2897  2904   2911  2917  2924   2931  2938  2944 

2 

3 

3 

•47 

2951   2958  2965  2972   2979  2985  2992   2999  3006  3013 

2 

3 

3 

.48 

3020   3027  3034  3041   3048  3055  3062   3069  3076  3083 

I 

2 

3 

4 

•49 

3090   3097  3105  3112   3119  3126  3133   3141  3M8  3*55 

I 

2 

3 

4 

SMITHSONIAN  TABLES. 


TABLE    12    (continued). 

ANTILOGARITHMS. 


0     123      456      789 

] 

3.  F 

1 

2 

3 

4 

5 

.50 

3162   3170  3177  3184   3192  3199  3206   3214  3221  3228 

i 

2 

3 

4 

•51 

3236   3243  3251  3258   3266  3273  3281    3289  3296  3304 

2 

2 

3 

4 

•S2 

3311   33T9  3327  3334   3342  3350  3357   3365  3373  3381 

2 

2 

3 

4 

•53 

3388   3396  3404  3412   3420  3428  3436   3443  3451  3459 

2 

2 

3 

4 

•54 

3467   3475  3483  349i   3499  35°8  35*6   3524  3532  3540 

2 

2 

3 

4 

.55 

3548   3556  3565  3573   358i  3589  3597   3606  3614  3622 

2 

2 

3 

4 

.56 

363!   3639  3648  3656   3664  3673  368i   369o  3698  3707 

2 

3 

3 

4 

•57 

37i5   3724  3733  374i   3750  3758  3767   3776  3784  3793 

2 

3 

3 

4 

•58 

3802   3811  3819  3828   3837  3846  3855   3864  3873  3882 

2 

3 

4 

4 

•59 

3890   3899  3908  3917   3926  3936  3945   3954  3963  3972 

2 

3 

4 

5 

.60 

3981   3990  3999  4009   4018  4027  4036   4046  4055  4064 

2 

3 

4 

5 

.61 

4074   4083  4093  4102   4111  4121  4130   4140  4150  4159 

2 

3 

4 

5 

.62 

4169   4178  4188  4198   4207  4217  4227   4236  4246  4256 

2 

3 

4 

5 

•63 
.64 

4266   4276  4285  4295   4305  4315  4325   4335  4345  4355 
4365   4375  4385  4395   44°6  4416  4426   4436  4446  4457 

2 
2 

3 
3 

4 
4 

5 
5 

.65 

4467   4477  4487  4498   4508  4519  4529   4539  4550  4560 

2 

3 

4 

5 

.66 

4571   4581  4592  4603   4613  4624  4634   4645  4656  4667 

2 

3 

4 

5 

.67 

4677   4688  4699  4710   4721  4732  4742   4753  4764  4775 

2 

3 

4 

.68 

4786   4797  4808  4819   4831  4842  4853   4864  4875  4887 

2 

3 

4 

6 

.69 

4898   4909  4920  4932   4943  4955  4966   4977  4989  5000 

2 

3 

5 

6 

.70 

5012   5023  5035  5047   5058  5070  5082   5093  5105  5117 

2 

4 

5 

6 

•7i 

5129   5140  5152  5164   5176  5188  5200   5212  5224  5236 

2 

4 

5 

6 

.72 

5248   5260  5272  5284   5297  5309  5321    5333  5346  5358 

2 

4 

5 

6 

•73 

5370   5383  5395  5408   5420  5433  5445   5458  5470  5483 

3 

4 

5 

6 

•74 

5495   55o8  5521  5534   5546  5559  5572   5585  5598  5610 

3 

4 

5 

6 

.75 

.76 

5623   5636  5649  5662   5675  5689  5702   5715  5728  5741 
5754   5768  5781  5794   5808  5821  5834   5848  5861  5875 

3 
3 

4 

4 

5 
5 

7 
7 

•77 
.78 

5902  5916  5929   5943  5957  5970   5984  5998  6012 
6026   6039  6053  6067   6081  6095  6TO9   6124  6138  6152 

3 
3 

4 
4 

I 

7 
7 

•79 

6166   6180  6194  6209   6223  6237  6252   6266  6281  6295 

3 

4 

6 

7 

.80 

6310   6324  6339  6353   6368  6383  6397   6412  6427  6442 

i 

3 

4 

6 

7 

.81 

6457   6471  6486  6501   6516  6531  6546   6561  6577  6592 

2 

3 

5 

6 

8 

.82 
•83 

6607   6622  6637  6653   6668  6683  6699   6714  6730  6745 
6761   6776  6792  6808   6823  6839  6855   6871  6887  6902 

2 

2 

3 
3 

5 
5 

6 
6 

8 
8 

.84 

6918   6934  6950  6966   6982  6998  7015   7031  7047  7063 

2 

3 

5 

6 

8 

.85 

7079   7096  7112  7129   7145  7161  7178   7194  7211  7228 

2 

3 

5 

7 

8 

.86 

7244   7261  7278  7295   7311  7328  7345   7362  7379  7396 

2 

3 

5 

7 

8 

•87 

7413   743°  7447  7464   7482  7499  75l6   7534  7551  75^8 

2 

3 

5 

7 

9 

.88 

7586   7603  7621  7638   7656  7674  7691   7709  7727  7745 

2 

4 

5 

7 

9 

.89 

7762   7780  7798  7816   7834  7852  7870   7889  7907  7925 

2 

4 

5 

7 

9 

.90 

7943   7962  7980  7998   8017  8035  8054   8072  8091  8110 

2 

4 

6 

7 

9 

.91 

8128   8147  8166  8185   8204  8222  8241   8260  8279  8299 

2 

4 

6 

8 

9 

.92 

8318   8337  8356  8375   8395  8414  8433   8453  8472  8492 

2 

4 

6 

8 

10 

•93 

8511   8531  8551  8570   8590  8610  8630   8650  8670  8690 

2 

4 

6 

8 

10 

•94 

8710   8730  8750  8770   8790  8810  8831   8851  8872  8892 

2 

4 

6 

8 

10 

.95 

89!3   8933  8954  8974   8995  9016  9036   9057  9078  9099 

2 

4 

6 

8 

10 

.96 

9120   9141  9162  9183   9204  9226  9247   9268  9290  9311 

2 

4 

6 

8 

ii 

'9l 

9333   9354  9376  9397   9419  9441  9462   9484  9506  9528 

2 

4 

7 

9 

ii 

.98 

955°   9572  9594  96r6   9638  9661  9683   9705  9727  9750 

2 

4 

7 

9 

ii 

•99 

9772   9795  98i7  9840   9863  9886  9908   9931  9954  9977 

2 

5 

7 

9 

ii 

SMITHSONIAN  TABLES. 


TABLE  13. 
ANTILOGARITHMS. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.900 

7943 

7945 

7947 

7949 

7951 

7952 

7954 

7956 

7958 

7960 

7962 

.901 

7962 

7963 

7965 

7967 

7969 

7971 

7973 

7974 

7976 

7978 

798o 

.902 

7980 

7982 

7984 

7985 

7987 

7991 

7993 

7995 

7997 

7998 

•9°3 

7998 

8000 

8002 

8004 

8006 

8008 

8009 

Sou 

8013 

8015 

8017 

.904 

8017 

8019 

8020 

8022 

8024 

8026 

8028 

8030 

8032 

8033 

8035 

.905 

8035 

8037 

8039 

8041 

8043 

8045 

8046 

8048 

8050  8052 

8054 

.906 

8054 

8056 

8057 

8059 

8061 

8063  8065 

8067 

8069  8070 

8072 

8072 

8074  8076 

8078 

8080 

8082 

8084 

8085 

8087 

8089 

8091 

.908 

8091 

8093  809  S 

8097 

8098 

8100 

8102 

8104 

8106 

8108 

8110 

.909 

8110 

8ui 

8113 

8115 

8117 

8119 

8121 

8123 

8125 

8126 

8128 

.910 

8128 

8130 

8132 

8134 

8136 

8138 

8140 

8141 

8143 

8i45 

8i47 

.911 

8147 

8149  8151 

8153 

8155 

8156 

8158 

8160 

8162 

8164 

8166 

.912 

8166 

8168  8170 

8171 

8173 

8i75 

8i77 

8179 

8181 

8183 

8185 

•913 

8185 

8187 

8188 

8190 

8192 

8194 

8196 

8198 

8200 

8202 

8204 

.914 

8204 

8205 

8207 

8209 

8211 

8213 

8215 

8217 

8219 

8221 

8222 

.915 

8222 

8224 

8226 

8228 

8230 

8232 

8234 

8236 

8238 

8239 

8241 

.916 

8241 

8243 

8245  8247 

8249 

8251 

8253 

8255 

8257 

8258 

8260 

.917 

8260 

8262 

$264  8266 

8268 

8270 

8272 

8274 

8276 

8278 

8279 

.918 

8279 

8281 

8283 

8285 

8287 

8289 

8291 

8293 

8295 

8297 

8299 

.919 

8299 

8300 

8302 

8304 

8306 

8308 

8310 

8312 

83H 

8316 

8318 

.920 

.921 

8318 
8337 

8320 
8339 

8321 
8341 

8323 
8343 

8325 
8344 

8327 
8346 

8329 
8348 

8331 
8350 

8333 

8352 

8335 
8354 

8337 
8356 

.922 

8356 

8358  8360 

8362 

8364 

8366 

8368 

8370 

8371 

8373 

8375 

•923 

8375 

8377 

8379  8381 

8383 

8385 

8387 

8389 

8391 

8393 

83951 

•924 

8395 

8397 

8398 

8400 

8402 

8404 

8406 

8408 

8410 

8412 

8414 

.925 

8414 

8416 

8418 

8420 

8422 

8424 

8426 

8428 

8429 

843  i 

8433 

.926 

8433 

8435 

8437  !  8439 

8441 

8443 

8445 

8447 

8449 

8451 

8453 

.927 

8453 

8455 

8457 

8459 

8461 

8463 

8464 

8466 

8468 

8470 

8472 

.928 

8472 

8474 

8476 

8478 

8480 

8482 

8484 

8486 

8488 

8490 

8492 

•929 

8492 

8494 

8496 

8498 

8500 

8502 

8504 

8506 

8507 

8509 

8511 

.930 

8511 

8513 

8515 

8517 

8519 

8521 

8523 

8525 

8527 

8529 

8531 

•93  * 

8531 

8533 

8535  8537 

8539 

8541 

8543 

8545 

8547 

8549 

8551 

•932 

8551 

8553 

8555 

8557 

8559 

8561 

8562 

8564  8566 

8568 

8570 

•933 

8570 

8572 

8574 

8576 

8578 

8580 

8582 

8584 

8586 

8588 

8590 

•934 

8590 

859? 

8594 

8596 

8598 

8600 

8602 

8604 

8606 

8608 

8610 

.935 

8610 

8612 

8614 

8616 

8618 

8620 

8622 

8624 

8626 

8628 

8630 

•936 

8630 

8632 

8634 

8636 

8638 

8640  8642 

8644 

8646 

8648 

8650 

•937 

8650 

8652 

8654 

8656 

8658 

8660  !  8662 

8664 

8666  8668 

8670 

•938 

8670 

8672 

8674 

8676 

8678 

8680 

8682 

8684 

8686 

8688 

8690 

•939 

8690 

8692 

8694 

8696 

8698 

8700 

8702    8704 

8706 

8708 

8710 

.940 

8710 

8712 

8714 

8716 

8718 

8720  8722   8724 

8726 

8728 

8730 

.941 

8730 

8732 

8734 

8736 

8738 

8740 

8742    8744 

8746 

8748 

8750 

•942 

8750 

8752 

8754 

8756 

8758 

8760 

8762 

8764 

8766 

8768 

8770 

•943 

8770 

8772 

8774 

8776 

8778 

8780 

8782 

8784 

8786 

8788 

8790 

•944 

8790 

8792 

8794 

8796 

8798 

8800 

8802 

8804 

8806 

8808 

8810 

945 

8810 

8813 

8815 

8817 

8819 

8821 

8823 

8825 

8827 

8829 

8831 

.946 

8831 

8831 

8835 

8837 

8839 

8841 

8843 

8845  8847 

8849 

8851 

•947 

8851    8853 

8855 

8857 

8859  8861 

8863 

8865   8Sf>7 

8870 

8872 

.948 

8872 

8874 

8876 

8878 

8880 

8882 

8884 

8886 

8888 

8890 

8892 

•949 

8892 

8894 

8896 

8898 

8900 

8902 

8904 

8906 

8908 

8910 

8913 

SMITHSONIAN  TABLES. 


TABLE    13  (continued). 

ANTILOGARITHMS. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1C 

.950 

•95  i 

8913 
8933 

8915 
8935 

8917 

8937 

8919 
8939 

8921 
8941 

8923 
8943 

8925 
8945 

8927 
8947 

8929 
8950 

8931 
8952 

8933 
8954 

•952 

8954 

8956 

8958 

8960 

8962 

8964 

8966 

8968 

8970 

8972 

8974 

•953 

8974 

8976 

8978 

8980 

8983 

8985 

8987 

8989 

8991 

8993 

8995 

•954 

8995 

8997 

8999 

9001 

9003 

9005 

9007 

9009 

9012 

9014 

9016 

.955 

9016 

9018 

9020 

9022 

9024 

9026 

9028 

9030 

9032 

9034 

9036 

.956 

9036 

9039 

9041 

9043 

9045 

9047 

9049 

9Q51 

9053 

9055 

9057 

•957 

9C57 

9°59 

9061 

9064 

9066 

9068 

9070 

9072 

9074 

9076 

9078 

•958 

9078 

9080 

9082 

9084 

9087 

9089 

9091 

9093 

9095 

9097 

9099 

•959 

9099 

9101 

9103 

9I05 

9108 

9110 

9112 

9114 

9116 

9118 

9120 

.960 

9120 

9122 

9124 

9126 

9129 

9131 

9133 

9135 

9M7 

9139 

9141 

.961 

9141 

9'43 

9'45 

9*47 

9r5° 

9152 

9154 

9156 

9158 

9160 

9162 

.962 

9162 

9164 

9166 

9169 

9171 

9173 

9J75 

9177 

9179 

9181 

9183 

•963 

9183 

9185 

9188 

91.90 

9192 

9194 

9196 

9198 

9200 

9202 

9204 

.964 

9204 

9207 

9209 

9211 

9213 

9215 

9217 

9219 

9221 

9224 

9226 

.965 

9226 

9228 

9230 

9232 

9234 

9236 

9238 

9241 

9243 

9245 

9247 

.966 

9247 

9249 

9251 

9253 

9256 

9258 

9260 

9262 

9264 

9266 

9268 

.967 

9268 

9270 

9273 

9275 

9277 

9279 

9281 

9283 

9285 

9288 

9290 

.968 

9290 

9292 

9294 

9296 

9298 

9300 

93°3 

93°5 

93°7 

93°9 

9311 

.969 

93" 

9313 

9315 

9320 

9322 

9324 

9326 

9328 

933° 

9333 

,970 

9333 

9335 

9337 

9339 

934i 

9343 

9345  . 

9348 

9350 

9352 

9354 

.971 

9354 

9356 

9358 

9361 

9363 

9365 

9367 

9369 

937i 

9373 

9376 

•972 

9376 

9378 

938o 

9382 

9384 

9386 

9389 

939  i 

9393 

9395 

9397 

•973 

9397 

9399 

9402 

9404 

9406 

9408 

9410 

9412 

9417 

9419 

•974 

9419 

942i 

9423 

9425 

9428 

943° 

9432 

9434 

9436 

9438 

9441 

.975 

9441 

9443 

9445 

9447 

9449 

945  i 

9454 

9456 

9458 

9460 

9462 

.976 

9462 

9465 

9467 

9469 

9473 

9475 

9478 

9480 

9482 

9484 

•977  . 

9484 

9486 

9489 

949  1 

9493 

9495 

9497 

9499 

9502 

9504 

9506 

•978 

9506 

9508 

9510 

95T3 

95T5 

95!7 

9S19 

9524 

9526 

9528 

•979 

9528 

953° 

9532 

9535 

9537 

9539 

954i 

9543 

9546 

9548 

955° 

980 

955° 

9552 

9554 

9557 

9559 

956i 

9563 

9565 

9568 

9570 

9572 

.981 

9572 

9574 

9576 

9579 

9581 

9583 

9585 

9587 

959° 

9592 

9594 

.982 

9596 

9598 

9601 

9603 

9605 

9609 

9612 

9614 

9616 

•983 

9616 

9618 

9621 

9623 

9625 

9627 

9629 

9632 

9634 

9636 

9638 

.984 

9638 

9641 

9643 

9645 

9647 

9649 

9652 

9654 

9656 

9658 

9661 

.985 

9661 

9663 

9665 

9667 

9669 

9672 

9674 

9676 

9678 

9681 

9683 

.986 

9683 

9685 

9687 

9689 

9692 

9694 

9696 

9698 

9701 

9703 

9705 

.987 

9705 

9707 

9710 

9712 

97  H 

9716 

9719 

9721 

9723 

9725 

9727 

.988 

9727 

973° 

9732 

9734 

97  36 

9739 

974i 

9743 

9748 

9750 

.989 

975° 

9752 

9754 

9757 

9759 

9761 

9763 

9766 

9768 

9770 

9772 

.990 

9772 

9775 

9777 

9779 

9781 

9784 

9786 

9788 

9790 

9793 

9795 

•99  * 

9795 

9797 

9799 

9802 

9804 

9806 

9808 

9811 

9813 

9815 

9817 

.992 

9817 

9820 

9822 

9824 

9827 

9829 

9831 

9833 

9836 

9838 

9840 

i  -993 

9840 

9842 

9845 

9847 

9849 

9851  9854 

9856 

9861 

9863 

•994 

9863 

9865 

9867 

9870 

9872 

9874 

9876 

9879 

98^1 

9883 

9886 

.995 

9886 

9888 

9890 

9892 

9895 

9897 

9899 

9901 

9904 

9906 

9908 

.996 

9908 

9911 

9913 

9917 

9920 

9922 

9924 

9927 

9929 

993  l 

•997 

993  r 

9933 

9936 

993» 

9940 

9945 

9947 

9949 

9952 

9954 

.998 

9954 

9956 

9959 

9961 

9963 

9966 

9968 

9970 

9972 

9975 

9977 

i  -999 

9977 

9979 

9982 

9984 

9986 

9988 

9991 

9993 

9995 

0000 

SMITHSONIAN  TABLES. 


TABLE  14. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 

(Taken  from  B.  O.  Peirce's  "  Short  Table  of  Integrals,"  Ginn  &  Co.) 


3^ 

U% 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

2* 

O 

Nat.    Log. 

Nat.    Log. 

Nat.    Log. 

Nat.     Log. 

o.oooo 

0°00' 

.OOOO    00 

I.  OOOO  O.OOOO 

.OOOO    00 

oo       oo   !  9O°OO' 

1.5708 

0.0029 

10 

.0029  7.4637 

i.  oooo  .oooo  .0029  7.4637 

343-77   2.5363!  '  50 

0.0058 

20 

.0058  .7648 

i.  oooo  .oooo  .0058  .7648 

171.89    .2352,;   40 

1.5650 

0.0087 

3° 

.0087  .9408 

i.  oooo   .oooo  .0087   .9409 

114-59    -0591    30 

1.5621 

0.0116 

40 

.0116  8.0658 

.9999  .oooo  i  .0116  8.0658 

85.940   1.9342      20 

'.5592 

0.0145 

50 

.0145  .1627 

.9999  .oooo 

.0145  .1627 

60.75°   -8373    10 

'•5563 

0.0175 

I°00' 

.0175  8.2419 

.9998  9.9999 

.0175  8.2419 

57.290  1.7581  89°oo' 

'•5533 

0.0204 

IO 

.0204  .3088 

.9998  .9999 

.0204   .3089 

49.104   .6911    50 

1-5504 

0.0233 
0.0262 

20 

30 

.0233  .3668 

.0262  .4179 

•9997  -9999 
•9997  -9999 

•0233  -3669 

.0262  .4181 

42.964   .6331 
38.188   .5819 

40 
30 

J-5475 
1.5446 

0.0291 

40 

.0291  .4637 

.9996  .9998 

.0291  .4638 

34-368   .5362 

2O 

I-54I7 

0.0320 

50 

.0320  .5050 

•9995  -9998 

•0320  .5053 

31.242   -4947J   I0 

1.5388 

0.0349 

2°00' 

•0349  8.5428 

•9994  9-9997 

•0349  8.5431. 

28.636  1.4569 

S8°oo' 

'•5359 

0.0378 

IO 

•0378  .5776 

•9993  -9997 

•0378  .5779 

26.432   .4221 

50 

0.0407 

20 

.0407  .6097 

•9992  -9996 

.0407   .6101 

24.542   .3899 

40 

1.5301 

0.0436 

30 

.0436  .6397 

.9990  .9996 

.0437  .6401 

22-904   -3599 

3° 

1.5272 

0.0465 

40 

.0465  .6677 

•9989  -9995 

.0466  .6682 

21.470   .3318 

20 

1-5243 

0.0495 

50 

.0494  .6940 

.9988  .9995 

.0495  -6945 

20.206   .3055 

10 

0.0524 

3°oo' 

.0523  8.7188 

.9986  9.9994 

•0524  8.7194 

19.081   1.2806 

87°oor 

1.5184 

0-0553 

IO 

•0552  .7423 

.9985  .9993 

•0553  -7429 

18.075   -2571 

50 

i-5i55 

0.0582 

20 

.0581  .7645 

.9983  .9993 

.0582   .7652 

17.169   .2348 

40 

1.5126 

0.06  1  1 

30 

.0610  .7857 

.9981   .9992 

.0612   .7865 

16.350   .2135 

3° 

I-5°97| 

0.0640 

40 

.0640  .80  ?9 

.9980  .9991 

.0641  .8067 

,  15.605   .1933 

20 

1.5068 

0.0669 

50 

.0669  .8251 

•9978  -9990 

.0670   .8261 

14.924   .1739 

IO 

I-5°39 

0.0698 

4°oo' 

.0698  8.8436 

.9976  9.9989 

.0699  8.8446 

14.301   1.1554 

86°oo' 

1.5010 

0.0727 

IO 

.0727  .8613 

•9974  -9989 

.0729  .8624 

I3-727   -1376 

5° 

1.4981 

0.0756 

20 

.0756  .8783 

.9971   .9988 

•0758  .8795 

13.197   .1205 

40 

I-4952 

0.0785 

3° 

.0785  .8946 

.9969  .9987 

.0787  .8960 

12.706   .1040 

3° 

1.4923 

0.0814 

40 

.0814   .9104 

.9967   .9986 

.0816  .9118 

12.251   .0882 

20 

1.4893 

0.0844 

50 

.0843  .9256 

.9964  .9985 

.0846  .9272 

11.826   .0728 

10  1.4864 

0.0873 

5°oo/ 

•0872  8.9403 

.9962  9.9983 

.0875  8.9420 

11.430  1.0580 

85°oo'  1-4835 

0.0902 

IO 

•0901   .9545 

•9959  -9982 

•0904  -9563 

11.059   .0437 

50  i  .4806 

0.0931 

20 

•0929  .9682 

•9957   -9981 

.0934  .9701 

10.712   .0299 

40  1.4777 

0.0960 

30  1 

•0958  .9816 

•9954  .9980 

.0963  .9836 

10.385   .0164 

30  1.4748 

0.0989 

40 

•0987   .9945 

•995  *   -9979 

.0992  .9966 

10.078    .0034      20 

1.4719 

0.1018 

50 

.1016  9.0070 

•9948  -9977 

.1022  9.0093 

9.7882  0.9907    10 

1.4690 

0.1047 

6°oo 

.1045  9.0192 

•9945  9-9976 

.1051   9.0216 

9.5144  0.9784  84°oo'  1.4661 

0.1076 

10 

.1074  .0311 

•9942  -9975 

,I080   .0336 

9.2553  .9664 

50  1.4632 

0.1105 

20 

.1103  .0426 

•9939  -9973 

.1110  .0453 

9.0098  -9547 

40  1.4603 

0.1134 
0.1164 

30 
40  i 

•1132   -0539 
.1161   .0648 

•9936  -9972 
.9932  .9971 

.1139  .0567 
.1169  .0678 

8.7769  .9433 
8-5555  -9322 

30 

20 

1-4574 
1-45441 

0.1193 

50 

.1190  .0755 

.9929  .9969 

.1198  .0786 

8.3450  .9214 

IO 

I45I5 

0.1222 

7°oo' 

.1219  9.0859 

.9925  9.9968 

.1228  9.0891 

8.1443  0.9109 

83°oo' 

1.4486 

0.1251 
0.1280 

IO 
20 

.1248  .0961 
.1276  .1060 

.9922   .9966 
.9918  .9964 

•I257   -0995 
.1287   .1096 

7-953°  .9OO5 
7.7704  .8904 

5° 
40 

1-4457 
1.4428 

0.1309 

30 

•1305  -"57 

.9914  .9963 

.1317   .1194 

7.5938  .8806 

30 

1.4399 

0-I338 

40 

.1334  .1252 

.9911   .9961 

.1346  .1291 

7.4287  .8709 

20 

1-4370 

0-1367 

50 

•T363  -'345 

•9907   -9959 

•1376  -1385 

7.2687  .8615 

10 

I-434I 

0.1396 

8°oo' 

.1392  9.1436 

•9903  9-9958 

.1405  9.1478 

7.1154  0.8522 

82°00' 

1.4312 

0.1425 

10 

.1421   .1525 

.9899  .9956 

•M35  ^569 

6.9682  .8431 

50 

1.4283 

0.1454 

20 

.1449   .1012 

.9894  .9954 

.1465  .1658 

6.8269  .8342 

40 

1.4254 

0.1484 

30 

.1478   .1697 

.9890  .9952 

•1495   -'745 

6.6912  .8255 

30 

1.4224 

O.I5I3 

40 

.1507   .1781 

.9886  .9950 

.1524   .1831 

6.5606  .8169 

20 

I-4I95 

0.1542 

50 

.1536   .1863 

.9881   .9948 

•1554  'i9l$ 

6.4348  .8085 

IO 

1.4166 

O.I57I 

9°oo' 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

8i°oo' 

I.4I37 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

Nat.      Log. 

0) 

AM 

j^ 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

w  y 

Off! 
O 

SMITHSONIAN  TABLES. 


TABLE  14  (.continued}. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


33 


1 

P| 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

Pi  *** 

O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.1571 

9°oo/ 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

8l°0& 

1.4137 

0.1600 

10 

.1593   .2O22 

•9872   -9944 

.1614   .2078 

6.1970   .7922 

5° 

1.4108 

0.1629 

20 

.1622   .2IOO 

.9868   .9942 

.1644   .2158 

6.0844   .7842 

40 

1.4079 

0.1658 

3° 

.1650   .2176 

.9863   .9940 

.1673   -2236 

5.9758   .7764 

30 

1.4050 

0.1687 

40 

.1679   .2251 

.9858   .9938  .1703   .2313 

5.8708   .7687 

20 

1.4021 

0.1716 

50 

.1708   .2324  .9853   .9936 

•'733  -2389 

5.7694   .7611 

IO 

1.3992 

0.1745 

I0°00' 

•1736  9-2397 

.9848  9.9934 

.1763  9.2463 

5-67I3  0.7537 

8o°oo' 

1-3963 

0.1774 

IO 

.1765   .2468 

•9843  -993  ' 

•'793  -2536 

5.5764   .7464 

50 

!-3934 

0.1804 

20 

.1794   .2538 

.9838  .9929 

.1823  .2609 

5.4845   .7391 

40 

1.3904 

0-1833 

30 

.1822   .2606 

•9833  .9927 

.1853  -2680 

5-3955  .7320 

30 

I-3875 

0.1862    40 

.1851   .2674 

.9827  .9924 

.1883  .2750 

5-3093  -7250 

20 

1.3846 

0.1891    50 

.1880   .2740 

.9822  .9922 

.1914  .2819 

5.2257  .7181 

10 

1.3817 

0.1920  ii°oo' 

.1908  9.2806 

.9816  9.9919 

.1944  9.2887 

5.1446  0.7113 

79°oo' 

1.3788 

0.1949 

IO 

.1937   .2870 

.9811   .9917 

•1974  -2953 

5.0658  .7047 

50 

1-3759 

0.1978 

20 

•1965   -2934 

.9805  .9914 

.2004  .3020  4.9894  .6980 

40 

1-373° 

0.2007 

3° 

.1994   .2997 

•9799  -99  i  2 

•2035  .3085  4-9r52  -6915 

3° 

1.3701 

0.2036 

40 

.2O22   .3058 

•9793  --9909 

.2065  .3149 

4.8430  .6851 

20 

1.3672 

0.2065 

50 

•2051   .3119 

.9787   .9907 

.2095  .3212 

4.7729  -6788 

10 

1.3643 

0.2094 

I2°00' 

•2079  9-3J79 

.9781  9.9904 

.2126  9.3275 

4.7046  0.6725 

78°oo' 

1.3614 

0.2123 

IO 

.2108  .3238 

•9775  -9901 

•2156  -3336  4.6382  .6664 

50 

I-3584 

0.2153 

20 

.2136  .3296 

.9769  .9899 

.2186  .3397 

4.5736  .6603 

40 

1-3555 

0.2182 

30 

.2164  .3353 

.9763  .9896 

.2217   .3458 

4.5107  .6542 

3° 

1-3526 

O.22II 

40 

.2193  .3410 

•9757   -9893 

•2247   .35*7 

4.4494  .6483 

20 

1-3497 

0.2240 

50 

.2221    .3466 

.9750  .9890 

.2278  .3576 

4.3897  .6424 

10 

1.3468 

0.2269 

13000' 

.2250  9.3521 

•9744  9-9887 

.2309  9.3634 

4-33  i  5  0-6366 

77°00' 

J-3439 

0.2298 

IO 

.2278   -3575 

•9737   -9884 

.2339  .3691 

4.2747  .6309 

50 

1.3410 

0.2327 

20 

.2306   .3629 

.9730  .9881 

.2370  .3748 

4.2193  .6252 

40 

1.3381 

0.2356 
0-2385 

30 
40 

.2334   .3682 
•2363   -3734 

.9724   .9878 
•97i7   -9875 

.2401   .3804 
•2432  -3859 

4.1653  .6196 
4.1126  .6141 

30 

20 

1-3352 

0.2414 

5° 

.239I    .3786 

.9710  .9872 

.2462  .3914 

4.061  1  .6086 

IO 

1-3294 

0.2443 

i4°oo' 

•2419  9-3837 

.9703  9.9869 

.2493  9-3968 

4.0108  0.6032 

76°oo' 

1-3265 

0.2473 

10 

.2447   .3887 

.9696   .9866 

.2524  .4021 

3.9617  .5979 

50 

L3235 

O.25O2 

20 

•2476   -3937 

-9689   -9863 

.2555  .4074 

3.9136  .5926 

40 

1.3206 

0.2531 

30 

.2504   .3986 

.9681   .9859 

.2586  .4127 

3.8667  .5873 

30 

I.3I77 

0.2560 

40 

•2532   4035 

.9674   .9856 

.2617   .4178 

3.8208  .5822 

20 

1.3148 

0.2589 

50 

.2560   .4083 

.9667   .9853 

.2648  .4230 

3-776o  .5770 

10 

1.3119 

0.26l8 

1  5°oo/ 

.2588  9.4130 

.9659  9.9849 

.2679  9.4281 

37321  0.5719 

75°oo/ 

1.3090 

0.2647 

IO 

.2616   4177 

.9652   .9846 

.2711   .4331 

3.6891  .5669 

50 

1.3061 

0.2676 

20 

.2644   .4223 

.9644   .9843 

.2742  .4381 

3.6470  .5619 

40 

1-3032 

0.2705 

30 

.2672    .4269 

.9636  .9839 

.2773  .4430 

3-6059  -5570 

3° 

1-3003 

0.2734 

40 

.2700   .4314 

.9628   .9836 

.2805  .4479 

3.5656  .5521 

20 

1.2974 

0.2763 

5° 

•2728   -4359 

.9621   .9832 

.2836  .4527 

3.5261  .5473 

10 

1-2945 

0.2793 

i6°oo' 

.2756  9.4403 

.9613  9.9828 

•2867  9-4575 

3.4874  0.5425 

74°oo' 

1.2915 

O.2822 

IO 

.2784   .4447 

.9605  .9825 

.2899   .4622 

3-4495  .5378 

50 

1.2886 

0.2851 
0.2880 

20 
3° 

.2812   .4491 
.2840   .4533 

.9596  .9821 
.9588  -.9817 

.2931   .4669 
.2962   .4716 

3.4124  .5331 
3-3759  -5284 

40 
30 

1.2857 
1.2828 

0.2909 

40 

.2868   .4576 

.9580  .9814 

.2994  .4762 

3.3402  .5238 

20 

1.2799 

0.2938 

50 

.2896   .4618 

.9572  .9810 

.3026  .4808 

3.3052   .5192 

IO 

1.2770 

0.2967 
0.2996 

I7°00' 
IO 

.2924  9.4659 
.2952   .4700 

•9563  9-98o6 
•9555  -9802 

•3°57  9-4853 
.3089  .4898 

3.2709  0.5147 
3.2371   .5102 

73°oo> 
50 

1.2741 
1.2712 

0.3025 

20 

.2979   .4741 

.9546  .9798 

.3121   .4943 

3.2041   .5057 

40 

1.2683 

0.3054 

30 

.3007    .4781 

•9537   -9794 

•3*53  -4987 

3.1716  .5013 

30 

1.2654 

0.3083 

40 

.3035   .4821 

.9528  .9790 

•3185  .5031 

3.1397   .4969 

20 

1.2625 

0.3H3 

5° 

.3062   .4861 

.9520  .9786 

•3217  -5075 

3.1084  .4925 

10 

1-2595 

0.3142 

i8°oo' 

.3090  94900 

.9511  9.9782 

.3249  9.5118 

3.0777  0.4882 

72°00/ 

1.2566 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

w3 

, 

Wy 

QJ5 

COSINES 

SINES. 

COTAN- 
GENTS. 

TANGENTS 

o 

3< 

SMITHSONIAN  TABLES. 


34 


TABLE   14  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS, 


~g 

c/5 
ww 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS 

x< 

O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.3142 

i8°oo' 

.3090  9.4900 

.9511  9.9782 

.3249  9.5118 

3.0777  0.4882 

72°00' 

0.3171 

10 

.3118  .4939 

.9502   .9778 

.3281   .5161 

3.0473   .4839 

50 

I-2537 

0.3200 

20 

•3'45   -4977 

.9492   .9774 

.3314   .5203 

3.0178   .4797 

40 

1.2508 

0.3229 

30 

•3'73  -5015 

•9483   -97/0 

•3346   .5245 

2.9887   .4755 

3° 

1.2479 

0.3258 

40 

.3201   .5052 

•9474   -9765  O378   .5287 

2.9600   .4713 

20 

1.2450 

0.3287 

50 

.3228  .5090 

.9465   .9761  .3411   .5329 

2.9319   .4671 

10 

1.2421 

0.3316 

i9°oo' 

.3256  9.5126 

•9455  9-9757  -3443  9-537O 

2.9042  0.4630 

7i°oo' 

1.2392 

0-3345 

10 

•3283  -5163 

•9446  .9752  .3476  .5411 

2.8770   .4589 

5° 

1.2363 

0-3374 

20 

•33'  i   -5199 

.9436  .9748  .3508  .5451 

2.8502   .4549 

40 

0.3403 

30 

•3338  -5235  -9426  .9743  .3541   .5491 

2.8239   .4509 

30 

I-23°5 

0.3432 

40 

.3365  .5270  .9417   .9739  .3574  .5531 

2.7980   .4469 

20   1.2275 

0.3462 

50 

•3393  -5306 

•9407  -9734  -3607   .5571 

2.7725   -4429 

IO 

1.2246 

0.3491 

20°00' 

.3420  9.5341 

•9397  9-973°  -364O  9-56" 

2-7475  0-4389 

7o°oo' 

1.2217 

0.3520 

10 

•3448  -5375 

•9387  -9725  -3673  -5650 

2.7228   .4350 

5° 

1.2188 

0-3549 

20 

•3475  -5409  -9377   -972  1  .3706   .5689 

2.6985   .4311 

40 

1.2159 

0.3578 

30 

.3502  .5443  !  .9367  .9716  .3739  .5727 

2.6746   .4273 

3° 

1.2130 

0.3607 

40 

•3529  -5477  -9356  -9711  -3772  '.5766 

2.6511   .4234 

20 

I.2IOI 

0.3636 

50 

•3557  -55'°  .9346  .9706  |  .3805  .5804 

2.6279   .4196 

10 

I.2O72 

0.3665 

2I°00' 

•3584  9-5543 

•9336  9-9702  .3839  9.5842 

2.6051  0.4158 

69°oo' 

1.2043 

0.3694 

10 

.3611   .5576 

•9325  -9697  -3872  .5879 

2.5826   .4121 

5° 

I.2OI4 

0.3723 

20 

.3638  .5609  .9315  .9692  .3906  .5917 

2.5605   .4083 

40 

1.1985 

0.3752 

3° 

.3665  .5641  ;  .9304  .9687  .3939  .5954 

2.5386   .4046 

3° 

1.1956 

0.3782 
0.3811 

40 
50 

.3692  .5673  .9293  .9682  i  .3973  .5991 
.3719  .5704  .9283  .9677  .4006  .6028 

2.5172   .4009 
2.4960   .3972 

20 

IO 

I.I926 
I.I897 

0.3840 

22°00' 

.3746  9-5736  -9272  9-9672 

.4040  9.6064 

2.4751  0.3936 

68°oo' 

I.I868 

0.3869 

10 

•3773  -5767  -9261   .9667 

.4074   .6100 

2.4545   .3900 

5° 

1.1839 

0.3898 

2O 

.3800  .5798  .9250  .9661 

.4108   .6136 

2.4342   .3864 

40 

0.3927 

3° 

.3827   .5828  '  .9239  .9656 

.4142   .6172 

2.4142   .3828 

30 

!:!78? 

0.3956 

40 

•3854  -5859  :  -9228  .9651. 

.4176   .6208 

2-3945  -3792 

20 

1.1752 

0-3985 

50 

.3881   .5889  .9216  .9646 

.4210   .6243 

2.3750  -3757 

IO 

1.1723 

0.4014 

23°00' 

.3907  9.5919 

.9205  9.9640 

.4245  9.6279 

2-3559  0.3721 

67°oo' 

1.1694 

0.4043 
0.4072 

10 
20 

•3934  -5948 
.3961   .5978 

.9194  .9635 
.9182  .9629 

.4279   .6314 
.4314   .6348 

2.3369  .3686 
2.3183  .3652 

50 
4° 

1.1665 
1.1636 

0.4102 

3° 

.3987   .6007  .9171   -9624 

.4348   .6383 

2.2998  .3617 

30 

1.  1606 

0.4131 

40 

.4014  .6036  .9159  .9618 

.4383   .6417 

2.2817   .3581 

20 

1.1577 

0.4160 

50 

.4041   .6065  .9147   .9613 

.4417   .6452 

2.2637   .3548 

10 

1.1548 

0.4189 

24°00' 

.4067  9.6093 

.9135  9.9607 

.4452  9.6486 

2.2460  0.3514 

66°oo' 

1.1519 

0.4218 

IO 

.4094  .6121 

.9124  .9602 

.4487   .6520 

2.2286  .3480 

5° 

1.1490 

0.4247 

20 

.4120  .6149 

.9112  .9596 

•4522   .6553 

2.2113  .3447 

40 

1.1461 

0.4276 
0.4305 

30 
40 

.4147   .6177 
.4173  .6205 

.9100  .9590 
.9088  .9584 

•4557   -6587 
.4592  .6620 

2.1943  .3413 
2-1775  -3380 

30 

20 

1.1432 
.1403 

0.4334 

50 

.4200  .6232 

•9075  -9579 

.4628  .6654 

2.1609  .3346 

10 

1-1374 

0-4363 

25°00' 

.4226  9.6259 

•9063  9.9573 

.4663  9.6687 

2.1445  0.3313 

65°oo' 

1-1345 

0.4392 

IO 

.4253  .6286 

.9051   .9567 

.4699  .6720 

2.1283  -3280 

50 

1.1316 

0.4422 

20 

.4279  .6313 

.9038  .9561 

.4734  .6752 

2.1123  .3248 

40 

1.1286 

0.4451 

30 

•43°5  -6340 

.9026  .9555 

.4770  .6785 

2.0965  -3215 

30 

1-1257 

0.4480 

40 

.4331   .6366 

.9013  .9549 

.4806  .6817 

2.0809  -3  '83 

20 

1.1228 

0.4509 

5° 

•4358  .6392 

.9001   .9543 

.4841   .6850 

2-0655   .3150 

IO 

1.1199 

0.4538 

26°00' 

.4384  9.6418 

-8988  9-9537 

.4877  9.6882 

2.0503  0.3118 

64°oo' 

1.1170 

0.4567 

10 

.4410  .6444 

•8975  -953° 

.4913  .6914 

2-0353   -3086 

5° 

1.1141 

0.4596 

20 

.4436  .6470 

.8962   .9524 

.4950  .6946 

2.0204   -3OS4 

40 

I.I  I  12 

0.4625 

30 

.4462  .6495 

.8949  .9518 

.4986  .6977 

2.0057   .3023 

30 

I.I083 

0-4654 

40 

.4488  .6521 

.8936  .9512 

.5022   .7009 

1.9912   .2991 

20 

I.I054 

0.4683 

50 

.4514  .6546 

.8923  .9505 

•5°.59  -7040 

1.9768   .2960 

IO 

I.IO25 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°oo' 

1.0996 

Nat.    Log. 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

c/i 

~ri 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

O 

l< 

SMITHSONIAN  TABLES. 


TABLE  14   (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


35 


Q"3 

C/) 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

S« 

O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°00' 

1.0996 

0.4741 

IO 

.4566   .6595 

.8897   .9492 

.5132   .7103 

1.9486   .2897 

5° 

1.0966 

0.4771 

20 

.4592   .6620 

.8884   .9486 

•5'69  7134 

1.9347   .2866 

40 

1-°937 

0.4800 

3° 

.4617   .6644 

.8870   .9479 

.5206  .7165 

1.9210   .2835 

30 

1.0908 

0.4829 

40 

.4643  .6668 

-8857   -9473 

•5243  -7196 

1.9074   .2804 

20 

1.0879 

0.4858 

50 

.4669  .6692 

.8843   -9466 

.5280  .7226 

1.8940   .2774 

IO 

1.0850 

0.4887 

28°00/ 

.4695  9.6716 

.8829  9-9459 

•53!7  9-7257 

1.8807  0.2743 

62°00' 

1.0821 

0.4916 

10 

.4720  .6740 

•8816   .9453 

•5354  -7287 

1.8676   .2713 

5° 

1.0792 

0.4945 

20 

.4746  .6763 

.8802   .9446 

•5392  -73'7 

1.8546   .2683 

40 

1.0763 

0.4974 

3° 

.4772   .6787 

.8788   .9439 

.5430  .7348 

1.8418   .2652 

3° 

1-0734 

0.5003 

40 

.4797   .6810 

.8774   .9432 

.5467   .7378 

1.8291   .2622 

20 

1.0705 

0.5032 

50 

.4823  .6833 

.8760   .9425 

.5505  .7408 

1.8165   .2592 

10 

1.0676 

0.5061 

29°00' 

.4848  9.6856 

.8746.  9.9418 

•5543  9-7438 

1.8040  0.2562 

6i°oo' 

1.0647 

0.5091 

10 

.4874   .6878 

.8732'  .9411 

.5581   .7467 

I-79I7   -2533 

5° 

1.0617 

0.5120 

20 

.4899   .6901 

.8718   -9404 

.5619  .7497 

1.7796   .2503 

40 

1.0588 

0.5149 

3° 

.4924  .6923 

•8704  -9397 

•5658  -7526 

1.7675   .2474 

30 

1-0559 

0.5178 

40 

.4950  .6946 

.8689  .9390 

.5696  .7556 

1.7556   .2444 

20 

'•0530 

0-5207 

50 

.4975  .6968 

-8675  -9383 

•5735  7585 

1.7437   .2415 

IO 

1.0501 

0.5236 

30°oo' 

.5000  9.6990 

.8660  9.9375 

•5774  97614 

1.7321  0.2386 

6o°oo' 

.0472 

0.5265 

IO 

.5025   .7012 

.8646  .9368 

.5812   .7644 

1.7205   .2356 

5° 

•0443 

0.5294 

20 

•5050  '  -7033 

.8631   .9361 

•5851   -7673 

1.7090   .2327 

40 

.0414 

0-5323 

3° 

•5°75   -7055 

•8616  .9353 

.5890  .7701 

1.6977   -2299 

30 

•0385 

0-5352 

40 

.5100  .7076 

.8601   .9346 

•5930  -773° 

1.6864   .2270 

20 

•0356 

0.5381 

50 

•5I25  -7097 

•8587  .9338 

•5969  -7759 

1.6753   -2241 

10 

.0327 

0.5411 

3i°oo' 

.5150  9.7118 

•8572  9-9331 

.6009  9.7788 

1.6643  O.22I2 

59°oo' 

.0297 

0.5440 

IO 

•5'75  -7T39 

•8557  -9323 

.6048  .7816 

1.6534   .2184 

5° 

.0268 

0.5469 

20 

.5200  .7160 

.8542  .9315 

.6088  .7845 

1.6426   .2155 

40 

.0239 

0.5498 

3° 

•5225  -7181 

.8526  .9308 

.6128  .7873 

1.6319   .2127 

30 

.0210 

40 

.5250  .7201 

.8511   .9300 

.6168  .7902 

I.62I2   .2098 

20 

1.0181 

0.5556 

5° 

.5275  .7222 

.8496  .9292 

.6208  .7930 

I.6lO7   .2070 

IO 

1.0152 

0-5585 

32°00' 

.5299  9.7242 

.8480  9.9284 

.6249  9.7958 

1.6003  0.2042 

58°oo' 

1.0123 

0.5614 

IO 

.5324  .7262 

.-8465  .9276 

.6289  .7986 

I.59OO   .2OI4 

50 

1.0094 

0.5643 

20 

.5348  .7282 

.8450  .9268 

.6330  .8014 

1.5798   .1986 

40 

1.0065 

0.5672 
0.5701 

3° 

40 

•5373  -7302 
•5398  -7322 

.8434  .9260 
.8418  .9252 

.637  1   .8042 
.6412  .8070 

I-5697   -1958 

'•5597  -'93° 

3° 
20 

i  .0*036 
i  .0007 

0.5730 

50 

.5422  .7342 

.8403  .9244 

.6453  .8097 

1.5497  .1903 

10 

0.9977 

0.5760 

33000' 

.5446  9.7361 

•8387  9-9236 

.6494  9.8125 

1.5399  0.1875 

57°oo' 

0.9948 

0.5789 

10 

.5471   .7380 

.8371   .9228 

•6536  -8133 

1.5301   .1847 

50 

0.9919 

0.5818 

20 

.5495  .7400 

•8355  -9219 

.6577   .8180 

1.5204  .1820 

40 

0.9890 

0.5847 

3° 

•55*9  -7419 

•8339  -92H 

.6619  .8208 

1.5108  .1792 

30 

0.9861 

0.5876 

40 

•5544  .7438 

•8323  -9203 

.6661   .8235 

1.5013  .1765 

20 

0.9832 

0.5905 

50 

.5568  .7457 

.8307   .9194 

.6703  .8263 

1.4919  .1737 

IO 

0.9803 

0-5934 
0-5963 

34°oo' 

IO 

•5592  9-7476 
.5616  .7494 

.8290  9.9186 
.8274  .9177 

.6745  9.8290 
.6787   -8317 

1.4826  0.1710 
1.4733  .1683 

56°oo' 
50 

0.9774 
0-9745 

0.5992 

20 

.5640  .7513 

.8258  .9169 

.6830  .8344 

1.4641   .1656 

40 

0.9716 

0.602  1 

3° 

.5664  .7531 

.8241   .9160 

.6873  .837' 

1.4550  .1629 

30 

0.9687 

0.6050 
0.6080 

40 

5° 

.5688  .7550 
.5712  .7568 

.8225  .9151 
.8208  .9142 

.6916  .8398 
•6959  -8425 

1.4460  .1602 
1.4370  .1575 

20 

10 

0-9657 
0.9628 

0.6109 

35°oo' 

•5736  97586 

.8192  9.9134 

.7002  9.8452 

1.4281  0.1548 

55°oo' 

0.9599 

0.6138 

10 

.5760  .7604 

.8175  .9125 

.7046  .8479 

1.4193  .1521 

50 

0.95/0 

0.6167 

20 

.5783  .7622 

.8158  .9116 

.7089  .8506 

1.4106  .1494 

40 

0.9541 

0.6196 

3° 

.5807  .7640 

.8141   .9107 

•7133  -8533 

1.4019  .1467 

30 

0.9512 

0.6225 

40 

•5831   -7657 

.8124  .9098 

•7177   -8559 

1.3934  .1441 

20 

0.9483 

0.6254 

5° 

•5854  -7675 

8107  .9089 

7221   .8586 

1.3848  .1414 

IO 

0.9454 

0.6283 

36°oo' 

.5878  9.7692 

8090  9.9080 

.7265  9.8613 

1.3764  0.1387 

54°oo' 

0.9425. 

Nat.    Log. 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

:  W 

Arf 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

O 

P 

SMITHSONIAN  TABLES. 


TABLE  14  (continued). 

CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


I 

c/3 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

«« 

O 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

0.6283 

36°oo' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613 

.3764  0.1387 

54°oo' 

0.9425 

0.6312 

10 

.5901   .7710 

.8073   .9070 

.7310   .8639 

.3680   .1361 

50 

0.9396 

0.6341 
0.6370 

20 
3° 

.5925   .7727 
.5948   .7744 

.8056   .9061 
.8039   .9052 

•7355  -8666 
.7400  .8692 

•3597   -1334 
.3514  .1308 

40 

3° 

0.9367 
0-9338 

0.6400 

40 

.5972   .7761 

.8021   .9042 

•7445   -8718 

.3432   .1282 

20 

0.9308 

0.6429 

50 

•5995  7778 

.8004   .9033 

.7490   .8745 

•3351   -I255 

IO 

0.9279 

0.6458 

37°oo' 

•6018  9-7795 

.7986  9.9023 

•7536  9-877I 

.3270  0.1229 

53°oo' 

0.9250 

0.6487 

IO 

.6041   .7811 

.7969   .9014 

.7581   .8797 

.3190  .1203 

5° 

0.9221 

0.6516 

20 

.6065   .7828 

.7951   .9004 

.7627   .8824 

.3111   .1176 

40 

0.9192 

0.6545 

3° 

.6088  .7844 

•7934   -8995 

.7673   .8850 

.3032   .1150 

3° 

0.9163 

0.6574 

40 

.6111   .7861 

.7916  .8985 

.7720   .8876 

.2954  .1124 

20 

0.9134 

0.6603 

50 

.6134  .7877 

.7898   .8975 

.7766   .8902 

.2876  .1098 

10 

0.9105 

0.6632 
0.6661 

38°oo' 

IO 

•6157  97893 
.6180  .7910 

.7880  9.8965 
.7862   .8955 

.7813  9.8928 
.7860   .8954 

.2799  0.1072 
.2723  .1046 

52°00' 

5° 

0.9076 
0.9047 

0.6690 

20 

.6202  .7926 

.7844   .8945 

.7907   .8980 

.2647   .1020 

40 

0.9018 

0.6720 

3° 

.6225  .7941 

.7826  .8935 

.7954   .9006 

.2572   .0994 

30 

0.8988 

0.6749 

40 

.6248  .7957 

.7808   .8925 

.8002   .9032 

.2497  .0968 

20 

0.8959 

0.6778 

50 

.6271   .7973 

.7790  .8915 

.8050   .9058 

.2423  .0942 

10 

0.8930 

0.6807 

39°oo' 

.6293  9.7989 

.7771  9.8905 

.8098  9.9084 

.2349  0.0916 

5i°oo' 

0.8901 

0.6836 

IO 

.6316  .8004 

•7753  -8895 

.8146   .9110 

.2276  .0890 

5° 

0.8872 

0.6865 

20 

.6338  .8020 

.7735  .8884 

.8195   .9135 

.2203  .0865 

40 

0.8843 

0.6894 

3° 

.6361   .8035 

.7716  .8874 

.8243   .9161 

.2131   .0839 

3° 

0.8814 

0.6923 

40 

.6383  .8050 

.7698  .8864 

.8292   .9187 

.2059  .0813 

20 

0.8785 

0.6952 

50 

.6406  .8066 

.7679  .8853 

.8342   .9212 

.1988  .0788 

10 

0.8756 

0.6981 

40°oo' 

.6428  9.8081 

.7660  9.8843 

.8391  9.9238 

.1918  0.0762 

5o°oo' 

0.8727 

0.7010 

IO 

.6450  .8096 

.7642  .8832 

.8441   .9264 

.1847   .0736 

5° 

0.8698 

0.7039 

20 

.6472  .8111 

.7623  .8821 

.8491   .9289 

.1778  .0711 

40 

0.8668 

3° 

.6494  .8125 

.7604  .8810 

•8541   -93J5 

.1708  .0685 

3° 

0.8639 

0.7098 

40 

.6517   .8140 

.7585  .8800 

•8591   -9341 

.1640  .0659 

20 

0.8610 

0.7127 

5° 

•6539  -8l55 

.7566  .8789 

.8642   .9366 

.1571   .0634 

10 

0.8581 

0.7156 

4i°oo' 

.6561  9.8169 

•7547  9-8778 

•8693  9-9392 

.  1  504  0.0608 

49°oo' 

0.8552 

0.7185 

IO 

.6583  .8184 

.7528  .8767 

.8744  .9417 

.1436  .0583 

50 

0.8523 

0.72,14 

20 

.6604  .8198 

.7509  .8756 

.8796  .9443 

•J369  -°557 

40 

0.8494 

0.7243 

30 

.6626  .8213 

.7490  .8745 

.8847   -9468 

.1303  .0532 

3° 

0.8465 

0.7272 

40 

.6648  .8227 

•7470  .8733 

.8899  .9494 

.1237   .0506 

20 

0.8436 

0.7301 

50 

.6670  .8241 

.7451   .8722 

•8952   -95T9 

.1171   .0481 

10 

0.8407 

0.7330 

42°00' 

.6691  9.8255 

.7431  .9.8711 

.9004  9.9544 

.1106  0.0456 

48°oo' 

0.8378 

0.7359 

IO 

.6713  .8269 

.7412   .8699 

•9057   -9570 

.1041   .0430 

50  • 

0.8348 

0.7389 

20 

.6734  .8283 

.7392  -8688 

.9110  .9595 

.0977   .0405 

40 

0.8319 

0.7418 

30 

.6756  .8297 

•7373   -8676 

.9163  .9621 

•0913  -°379 

3° 

0.8290 

0-7447 

40 

.6777  .8311 

•7353  -8665 

.9217   .9646 

.0850  .0354 

20 

0.8261 

0.7476 

5° 

.6799  .8324 

•7333   -8653 

.9271   .9671 

.0786  .0329 

IO 

0.8232 

0.7505 

43°oo' 

.6820  9.8338 

.7314  9.8641 

.9325  9.9697 

.0724  0.0303 

47°oo' 

0.8203 

0-7534 

10 

.6841   .8351 

.7294  .8629 

.9380  .9722 

.0661   .0278 

50 

0.8174 

o-7563 

20 

.6862  .8365 

.7274  .8618 

•9435  -9747 

•0599  -0257 

40 

0.8145 

0.7592 

30 

.6884  .8378 

.7254  .8606 

.9490  .9772 

.0538  .0228 

3° 

0.8116 

0.7621 

40 

.6905  .8391 

.7234  .8594 

•9545  -9798 

.0477   .0202 

20 

0.8087 

0.7650 

50 

.6926  .8405 

.7214  .8582 

.9601   .9823 

.0416  .0177 

10 

0.8058 

0.7679 

44°oo' 

.6947  9.8418 

.7193  9.8569 

.9657  9.9848 

•0355  °-OI52 

46°oo/ 

0.8029 

0.7709 

IO 

.6967  .8431 

•7173  -8557 

.9713  .9874 

0295   .0126 

50 

0.7999 

0.7738 

20 

.6988  .8444 

•7153  -8545 

•9770  .9899 

0235   .0101 

40 

0.7970 

0.7767 
0.7796 

3° 
40 

.7009  .8457 
.7030  .8469 

•7133  -8532 
.7112  .8520 

.9827   .9924 
.9884  .9949 

0176  .0076 
0117   .0051 

30 
20 

0.7941 
0.7912 

0.7825 

50 

.7050  .8482 

.7092  .8507 

.9942  .9975 

0058   .0025 

IO 

0.7883 

0.7854 

45°oo' 

.7071  9.8495 

.7071  9.8495 

I.OOOO  O.OOOO 

I  .OOOO  O.OOOO 

45°oo/ 

0.7854 

Nat.   Log. 

Nat    Log. 

Nat.    Log. 

Nat.   Log. 

c/i 

-c/5 

COSINES. 

SINES. 

COTAN- 
GENTS 

TANGENTS. 

O 

2* 

SMITHSONIAN   TABLES. 


TABLE  15. 
CIRCULAR  (TRIGONOMETRIC)   FUNCTIONS. 


37 


C/3 
* 

< 

s 

< 
Pti 

o.oo 
.01 

.02 

•°3 

.04 

SINES. 

COSINES. 

TANGENTS 

COTANGENTS. 

DEGREES. 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

Nat.       Log. 

o.ooooo   —  oo 
.01000  7-99999 
.02000  8.30100 
.03000   -47706 
•03999   -6oi94 

I  .OOOOO   O.OOOOO 

0-99995  9-99998 
.99980   .99991 
•99955   -99980 
.99920   .99965 

—  oo     —  co 
o.oiooo  8.00001 
.02000   .30109 

.03001   .47725 
.04002   .60229 

oo       oo 
99-997   1-99999 
49-993    -69891 
33-323    -52275 
24.987    .39771 

oo°oo' 
oo  34 
01  09 
oi  43 
02  18 

°% 

.07 
.08 
.09 

0.04998  8.69879 
•05996   77789 
.06994   .84474 
.07991   .90263 
.08988   .95366 

0.99875  9.99946 
.99820   .99922 

•99755   -99894 
.99680   .99861 

•99595   -99824 

0.05004  8.69933 
.06007   -77867 
.07011   .84581 
.08017   .90402 

.09024  .95542 

19.983   1.30067 
16.647    -22133 
14.262    -15419 
12.473    -09598 
11.081    -04458 

02°52' 
03  26 

04  oi 

0435 
°5  °9 

O.IO 

.11 

.12 

•T3 
.14 

0.09983  8.99928 
.10978  9.04052 
.11971   .07814 
.12963   .11272 
.13954   .14471 

0.99500  9.99782 
.99396   .99737 
.99281   .99687 
.99156   .99632 
.99022   .99573 

0.10033  9.00145 
.11045   -043I5 
.12058   .08127 
.13074   .11640 
.14092   .14898 

9.9666  0.99855 
9.0542   .95685 
8.2933   -9J873 
7.6489   .88360 
7.0961   .85102 

^84' 

06  53 
07  27 
08  oi 

°;!l 

•17 
.18 
.19 

0.14944  9.17446 
.15932   .20227 
.16918   .22836 
.17903   .25292 
.18886   .27614 

0.98877  9.99510 
.98723   .99442 

•98558   -99369 
.98384   .99293 
.98200   .99211 

0.15114  9.17937 
.16138   .20785 
.17166   .23466 
.18197   .26000 
.19232   .28402 

6.6  1  66  0.82063 
6.1966   .7921; 
5.8256   .76534 
5.4954   .74000 
5-  '997   -71598 

o8°36' 
09  10 
09  44 
10  19 
!o  53 

O.2O 
.21 

.23 
.24 

0.19867  9.29813 
.20846   -31902 
.21823   .33891 
.22798   .35789 
•23770   -37603 

0.98007  9.99126 
.97803   .99035 
.97590   .98940 
•97367   -98841 
.97134   .98737 

0.20271   9.30688 
.21314   .32867 
.22362   .34951 
.23414   .36948 
.24472   .38866 

4.9332  0.69312 
4.6917   .67133 
4.4719   .65049 
4.2709   .63052 
4.0864   .61134 

II°28' 
12  02 
12  36 
I3  II 

1345 

°3 

.27 
.28 
.29 

0.24740  9.39341 
.25708   .41007 
.26673   -42607 
.27636   .44147 
.28595   .45629 

0.96891  9.98628 
.96639   .98515 

•96377   -98397 
.96106   -98275 
.95824   .98148 

0.25534  9.40712 
.26602   .42491 
.27676   .44210 

.28755.   -45872 
.29841   .47482 

3.9163  0.59288 
3-7592   .57509 
3-6i33   -55790 
3.4776   .54128 
3.3511   .52518 

I40i9' 

1454 
1528 
16  03 
1637 

0.30 

•31 
•32 

•33 
•34 

0.29552  9.47059 
.30506   .48438 
•3J457   -4977  T 
.32404   .51060 

•33349   -52308 

°-95534  9-98016 
•95233   -97879 
.94924   .97737 
.94604   -97591 
•94275   -97440 

0-30934  9-49043 
•32033   -50559 
•33  '39   -52034 
.34252   .53469 
•35374   -54868 

3.2327  0.50957 
3.1218   .49441 
3.0176   .47966 
2.9195   .46531 
2.8270   .45132 

17°!  i' 
17  46 
18  20 
18  54 
1929 

o-35 
•36 

:| 

•39 

0.34290  9.53516 
.35227   .54688 
.36162   .55825 
.37092   .56928 
.38019   .58000 

0-93937  9-97284 
•93590   .97123 
•93233   -96957 
.92866   .96786 
.92491   .96610 

0-36503  9-56233 
.37640   -57565 
.38786   .58868 
.39941   .60142 
.41105   -61390 

2-7395  0.43767 
2.6567   .42435 
2.5782   .41132 
2-5037   -39858 
2.4328   .38610 

20°03' 

2038 

21  12 
21  46 

22  21 

0.40 
.41 

.42 

;  -43 

•44 

0.38942  9.59042 
.39861   -60055 
.40776   .61041 
41687   .62000 
.42594   .62935 

0.92106  9.96429 
.91712   .96243 
.91309   .96051 
.90897   .95855 
.90475   .95653 

0.42279  9.62613 
.43463   .63812 
.44657   .64989 
.45862   .66145 
.47078   .67282 

2-3652  0.37387 
2.3008   .36188 
2-2393   -35011 
2.1804   -33855 
2.1241   .32718 

22°55/ 

23  29 
24  04 

2438 
25  13 

0-45 
.46 

•47 
.48 

•49 

0.43497  9-63845 
.44395   .64733 
.45289   .65599 
.46178   .66443 
.47063   .67268 

0.90045  9.95446 
.89605   .95233 

•89157   -95015 
.88699   .94792 
•88233   .94563 

0.48306  9.68400 
•49545   -69500 
•5°797   .70583 
.52061   .71651 

-53339   -72704 

2.0702  0.31600 
2.0184   .30500 
1.9686   .29417 
1.9208   .28349 
1.8748   .27296 

25°47' 

26  21 
2656 

27  30 
28  04 

o  50 

0.47943  9.68072 

0.87758  9.94329 

0.54630  9-73743 

1.8305  0.26257 

28°39' 

SMITHSONIAN  TABLES. 


TABLE    1  5  (continued). 

CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


RADIANS.  II 

SINES. 

COSINES. 

TANGENTS    I  COTANGENTS. 

DEGREES.  1 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

0.50 

0-47943   9-68072 

0.87758   9.94329 

0.54630   9-73743 

1.8305    0.26257 

2S°39' 

•51 

.48818    .68858 

.87274    .94089 

•55936    .74769 

.7878     -25231 

29  '3 

•52 

.49688    .69625 

.86782    .93843 

.57256    .75782 

.7465     .24218 

2948 

•53 

•50553    -70375 

.86281    .93591 

.58592    .76784 

.7067     .23216 

30  22 

•54 

.51414   .71108 

•85771   -93334 

•59943   -77774 

.6683     .22226 

3°  56 

o-55 

0.52269   9.71824 

0.85252  9.93071 

0.61311   9.78754 

1.6310    0.21246 

3I°3I/ 

•56 

.53119   .72525 

.84726   .92801 

•62695   .79723 

.5950     .20277 

32  05 

•57 

•53963   -73210 

.84190   .92526 

.64097   .80684 

.5601     .19316 

32  40 

.58 

.54802   .73880 

.83646   .92245 

•65517   -81635 

.5263     .18365 

33  H 

•59 

-55636   .74536 

.83094   .91957 

.66956   .82579 

•4935    -17421 

3348 

0.60 

0.56464  9.75177 

0.82534  9.91663 

0.68414  9.83514 

1.4617   0.16486 

34°23' 

.61 
.62 

.57287   .75805 
.58104   .76420 

.81965   .91363 
.81388   .91056 

.69892   .84443 
.71391   .85364 

•4308    .15557 
.4007    .14636 

34  57 
35  31 

•63 

.58914   .77022 

.80803   -9°743 

.72911   .86280 

.3715    .13720 

3606 

.64 

.59720   .77612 

.80210   .90423 

.74454   .87189 

.3431    .12811 

36  40 

0.65 

0.60519  9.78189 

0.79608  9.90096 

0.76020  9.88093 

1.3154   0.11907 

37°i5' 

.66 

.61312   .78754 

.78999   .89762 

.77610   .88992 

.2885    .11008 

37  49 

.67 

.62099   .79308 

.78382   .89422 

.79225   .89886 

.2622    .10114 

3823 

.68 

.62879   .7985  r 

•77757   -89074 

.80866   .90777 

.2366    .09223 

38  58 

-69 

.63654   .80382 

.77125   .88719 

.82534   .91663 

.2116    .08337 

3932 

0.70 

0.64422   9.80903 

0.76484  9.88357 

0.84229  9.92546 

1.1872   0.07454 

40°o6' 

-7i 

.65183   .81414 

.75836   .87988 

.85953   .93426 

.1634    .06574 

4041 

.72 

.65938   .81914 

.75181   .87611 

•87707   .94303 

.1402    .05697 

41  15 

•73 

.66687   .82404 

.74517   .87226 

.89492   .95178 

.1174    .04822 

41  5° 

•74 

.67429   .82885 

.73847   .86833 

.91309   .96051 

.0952    .03949 

42  24 

o-75 

0.68164  9.83355 

0.73169  9.86433 

0.93160  9-96923 

1.0734   0.03077 

42°58' 

.76 

.68892   .83817 

.72484   .86024 

.95045   -97793 

.0521    .02207 

4333 

•77 

.69614   .84269 

.71791   .85607 

•96967   .98662 

.0313    .01338 

44  07 

-78 

.70328   .84713 

.71091   .85182 

.98926  9.9953  1 

1.0109    .00469 

44  41 

•79 

.71035   .85147 

.70385   .84748 

i  .0092   0.00400 

0.99084  9.99600 

45  l6 

0.80 

0.71736  9.85573 

0.69671   9.84305 

1.0296   0.01268 

0.97121  9.98732 

45°5o' 

.81 

.72429   .85991 

.68950   .83853 

.0505    .02138 

.95197   .97862 

46  25 

.82 

.73115   .86400 

.68222   -83393 

.07  1  7    .03008 

•93309   -96992 

46  59 

•83 

•73793   -86802 

.67488   .82922 

•0934    -03879 

.91455   .96121 

47  33 

.84 

.74464   .87195 

.66746   .82443 

.1156    .04752 

•89635   -95248 

48  08 

0.85 

0.75128  9.87580 

0.65998  9.81953 

1.1383   0.05627 

0.87848  9-94373 

48°42' 

.86 

.75784   .87958 

.65244   .81454 

.1616    .06504 

.86091   -93496 

49  16 

.87 
.88 

.76433   .88328 
.77074   .88691 

.64483   .80944 
.63715   .80424 

.1853    .07384 
.2097    .08266 

.84365   .92616 
.82668   .91734 

49  51 
5025 

.89 

.77707   .89046 

.62941   .79894 

.2346    .09153 

.80998   .90847 

51  oo 

0.90 

0-78333  9-89394 

0.62161   9-79352 

1.2602   0.10043 

0-79355  9-89957 

5'°34' 

.91 

.78950   .89735 

•6i375   -78799 

.2864    .10937 

.77738   .89063 

52  08 

.92 

.79560   .90070 

.60582   .78234 

•3'33    'Il835 

.76146   .88165 

5243 

•93 

.80162   -90397 

•59783   -77658 

.3409    .12739 

.74578   .87261 

53  17 

-94 

.80756   .90717 

•58979   -77070 

.3692    .13648 

.73034   .86352 

53  51 

o-95 

0.81342  9.91031 

0.58168  9.76469 

1.3984   0.14563 

0.71511  9.85437 

54°26' 

.96 

.81919   .91339 

•57352   .75855 

.4284    .15484 

.70010   .84516 

5500 

•97 

.82489   .91639 

•56530   -75228 

.4592    .16412 

.68531   .83588 

5535 

.98 

.83050   .91934 

.55702   .74587 

.4910    .17347 

.67071   .82653 

5609 

.99 

.83603   .92222 

.54869   .73933 

.5237    .18289 

.65631   .81711 

5643 

1.  00 

0.84147  9.92504 

0.54030  9.73264 

1.5574   0.19240 

0.64209  9.80760 

57°i8' 

SMITHSONIAN  TABLES. 


TABLE    15    (.continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


39 


RADIANS.! 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES.  1 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

Nat.     Log. 

1.  00 

0.84147   9.92504 

0.54030   9.73264 

1.5574   0.19240 

0.64209   9.80760 

57°i8' 

.OI 
.02 

.84683    .92780 
.85211    -93°49 

.53186    .72580 
.52337    .71881 

.5922    .20200 
.6281    .21169 

.62806   .79800 
.61420    .78831 

57  52 
58  27 

•°3 

•8573°   -933  i  3 

.51482    .71165 

.6652    .22148 

.60051    .77852 

590i 

.04 

.86240   .93571 

.50622    .70434 

.7036    .23137 

.58699    .76863 

5935 

1.05 

0.86742  9-93823 

0-49757  9-69686 

1.7433   0.24138 

0.57362   9-75862 

60°  i  o' 

.06 

.87236   .94069 

.48887   .68920 

.7844    .25150 

.56040    .74850 

60  44 

.07 

.87720   .94310 

.48012   .68135 

.8270    -26175 

•54734   -73825 

61  18 

.03 

.88196   -94545 

•47133   -67332 

.8712    .27212 

.53441   .72788 

61  53 

.09 

.88663   -94774 

.46249   .66510 

.9171    .28264 

.52162   .71736 

6227 

I.IO 

0.89121-  9.94998 

0.45360  9.65667 

1.9648   0.29331 

0.50897  9.70669 

63°02' 

.11 

•89570   -952I6 

.44466   .64803 

2.0143    -30413 

.49644   .69587 

6336 

.12 

.90010   .95429 

•43568   -63917 

.0660    .31512 

.48404   .68488 

64  10 

•13 

.90441   .95637 

.42666   .63008 

.1198    .32628 

•47175   -67372 

6445 

•J4 

•90863   .95839 

.41759   .62075 

•1759    .33763 

.45959   .66237 

65  19 

'•15 

0.91276  9.96036 

0.40849  9.61118 

2.2345   0.34918 

0-44753  9-65082 

65°53' 

.16 

.91680   .96228 

•39934   -60134 

.2958    .36093 

•43558   -63907 

6628 

•17 

.92075   .96414 

.39015   .59123 

.3600    -37291 

.42373   .62709 

67  02 

.18 

.92461   -96596 

.38092   .58084 

•4273    -38512 

.41199   .61488 

67  37 

.19 

.92837   .96772 

.37166   -57015 

•4979   -39757 

.40034   .60243 

68  ii 

i.  20 

0.93204  9.96943 

0.36236  9.55914 

2.5722  0.41030 

0.38878  9.58970 

68°45' 

.21 

.93562   .97110 

.35302   .54780 

.6503   .42330 

•37731   -57670 

69  20 

.22 

.93910   .97271 

•34365   -53611 

.7328   .43660 

•36593   -56340 

69  54 

•23 

.94249   .97428 

.33424   .52406 

.8198   .45022 

•35463   -54978 

7028 

.24 

•94578   -97579 

.32480   .51161 

.9119   .46418 

•34341   -53582 

7i  03 

1.25 

0.94898  9.97726  0.31532  9.49875 

3.0096  0.47850 

0-33227  9-52  J  5° 

7i°37' 

.26 

.95209   .97868 

.30582   .48546 

.1133   .49322 

.32121   .50678 

72  12 

.27 

.95510   .98005 

.29628   -47[70 

.2236   .50835 

.31021   .49165 

7246 

.28 

.95802   -98137 

.28672   -45745 

.3413   -52392 

.29928   .47608 

73  20 

.29 

.96084   .98265 

.27712   .44267 

•4672   .53998 

.28842   .46002 

73  55 

I.30 

0.96356  9.98388 

0.26750  9.42732 

3.6021   0.55656  0.27762  9-44344 

74°29' 

•31 

.96618   .98506 

.25785   .41137 

.7471   -57369  i  -26687   -42631 

75  °3 

•32 

.96872   .98620 

.24818   .39476 

•9°33   -59*44  |  -25619   .40856 

7538 

•33 

.97115   .98729 

.  .23848   .37744 

4.0723   .60984   .24556   .39016 

7612 

•34 

.97348   .98833 

•22875   -35937    -2556   -62896 

•23498   -37104 

76  47 

i-35 

0-97572  9-98933 

0.21901  9.34046   4.4552  0.64887 

0.22446  9-35IJ3 

77W 

•36 

.97786   .99028 

.20924   .32064 

.6734   .66964 

•21398   -33036 

77  55 

•37 

.97991   .99119 

.19945   .29983 

•9l3l   -69135 

.20354   .30865 

78  3° 

•38 

.98185   .99205 

.18964   .27793 

5.1774   .71411 

.19315   .28589 

79  °4 

•39 

.98370   .99286 

.17981   .25482 

.4707   .73804 

.18279   .26196 

7938 

1.40 

0-98545  9-99363 

0.16997  9.23036 

5-7979  0.76327 

0.17248  9.23673 

80°  1  3' 

.41 

.98710   .99436 

.16010   .20440 

6.1654   .78996 

.16220   .21004 

8047 

.42 

•98865   .99504 

.15023   .17674 

6.5811   .81830 

.15195   .18170 

8l  22 

•43 

.99010   .99568 

.14033   .14716 

7.0555   .84853 

.14173   .15147 

•8  1  56 

•44 

.99146   .99627 

.13042   .11536 

7.6018   .88092   -13155   .11908 

82  30 

1.45 

0.99271  9.99682 

0.12050  9.08100 

8.2381  0.91583  0.12139  9.08417 

83°05' 

.46 

•99387   -99733 

.11057   .04364 

8.9886   .95369 

.11125   -04631 

83  39 

•47 

•99492   -99779 

.10063   .00271 

98874   .99508 

.10114   .00492 

84  13 

.48 

.99588   .99821 

.09067  8.95747 

10.983   1.04074 

.09105  8.95926 

8448 

49 

.99674   .99858 

.0807  1   .90692 

12.350    .09166 

.08097   .90834 

85  22 

1.50 

0.99749  9.99891 

0.07074  8.84965 

14.101   1.14926  0.07091  8.85074 

Q  PO  f^f 

°5  57 

SMITHSONIAN  TABLES. 


40 


TABLES     15   (continued)    AND     16. 

CIRCULAR   FUNCTIONS  AND   FACTORIALS. 
TABLE  15  (continued).  —  Circular  (Trigonometric)  Functions. 


RADIANS. 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES.  1 

Nat.            Log 

Nat.             Log 

Nat.             Log. 

Nat.             Log. 

1.50 

•51 
•52 
•53 

•54 

0-99749     9-9989I 
.99815        .99920 
.99871        .99944 
.99917        .99964 
•99953      -99979 

0.07074     8.84965 
.06076       -78361 
.05077        .70565 
.04079        .61050 
.03079       .48843 

14.101      1.14926 
16.428        -21559 
19.670        .29379 
24.498        .38914 
32.461        .51136 

0.07091      8.85074 
.06087        -78441 
.05084        .70621 
.04082       .6ro86 
.03081       .40864 

85^57' 
86  31 
87  05 
87  40 
88  14 

•56 

•59 

0.99978    9.99991 
0.99994    9-99997 

1.  00000      0.00000 

0.99996    9.99998 
0.99982    9.99992 

0.02079     8.31796 
.01080     8.03327 
.00080     6.90109 
-.00920     7.9639611 
-.01920     8.2833611 

48.078      1.68195 
92.621      1.96671 
1255.8          3.09891 

108.65      2-°36o3 
52.067     1.71656 

0.02080    8.31805 
.01080    8.03329 
.00080    6.90109 
-.00920    7-96397" 
-.01921     8.2834411 

88°49' 
8923 

89  57 
90  32 
91  06 

1.60 

0-99957    9-9998i 

-0.02920     8.4653811 

34-233     1-53444 

-0.02921     8.4655611 

9i°4o' 

90°==  1.570  7963  radians. 

TABLE   16.— Logarithmic  Factorials. 

Logarithms  of  the  products  1.2.3 n,  n  from  I  to  100. 

See  Table  iS'for  Factorials  I  to  20. 
See  Table  32  for  log.  r  (w+i),  values  of  n  between  I  and  2. 


«. 

log  (n!) 

n. 

log  («/) 

n. 

log  («/) 

n. 

log  («.') 

1 

2 

o.oooooo 
0.301030 

26 

27 

26.605619 

28.036983 

51 

52 

66.190645 
67.906648 

76 

77 

111.275425 
113.161916 

3 

0.778151 

28 

29.484141 

53 

69.630924 

78 

115.054011 

4 

1.380211 

29 

30.946539 

54 

71-363318 

79 

116.951638 

5 

2.079181 

30 

32.423660 

55 

73.103681 

80 

118.854728 

6 

2-857332 

31 

33.915022 

56 

74.851869 

81 

120.763213 

8 

3-702431 
4.605521 

32 
33 

35.420172 
36.938686 

3 

76.607744 
78.371172 

82 
83 

122.67/027 
124.596105 

9 

5-559763 

34 

38.470165 

59 

80.142024 

84 

126.520384 

10 

6.559763 

35 

40.014233 

60 

81.920175 

85 

128.449803 

11 

7.601156 

36 

41.570535 

61 

83-705505 

86 

130.384701 

12 

8.680337 

37 

43-  i  387  37 

62 

85.497896 

8/ 

132.323821 

J3 

9.794280 

38 

44.718520 

63 

87.297237 

88 

134.268303 

14 

10.940408 

39 

46-309585 

64 

89.103417 

89 

136.217693 

15 

12.116500 

40 

47.911645 

65 

90.916330 

90 

138.171936 

16 

13.320620 

41 

49.524429 

66 

92.735874 

91 

140.130977 

17 
18 

14.551069 
15.806341 

42 
43 

51.147678 

52.781147 

67 
68 

94.561949 
96.394458 

92 
93 

142.094765 
144.063248 

19 

17.085095 

44 

54.424599  i 

69 

98.233307 

94 

146.036376 

20 

18.386125 

45 

56.077812 

70 

100.078405 

95 

148.014099 

21 

19.708344 

46 

57.740570  ! 

71 

101.929663 

96 

149.996371 

22 

21.050767 

47 

59.412668 

72 

103.786996 

97 

151.983142 

23 

22.412494 

48 

61.093909 

73 

105.650319 

98 

I53-974368 

24 

23.792706 

49 

62.784105 

74 

107.51955°  ! 

99 

155.970004 

25 

25.190646 

50 

64.483075 

75 

109.394612  | 

IOO 

157.970004 

SMITHSONIAN   TABLES. 


TABLE  17. 
HYPERBOLIC  FUNCTIONS. 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u 

gd  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     LOR. 

O.OO 

.or 
.02 

•°3 
.04 

O.OOOOO    —  00 

.01000  8.00001 
.02000   .30106 
.03000   .47719 
.04001   .60218 

I  .OOOOO   O.OOOOO 
.OOOO5    .OOOO2 
.00020    .00009 
.OOO45    -OOO2O 
.00080    -00035 

0.00000    —  00 

.01000  7.99999 
.02000  8.30097 

.02999  .47699 

.03998   .60183 

00         00 
IOO.OO3    2.OOOOI 
50.007    1.69903 

33-343   1-52301 
25.013   1.39817 

oo°oo' 

o  34 
i  09 

1  43 
2  17 

°:o°l 

.07 
.08 
.09 

0.05002  8.69915 
.06004  .77841 
.07006   .84545 

.08009  .90355 
.09012  .95483 

I.OOI25   0.00054 
.OOlSo    .OOO/8 
.00245    .00106 
.00320    -00139 
.00405    .00176 

0.04996  8.69861 

.05993  -77763 

.06989   .84439 

.07983  .90216 
•08976  -95307 

20.017   1-30139 
16.687    -22237 
14.309   .15561 
12.527    .09784 
11.141    -04693 

2  5J 
3  26 
4  oo 

4  35 
5  09 

O.IO 

.11 

.12 

•13 
.14 

0.10017  9.00072 

.IIO22    .04227 

.12029  .08022 
.13037  .11517 
.14046  .14755 

I.OO5OO   O.OO2I7 
.00606    .OO262 
.00721    .00312 
.00846    .00366 
.00982    .00424 

0.09967  8.99856 
.10956  9-03965 
.11943  .07710 
.12927  .11151 
•13909  -14330 

10.0333  1.00144 
9.1275  0.96035 
8-3733   -92290 
7.7356   -88849 
7.1895   .85670 

5  43 
6  17 
652 
7  26 
8  oo 

1 

.19 

0.15056  9.17772 

.16068   .20597 
.17082   .23254 
.18097  .25762 

.19115   .28136 

I.OII27   0.00487 
.01283    .00554 
.01448    .00625 
.01624    .OO7OO 
.OlSlO    .00779 

0.14889  9.17285 
.15865   .20044 
.16838   .22629 

.17808  .25062 
•18775  -27357 

6.7166  0.82715 
6.3032   .79956 

5-9389   -77371 
5.6154   .74938 
5.3263   .72643 

834 
9  08 
9  42 
10  15 
10  49 

O.2O 
.21 
.22 

•23 
.24 

0.20134  9.30392 

•21155  -32541 
.22178  .34592 
•23203  .36555 
.24231  .38437 

I  .O2OO7   0.00863 
.O22I3    .00951 
.02430    .01043 
.02657    -01139 
.02894    -01239 

0.19738  9-29529 
•20697  .31590 
.21652  .33549 
•22603  .35416 
•23550  -37198 

5.0665  0.70471 
4.8317   .68410 
4.6186   .66451 
4.4242   .64584 
4.2464   .62802 

ii  23 
ii  57 

12  30 
13  04 

13  37 

°:ll 
% 

.29 

0.25261  9.40245 
.26294   .41986 

.27329  .43663 
.28367   .45282 
.29408  .46847 

1.03141   0.01343 
•03399    -QMS2 

.03667   .01  564 
.03946   .01681 
.04235   .01801 

0.24492  9.38902 
.25430  .40534 
.26362  .42099 
.27291  .43601 

.28213   .45046 

4.0830  0.61098 
3-9324   .59466 
3-7933   -57901 
3.6643   .56399 

3-5444   -54954 

14  ii 
14  44 
15  J7 
15  50 
16  23 

0.30 
•31 

•32 
•33 
•34 

0.30452  9.48362 
.31499  .4983° 
.32549  -51254 
.33602  .52637 

•34659  -53981 

1.04534  0.01926 
.04844  .02054 

.05164   .02187 

.05495  -02323 

.05836   .02463 

0.29131  9.46436 

.30044  .47775 
.30951  .49067 
.31852  .50314 
.32748  .51518 

34327  0.53564 
.3285   .52225 

•2309   -50933 
.1395   .49686 
.0536   .48482 

16  56 
17  29 
18  02 
18  34 
19  °7 

0-35 
•36 

% 

•39 

0.35719  9-55290 
.36783  .56564 
•37850  .57807 
.38921  .59019 

.39996   .60202 

1.  06188  0.02607 
.06550  .02755 
.06923  .02907 
.07307  .03063 

.07702   .03222 

0-33638  9.52682 
•34521  .53809 

•35399   -54899 
.36271   .55956 
.37136   .56980 

2.9729  0.47318 
.8968   .46191 
.8249   .45101 
.7570   .44044 
.6928   .43020 

i9  39 

2O  12 

20  44 

21  16 
21  48 

0.40 
.41 
.42 
•43 
•44 

0.41075  9.61358 
.42158  .62488 
.43246  .63594 
.44337  .64677 
.45434  .65738 

1.08107  0.03385 

•08523  -03552 
.08950  .03723 
.09388  .03897 
.09837  .04075 

0-37995  9-57973 
.38847   .58936 

•39693   -59871 
.40532   .60780 
.41364   .61663 

2.6319  0.42027 
.5742   .41064 
.5193   .40129 
.4672   .39220 
•4i75   -38337 

22  20 
22  52 
23  23 

23  55 
24  26 

0-45 
.46 

•47 
.48 

•49 

0.46534  9.66777 
.47640  .67797 
.48750  .68797 
.49865  .69779 
.50984  .70744 

1.102970  .04256 
.10768   .04441 
.11250   .04630 
.11743   .04822 
.12247   .05018 

0.42190  9.62521 
.43008   .63355 
.43820   .64167 
.44624   .64957 
.45422   .65726 

2.3702  0.37479 
.3251   .36645 
.2821   .35833 
.2409   .35043 
.2016   .34274 

24  57 
25  28 

25  59 
26  30 
27  01 

0.50 

0.52110  9.71692 

1.12763  0.05217 

0.46212  9.66475 

2.1640  0.33525 

27  31 

SMITHSONIAN  TABLES 


TABLE     17    (continued). 
HYBERBOLIC   FUNCTIONS. 


sinh.  u 

cosh,  u 

tanh.  u 

ooth.  u 

Nat,     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

0.50 

•51 

•52 
•53 
•54 

0.52110  9.71692 
.53240   .72624 

•54375   -73540 
.55516   .74442 
•56663   .75330 

1.12763  0.05217 
.13289   .05419 
.13827   .05625 
.14377    .05834 
.14938   .06046 

0.46212  9.66475 
.46995   .67205 
.47770   .67916 
.48538   .68608 
.49299   .69284 

2.1640   0.33525 
.1279    -32795 
.0934    .32084 
.0602    -31392 
.0284   .307  1  6 

27°3r 

28  02 

28  32 
29  02 

29  32 

°^ 

:§ 

•59 

0-57815  9-76204 
.58973   .77065 
.60137   .77914 
.61307   .7875! 
.62483   .79576 

1.15510  0.06262 
.16094   .06481 
.16690   .06/03 
.17297    .06929 
.17916   .07157 

0.50052  9.69942 
.50798   .70584 
.51536   .71211 
.52267   .71822 
.52990   .72419 

1.9979   0.30058 
.9686   .29416 
.9404   .28789 
.9133   .28178 
.8872   .27581 

30  02 

30  32 

31  01 

31  31 

32  oo 

0.60 
.61 
.62 

63 
.64 

0.63665  9.80390 
.64854   .81194 
.66049   -8l987 
.67251   .82770 
•68459   -83543 

1.18547   0.07389 
.19189   .07624 
.19844   .O/86l 
.20510   .08102 
.21189   .08346 

0-53705  9-73001 
•54413   -73570 
.55113   .74125 
.55805   .74667 
•56490   -751  97 

1.8620   0.26999 
.8378   .26430 
.8141;   .25875 

•7919   -25333 
.7702   .24803 

32  29 
32  58 

33  27 
33  55 
34  24 

0.65 
.66 
.67 
.68 
.69 

0.69675  9.84308 
.70897   .85063 
.72126   .85809 
.73363   -86548 
.74607   .87278 

1.21879  o.o8s93 
.22582   .08843 
.23297   .09095 
.24025   .09351 
.24765   .09609 

0.57167  9.75/15 
.57836   .76220 
.58498   .76714 
.59152   .77197 
.59798   .77669 

1.7493   0.24285 
.7290   .23780 
•7095   -23286 
.6906   .22803 
.6723   .22331 

34  52 
35  20 
3548 
36  16 
36  44 

0.70 

•7i 
.72 

•73 
•74 

0.75858  9.88000 
.77117   .88715 
.78384   .89423 
•79659   -90123 
.80941   .90817 

1.25517  0.09870 
.26282   .10134 
.27059   .10401 
.27849   .10670 
.28652   .10942 

0.60437  9.78130 
.61068   .78581 
.61691   .79022 
.62307   .79453 
.62915   .79875 

1.6546   0.21870 
.6375   .21419 
.6210   .20978 
.6050   .20547 
.5895    .20125 

37  " 
37  38 
3805 
38  32 
38  59 

I  0.75 
.76 
•77 
•78 
•79 

0.82232  9.91504 
.83530   .92185 
.84838   .92859 
•86153   .93527 
.87478   .94190 

1.29468  0.11216 
.30297   .11493 

•3"39   -"773 
.31994   .12055 
.32862   .12340 

0.63515  9.80288 
.64108   .80691 
.64693   .81086 
.65271   .81472 
.65841   .81850 

1.5744   0.19712 

•5599   -19309 
.5458   .18914 
.5321    .18528 
.5188   .18150 

39  26 

39  52 
40  19 

40  45 
41  ii 

\  0.80 
.81 
.82 

•83 
.84 

0.88811  9.94846 
.90152   .95498 
.91503   .96144 
.92863   .96784 
.94233   .97420 

1-33743  0.12627 
.34638   .12917 

•35547   -13209 
.36468   .13503 
.37404   .13800 

0.66404  9.82219 
.66959   .82581 

•67507   -82935 
.68048   .83281 
.68581   .83620 

1.5059   0.17781 

•4935    •174i9 
.4813    -17065 
.4696    .16719 
.4581    .16380 

4i  37 

42  02 
42  28 

42  53 
43  18 

!  is 

.87 

.88 
.89 

0.95612  9.98051 
.97000   .98677 

•98398   .99299 
.99806   .99916 
1.01224  0.00528 

1  -38353  0.14099 
.39316   .14400 
.40293   .14704 
.41284   .15009 
.42289   .15317 

0.69107  9.83952 
.69626   .84277 
.70137   .84595 
.70642   .84906 
.71139   .85211 

1.4470   0.16048 
.4362    .15723 
.4258    .15405 
.4156    .15094 
.4057    .14789 

43  43 
44  08 

44  32 
44  57 
45  21 

0.90 
.91 
.92 

•93 
•94 

1.02652  0.01137 
.04090   .01741 
•05539   -02341 
.06998   .02937 
.08468   .03530 

1.43309  0.15627 
•44342   .15939 
.45390   .16254 
.46453   .16570 
.47530   .16888 

0.71630  9.85509 
.72113   .85801 
.72590   .86088 
.73059   .86368 
.73522   .86642 

1.3961   0.14491 
.3867    .14199 
.3776    .13912 
.3687    .13632 
.3601    .13358 

45  45 
46  09 

46  33 
46  56 
47  20 

°$ 

•99 

1.09948  0.04119 
.11440   .04704 
.12943   .05286 
.14457   .05864 
.15983   .06439 

1.48623  0.17208 

•49729   -r753  i 
.50851   .17855 
.51988   .18181 
.53141   .18509 

0.73978  9.86910 
.74428   .87173 
.74870   .87431 
.75307   .87683 
.75736   .87930 

1.3517   0.13090 
.3436    .12827 
.3356    -12569 
.3279    .12317 
.3204    .12070 

47  43 
48  06 
48  29 
48  51 
49  M 

I.OO 

1.17520  0.07011 

1.54308  0.18839 

0.76159  9.88172 

1.3130   0.11828 

49  36 

SMITHSONIAN   TABLES. 


TABLE    17    (continued). 
HYPERBOLIC   FUNCTIONS. 


43 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth  u 

gd  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

1.  00 
.OI 
.02 

•03 
.04 

1.17520  0.07011 
.19069   -07580 
.20630   .08146 
.22203   -08708 
.23788   .09268 

1.54308   0.18839 
.55491    .19171 
.56689   .19504 
.57904   .19839 
.59134    .20176 

0.76159  9.88172 
.76576   .88409 
.76987   .88642 
.77391    .88869 
.77789   .89092 

1.3130   0.11828 
.3059    .11591 
.2989    .11358 
.2921    .11131 
.2855    .10908 

49036' 
49  58 

5O  21 

50  42 

51  04 

I>0| 
.06 

.07 
.08 
.09 

1.25386  0.09825 
.26996   .10379 
.28619   .10930 
.30254   .11479 
.31903   .12025 

1.60379   0.20515 
.61641    .20855 
.62919   .21197 
.64214   .21541 
.65525    .21886 

0.78181   9.89310 
.78566   .89524 
.78946   .89733 
.79320   .89938 
.79688   -90139 

1.2791   0.10690 
.2728    .10476 
.2667    .10267 
.2607    .10062 
.2549    .09861 

51  26 

51  47 
5208 
52  29 
52  5° 

1.  10 

.11 

.12 

•13 
.14 

1.33565  0.12569 
.35240   .13111 
.36929   .13649 
.38631   .14186 
.40347   .14720 

1.66852   0.22233 
.68196   .22582 
•69557    -22931 
.70934    .23283 
.72329   .23636 

0.80050  9-90336 
.80406   -90529 
.80757    .90718 
.8lIO2   -90903 
.81441    .91085 

1.2492   0.09664 
.2437   .  .09471 
.2383    .09282 
.2330    .09097 
.2279    .08915 

53  ii 
53  31 
53  52 
54  12 
54  32 

.l6 
.19 

1.42078  0.15253 
.43822   .15783 
.45581   .16311 
•47355   -16836 
.49143   .17360 

I.7374I   0.23990 
.75171    .24346 
.76618    -24703 
.78083    .25062 
•79565    ^5422 

0.81775  9.91262 
.82104   .91436 
.82427    .91607 
.82745   .91774 
.83058   .9193s 

1.2229   0.08738 
.2180    .08564 
.2132    .08393 
.2085    .08226 
.2040    .08062 

54  52 
55  ii 
55  3i 
55  50 
56  09 

1.20 
.21 
2^ 

•23 
.24 

1.50946  0.17882 
.52764   .18402 
.54598   .18920 
.56447   .19437 
.58311   .19951 

1.  81066  0.25784 
.82584    .26146 
.84121    .26510 
.85676    .26876 

.87250    .27242 

0.83365  9.92099 
.83668   .92256 
.83965   .92410 
.84258   .92561 
.84546   .92709 

1.1995   0.07901 
.1952    -07744 
.1910    .07590 
.1868    -07439 
.1828    .07291 

56  29 

56  47 
57  06 
57  25 
57  43 

l:ll 

.27 
.28 
.29 

1.60192  0.20464 
.62088   .20975 
.64001   .21485 
.65930   .21993 
.67876   .22499 

1.88842   0.27610 
.90454    .27979 
.92084    .28349 
.93734    .28721 
.95403    .29093 

0.84828  9.92854 
.85106   .92996 
•85380   .93135 
.85648   .93272 
•859*3   -93406 

1.1789   0.07146 
.1750    .07004 
.1712    .06865 
.1676    .06728 
.1640    .06594 

58  02 
58  20 
58  38 
58  55 
59  13 

T.30 

•31 

•32 

•33 
•34 

1.69838  0.23004 
.71818   .23507 
.73814   .24009 
.75828   .24509 
.77860   .25008 

1.97091   0.29467 
.98800    .29842 
2.00528    -30217 
.02276   .30594 
.04044    .30972 

0.86172  9.93537 
.86428   -93665 
.86678   .93791 
•86925   .93914 
.87167    .94035 

1.1605   0.06463 
•1570    -06335 
.1537    .06209 
.1504    .06086 
.1472    .05965 

59  3i 
59  48 

60  05 

60  22 

60  39 

i-35 

•36 

i 

•39 

1.79909  0.25505 
.81977   .26002 
.84062   .26496 
.86166   .26990 
.88289   -27482 

2.05833   0.31352 
.07643    .31732 
.09473    .32113 
.11324    .32495 
.13196   .32878 

0.87405  9.94154 
.87639   .94270 
.87869   .94384 
.88095   -94495 
.88317   .94604 

1.1441   0.05846 
.1410    .0573° 
.1381    .05616 

•i35T   -05505 
•1323   -05396 

60  56 
61  13 
61  29 
61  45 
62  02 

1.40 
.41 
.42 
•43 
•44 

1.90430  0.27974 
.92591   .28464 
.94770   .28952 
.96970   .29440 
.99188   .29926 

2.15090   0.33262 
•17005    .33647 
.18942    .34033 
.20900    .34420 
.22881    .34807 

0-88535  9.94712 
.88749   -94817 
.88960   .94919 
.89167   .95020 
.89370   .95119 

1.1295   0.05288 
.1268   .05183 
.1241    .05081 
.1215   .04980 
.1189   .04881 

62  18 

6234 
62  49 

63  05 
63  20 

1.45 
.46 

•47 
.48 

•49 

2.01427  0.30412 
.03686   .30896 

•05965   -3!379 
.08265   .31862 
.10586   .32343 

2.24884  0.35196 
•26910    .35585 
•28958    .35976 
.31029    .36367 
•33123   .36759 

0.89569  9.95216 
•89765   -95311 
•89958   .95404 
.90147   .95495 
•90332   .95584 

1.1165   0.04784 
.1140   .04689 
.1116   .04596 
•1093   -04505 
.1070   .04416 

63  36 
63  5i 

64  06 

64  21 

64  36 

|  1-50 

2.12928  0.32823 

2.35241   0.37151 

0.90515  9.95672 

1.1048   0.04328 

64  51 

SMITHSONIAN   TABLES. 


44 


TABLE  17  (continued). 
HYPERBOLIC    FUNCTIONS, 


u 

siiih.  u 

cosh.  u 

tanh.  u 

coth.  u 

gd.  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

1.50 

•51 
•52 
•53 
•54 

2.12928  0.32823 

•I5A9I  >333S3 

•'7676   .33781 
.20082   .34258 
.22510   .34735 

2.35241   0.37151 

•37382   -37545 
•39547   -37939 
•41736   .38334 
•43949   -3873° 

0.90515  9.95672 
.90694   .95758 
.90870   .95842 
.91042   .95924 
.91212   .96005 

1.1048   0.04328 
.1026    .04242 
.1005    .04158 
.0984    .040/6 
•0963    .03995 

64°  51' 

65  05 
65   2O 
65  34 
65  4» 

'3 

i 

•59 

2.24961   0.35211 
•27434   -35686 
.29930   .36160 
.32449   -36633 

•34991   -37105 

2.46186  0.39126 
.48448   .39524 

•50735   -39921 
.53047   .40320 
.55384   .40719 

0-9I379  9-96084 
.91542   .96162 
.91703   .96238 
.91860   .96313 
.92015   .96386 

1.0943   0.03916 
.0924    .03838 
•0905    -03762 
.0886    .03687 
.0868    .03614 

66  02 
66  16 
66  30 
66  43 

66  57 

1.60 
.61 
.62 

3 

2-37557  0.37577 
40146   .38048 
.42760   -38518 

•45397   -38987 
.48059   .39456 

2.57746  0.41119 
.60135   .41520 
.62549   .41921 
.64990   .42323 
.67457   .42725 

0.92167   9.96457 
.92316   .96528 
.92462   .96597 
.92606   .96664 
.92747   .96730 

1.0850   0.03543 
•0832    -03472 
.0815    .03403 
.0798    .03336 
.0782    .03270 

67  10 
67  24 
67  37 
67  50 
68  03 

'I 

'.69 

2.50746  0.39923 

•53459   -40391 
.56196   .40857 
.58959   .41323 
.61748   .41788 

2.69951  0.43129 
•72472   .43532 
.75021   .43937 

.77596   -44341 
.80200   -44747 

0.92886  9.96795 
.93022   .96858 

•93J55   -96921 
.93286   .96982 
•934i5   -9/042 

1.0766   0.03205 
.0750    .03142 

•°735    -03079 
.0720    .03018 
.0705    -02958 

68  15 
68  28 
68  41 
68  53 
69  05 

1.70 

•7i 

.72 

•73 
•74 

2.64563  0.42253 
.67405   .42717 
.70273   .43180 
.73168   .43643 
.76091   .44105 

2.82832  0.45153 

•85491   -45559 
.88180   .45966 
.90897   .46374 
.93643   .46782 

o.9354i  9-97ioo 
•93665   -97158 
.93786   .97214 
.93906   .97269 
•94023   .97323 

1.0691   0.02900 
.0676    .02842 
.0663    .02786 
.0649    .02731 
.0636    .02677 

69  18 
69  30 
69  42 
69  54 

70  05 

!-75 
.76 

•77 
.78 

•79 

2.79041  0.44567 
.82020   .45028 
.85026   .45488 
.88061   .45948 
.91125   .46408 

2.96419  0.47191 
.99224   .47600 
3.02059   .48009 
.04925   .48419 
.07821   .48830 

0.94138  9.97376 
.94250   .97428 
.94361   -97479 
•94470   .97529 
•94576   .97578 

1.0623   0.02624 
.0610    .02572 
.0598    .02521 
.0585    .02471 
.0574    .02422 

70  17 
70  29 
70  40 
70  51 
7i  03 

i.  80 
.81 
.82 

•83 
.84 

2.94217  0.46867 
-97340   47325 
3.00492   .47783 
.03674   .48241 
.06886   .48698 

3.10747  0.49241 
.13705   .49652 
.16694   .50064 
.19715   .50476 
.22768   .50889 

0.94681  9.97626 
.94783   .97673 
.94884   .97719 
.94983   .97764 
.95080   .97809 

1.0562   0.02374 
.0550    .02327 
.0539    .02281 
.0528    .02236 
.0518    .02191 

71  14 

71  25 

71  36 
71  46 

7i  57  , 

1.85 
.86 

•87 
.88 
.89 

3.10129  0.49154 
.13403   .49610 
.16709   .50066 
.20046   .50521 
.23415   .50976 

3-25853  0.51302 
.28970   .51716 
.32121   .52130 
•35305   -52544 
•38522   .52959 

0.95175  9-97852 
.95268   .97895 

•95359   -97936 
.95449   -97977 
•95537   -98017 

1.0507   0.02148 
.0497    .02105 
.0487    .02064 
.0477    .02023 
.0467    .01983 

72  08 

72  18  i 
72  29  ! 
72  39  i 
72  49 

1.90 
.91 
.92 

•93 
.94 

3.26816  0.51430 
.30250   .51884 
.33718   .52338 
.37218   .52791 
.40752   .53244 

3-4I773  0.53374 
•45058   .53789 
.48378   .54205 
•5*733   -54621 
•55123   -55038 

0.95624  9.98057 
.95709   .98095 

•95792   -98133 
.95873   .98170 
•95953   -98206 

1.0458   0.01943 

.0448   -oi905» 
.0439   .01867 
.0430   .01830 
.0422    .01794 

72  59 
73  09 
73  r9 
73  29 
73  39 

'28 

$ 

•99 

3.44321  0.53696 
.47923   .54148 
.51561   .54600 

•55234   -55051 
.58942   .55502 

3.58548  0.55455 
.62009   -55872 
•65507   -56290 
.69041   .56707 
.72611   .57126 

0.96032  9.98242 
.96109   .98276 
.96185   .98311 
•96259   -98344 
•96331   -98377 

1.0413   0.01758 
.0405    .01724 
.0397    .01689 
.0389   .01656 
.0381    .01623 

73  48 
73  58 
74  07 
74  17 
74  26 

2.00 

3.62686  0.55953 

3.76220  0.57544 

0.96403  9-98409 

1.0373   0.01591 

74  35 

SMITHSONIAN   TABLES. 


TABLE  17  (continued). 
HYPERBOLIC  FUNCTIONS. 


45 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u. 

gd.  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

2.OO 
.OI 
.02 

•°3 

.04 

3.62686  0.55953 
.66466   .56403 
.70283   .56853 
.74138   .57303 
.78029   .57753 

3.76220  0.57544 
.79865   .57963 
.83549   .58382 
.87271    .58802 
.91032   .59221 

0.96403  9.98409 
.96473   .98440 
.96541    .98471 
.96609   .98502 
.96675   .98531 

I-°373   0.01591 
.0366    .01560 
.0358    .01529 
.0351    .01498 

.0344   .01469 

74°35' 
74  44 
74  53 
75  02 
75  ii 

2:0°l 

.07 
.08 
.09 

3.81058  0.58202 
.85926   .58650 
•89932   ^9099 

•93977   -59547 
.98061   .59995 

3.94832  0.59641 
.98671    .60061 
4.02550   .60482 
.06470   .60903 
.10430   .61324 

0.96740  9.98560 
.96803   .98589 
.96865   .98617 
.96926   .98644 
.96986   .98671 

I-°337   0.01440 
.0330   .01411 
.0324   .01383 
.0317    .01356 
.0311    .01329 

75  20 
75  28 
75  37 
75  45 
75  54 

2.10 
.11 
.12 

•13 

.14 

4.02186  0.60443 
.06350   .60890 
•10555   -61337 
.14801   .61784 
.19089   .62231 

4.14431   0.61745 
.18474   .62167 
.22558   .62589 
.26685   -63011 
.30855   .63433 

0.97045  9.98697 
.97103    .98723 

•97*59   .98748 
.97215   .98773 
.97269   .98798 

1.0304   0.01303 
.0298   .01277 
.0292   .01252 
.0286   .01227 

.0281     .01202 

76  02 
76  10 
76  19  i 
76  27 
76  35 

2.15 
.l6 

.18 
.19 

4.23419  0.62677 
.27791   .63123 
•32205   -63569 
.36663   -64015 
.41165   .64460 

4.35067   0.63856 
.39323   .64278 
.43623   .64701 
.47967   .65125 
•52356   -65548 

0-97323  9-98821 
•97375   -98845 
.97426   .98868 
.97477   .98890 
.97526   .98912 

1.0275    O.OII79 
.O27O     -OII55 
.0264     .01132 

.0259    .01110 

.0254     .OIO88 

76  43 

76  51 
76  58 
77  06 
77  H 

2.  2O 
.21 
.22 

•23 
.24 

4.45711  0.64905 
.50301   .65350 
.54936   .65795 
.59617   .66240 
.64344   .66684 

4.56791   0.65972 
.61271    .66396 
•65797   .66820 
.70370   .67244 
.74989   .67668 

0-97574  9-98934 
.97622   .98955 
.97668   .98975 
.97714   .98996 
•97759   -99016 

I.O249    O.OIO66 
.0244     .01045 
.0239     .OIO25 
.0234     .OIOO4 
.0229     .00984 

77  21 
77  29 
77  36 
77  44 
77  51 

*:% 
3 

.29 

4.69117  0.67128 
•73937   -67572 
.78804   .68016 
.83720   .68459 
.88684   .68903 

4.79657  0.68093 
.84372   .68518 
.89136   .68943 
.93948   .69368 
.98810   .69794 

0.97803  9.99035 
.97846   .99054 
.97888   .99073 
.97929   .99091 
.97970   .99109 

1.0225    0.00965 
.O22O     .00946 
•O2l6     .00927 
.0211     .00909 
.0207     .00891 

77  58 
78  05 
78  12 
78  19 
78  26 

2.30 

•31 
•32 
•33 
•34 

4.93696  0.69346 
.98758   .69789 
5.03870   .70232 
.09032   .70675 
.14245   .71117 

5.03722  0.70219 
.08684   .70645 
.13697   .71071 
.18762   .71497 
.23878   .71923 

0.98010  9.99127 
.98049   .99144 
.98087   .99161 
.98124   .99178 
.98161   .99194 

1.0203    0.00873 
.0199     .00856 
.0195     .00839 
.0191     .OO822 
.0187     .00806 

78  33 
78  40  i 
78  46  j 
78  53 
79  oo 

2-35 
•36 

:$ 

•39 

5.19510  0.71559 
.24827   .72002 
.30196   .72444 
.35618   .72885 
•41093   .73327 

5.29047   0.72349 
.34269   .72776 
.39544   .73203 
.44873   .73630 
.50256   74056 

0.98197  9.99210 
.98233   .99226 
.98267   .99241 
.98301   .99256 
•98335   -99271 

1.0184    O.OO79O 
.Ol8o     .OO774 
•0176     -OO759 
.0173     .00744 
.0169     .00729 

79  06  1 
79  13 
79  T9 
79  25 
79  32 

2.40 
.41 
.42 
•43 
•44 

5.46623  0.73769 
.52207   .74210 
.57847   .74652 
•63542   .75093 
•69294   -75534 

5-55695  0.74484 
.61189   .749H 
•66739   75338 
.72346   .75766 
.78010   .76194 

0.98367  9.99285 
.98400   .99299 

•98431   -993  i  3 
.98462   .99327 

•98492   -99340 

I.  Ol66    0.00715 
•0163     .OO70I 
.0159     .00687 
.0156     -00673 
.0153     .00660 

7938 
79  44 
79  5° 
79  56 
80  02 

2.45 
.46 

•47 
.48 
.49 

5.75103  0.75975 

.86893   -76856 
.92876   .77296 
.98918   .77737 

5.83732  0.76621 
.89512   .77049 
•95352   -77477 
6.01250   .77906 
.07209   .78334 

0.98522  9.99353 
•98551   -99366 
•98579   -99379 
.98607   .99391 
.98635   .99403 

I.OI50    0.00647 
.OI47     .00634 
.OI44     .OO62I 
.0141     .00609 
.0138     .00597 

80  08 
80  14 

80  20 
80  26 
80  31 

2.50 

6.05020  0.78177 

6.13229  0.78762 

0.98661  9.99415 

I.OI36    0.00585 

80  37 

SMITHSONIAN   TABLES. 


46 


TABLE    17    (continued), 

HYPERBOLIC    FUNCTIONS. 


a 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u 

gd.  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

2.50 
•51 

•52 

•53 

•54 

6.05020  0.78177 
.11183   -78617 
.17407   .79057 
.23692   .79497 
.30040   .79937 

6.13229  0.78762 

.19310   •79I9I 

•25453   -79619 
.31658   .80048 
.37927   .80477 

0.98661  9.9941  5 
.98688   .99^26 
.98714   .99438 

•98739   -99449 
.98764   .99460 

1.0136   0.00585 

•OI33    .00574 
.0130    .00562 
.0128    .00551 
.0125    .00540 

80°  37' 
So  42 
80  48 
80  53 
80  59 

*$ 

:P 

•59 

6.36451  0.80377 
.42926   .80816 
.49464   .81256 
.56068   .81695 
.62738   .82134 

6.44259  0.80906 
.50656   .81335 
.57118   .81764 
.63646   .82194 
.70240   .82623 

0.98788  9.99470 
.98812   .99481 
•98835   .9949  i 
.98858   .99501 
.98881   .99511 

1.0123   0.00530 
.OI2O    .00519 
.OIl8    .00509 
.0115    .00499 
.0113    .00489 

81  04 
81  10 
81  15  ! 

81  20 
81  25 

2.60 
.61 
.62 

!  g 

6.69473  0.82573 
.76276   .83012 
.83146   .83451 
.90085   .83890 
.97092   .84329 

6.76901   0.83052 
.83629   .83482 
.90426   -83912 
.97292   .84341 
7.04228   .84771 

0.98903  9.99521 
.98924   .99530 
.98946   .99540 
.98966   .99549 
•98987   -99558 

i.oui   0.00479 
.0109    .00470 
.0107   .00460 
.0104    .00451 
.0102    .00442 

81  30 

81  35 
81  40 
81  45 
81  50 

\*% 

.67 

.68 

.69 

7.04169  0.84768 
.11317   .85206 
.18536   .85645 
.25827   .86083 
.33190   .86522 

7.11234  0.85201 
.18312   .85631 
.25461    .86061 
.32683   .86492 
.39978   .86922 

0.99007  9.99566 
.99026   .99575 

•99045   -99583 
.99064   .99592 
•99083   -99600 

i.oioo   0.00434 
.0098    .00425 
.0096   .00417 
.0094    .00408 
.0093    .00400 

81  55 
82  oo 
82  05 
82  09 
82  14 

2.70 
•7i 
•72 
•73 
•74 

7.40626  0.86960 

•48137   .87398 
.55722   .87836 
.63383   .88274 
.71121   .88712 

7.47347   0.87352 

•54791   -87/83 
.62310   .88213 
.69905   .88644 
.77578   .89074 

0.99101  9.99608 
.99118   .99615 
.99136   .99623 

•99153   -99631 
.99170   .99638 

1.0091   0.00392 
.0089    .00385 

.0087   .00377 
.0085   .00369 
.0084    .00362 

82  19 

82  23 
82  28 
82  32 
82  37 

!2£ 

9 

•79 

2.80 
.81 
.82 

•83 
.84 

7.78935  0.89150 
.86828   .89588 
.94799   .90026 
8.02849   .90463 
.10980   .90901 

8.19192  0.91339 
.27486   .91776 
.35862   .92213 
.44322   .92651 
.52867   .93088 

7.85328  0.89505 
•93  '57   -89936 
8.01065   -90367 
•09053   -90798 
.17122   .91229 

8.25273  0.91660 
.33506   .92091 
.41823   .92522 
.50224   .92953 
•58710   .93385 

0.99186  9.99645 
.99202   .99652 
.99218   .99659 
•99233   .99666 
.99248   .99672 

0.99263  9.99679 
.99278   .99685. 
,99292   .99691 
.99306   .99698 
.99320   .99704 

1.0082   0.00355 
.0080   .00348 
.0079   .00341 

.0077    -00334 
.0076    .00328 

1.0074   0.00321 
•0073    -00315 
.007  1    .00309 
.0070    .00302 
.0069    .00296 

82  41 
82  45 
82  50 
82  54 
82  58 

83   02 
83   07 
83   II 
83   15 
83   19 

2.85 
.86 
.87 
.88 
.89 

8.61497  0.93525 
.70213   .93963 
.79016   .94400 
.87907   .94837 
.96887   .95274 

8.67281  0.93816 
.75940   .94247 
.84686   .94679 
.93520   .95110 
9.02444   .95542 

0-99333  9-99709 
•99346   .99715 
•99359   -99721 
.99372   .99726 
.99384   .99732 

1.0067   0.00291 
.0066    .00285 
.0065    .00279 
.0063    .00274 
.0062    .00268 

83   23  i 
83   27  j 

&  £ 

83  34 
83  38 

2.90 
.91 
.92 
•93 
•94 

9.05956  0.95711 
.15116   .96148 
.24368   .96584 
.33712   .97021 
43  '49   -97458 

9.11458  0.95974 
.20564   .96405 
.29761   .96837 
.39051   .97269 
.48436   .97701 

0.99396  9-99737 
.99408   .99742 
.99420   .99747 
•99531   -99752 
•99443   -99757 

i.  006  r   0.00263 
.0060    .00258 
.0058    -00253 
.0057    .00248 
.0056    .00243 

83  42 
83  46 
83  50 

83  53 
83  57 

2-95 
.96 

•97 
.98 

•99 

9.52681  0.97895 
.62308   -98331 
.72031   .98768 
.81851   .99205 
.91770   .99641 

9-579I5  0.98133 
.67490   .98565 
.77161   .98997 
.86930   .99429 
.96798   .99861 

0.99454  9.99762 
.99464   .99767 
•99475   -99771 
•99485   .99776 
.99496   -99780 

1.0055   0.00238 
.0054    .00233 
.0053    .00229 
.0052    .00224 

.0051     .00220 

84  oo 
84  04 
84  08 
84  ii 
84  15 

3.00 

10.01787  1.00078 

10.06766  1.00293 

0.99505  9-99785 

1.0050    0.00215 

84  18 

SMITHSONIAN    TABLES. 


TABLE  17  (continued). 
HYPERBOLIC  FUNCTIONS. 


47 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u 

gd.  u 

Xat.      Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

3.0 

.2 
•3 

•4 

IO.OI79   1.00078 
11.0765   .04440 
12.2459   .08799 

'3-5379   -i3*SS 
14.9654   .17509 

10.0677  1.00293 
II.I2I5  .04616 
12.2866  .08943 
13.5748  .13273 
14.9987  .17605 

0.99505  9.99785 

•99595   -99824 

.99668   .99856 

.99728   .99882 

.99777  .99903 

1.0050   0.00215 
.0041     .00176 
.0033    .00144 
.0027    .OOIlS 
.OO22  '   .00097 

84°  1  8' 

84  50 

85  20 

85  47 
86  ii 

3-5 
•9 

16.5426  1.21860 
18.2855   .26211 
20.2113   .30559 

22-3394   -349°7 
.24.6911   .39254 

16.5728  1.21940 
18.3128  .26275 
20.2360  .30612 
22.3618  .34951 
24.7113  .39290 

0.99818  9.99921 

.99851  .99935 
.99878  .99947 
.99900  .99957 
.99918  .99964 

I.OOlS   0.00079 
.0015    .00065 
.0012     .00053 
.OOIO     .OOO43 
.OOO8     .00036 

86  32 
86  52 
87  10 
87  26 
87  41 

4.0 

.2 

•3 
•4 

27.2899  1.43600 
30.1619   47946 
33-3357   .5229i 
36.8431   .56636 
40.7193   .60980 

27.3082  1.43629 
30.1784  4797° 
33-3507  .52310 
36.8567  .56652 
40.7316  .60993 

0-99933  9-99971 
-99945   -99976 
•99955   -99980 
.99963   .99984 
.99970   .99987 

I.OOO7    O.OOO29 
.OOO5     .OOO24 
.0004     .00020 
.OOO4     .OOOl6 
.OOO3     .OOOI3 

11% 

88  17 
88  27 
88  36 

4-5 

'& 

•9 

45.0030  1.65324 
49-7371   .69668 
54.9690   .74012 
60.7511   .78355 
67.1412   .82699 

45.0141  1-65335 
49.7472  .69677 
54.9781  .74019 
60.7593  -78361 
67.1486  .82704 

0-99975  9-99989 
.99980   .99991 

•99983   -99993 
.99986   .99994 

.99989   -99995 

1.0002   o.ooen 
.0002    .00009 

.0002     .00007 

.0001    .00006 
.0001    .00005 

88  44 
88  51 
88  57 
8903 
8909 

5.0 

74.2032  1.87042 

74.2099  1.87046 

0.99991  9-99996 

i.oooi   0.00004 

89  M 

TABLE  18,— Factorials. 

See  Table  16  for  logarithms  of  the  products  1.2.3.  •  •  •*  from  i  to  100. 
See  Table  32  for  log.  T  (n  +  i)  for  values  of  n  between  i.ooo  and  2.000. 


n 

i 
n  : 

n:  =  i.  2.  3.  4  .  .  .  n 

n 

l 

i. 

i 

I 

2 

°-5 

2 

2 

3 

.16666  66666  66666  66666  66667 

6 

3 

4 

.04166  66666  66666  66666  66667 

24 

4 

5 

•00833  33333  33333  33333  33333 

1  20 

5 

6 

0.00138  88888  88888  88888  88889 

720 

6 

7 

.00019  84126  98412  69841  26984 

5040 

7 

8 
9 

.00002  48015  87301  58730  15873 
.00000  27557  31922  39858  90653 

40320 
3  62880 

8 
9 

10 

.00000  02755  73192  23985  89065 

36  28800 

10 

ii 

o.ooooo  00250  52108  38544  17188 

399  16800 

ii 

12 

.OOOOO  OOO2O  87675  69878  68099 

4790  01600 

12 

T3 

.00000  oooo  i  60590  43836  82161 

62270  20800 

J3 

14 
15 

.00000  ooooo  11470  74559  77297 
.00000  ooooo  00764  71637  31820 

8  71782  91200 
130  76743  68000 

H 
15 

16 

o.ooooo  ooooo  00047  79477  33239 

2092  27898  88000 

16 

T7 

.ooooo  ooooo  00002  81145  72543 

35568  74280  96000 

T7 

18 

.ooooo  ooooo  ooooo  15619  20697 

6  40237  37057  28000 

18 

^9 

.ooooo  ooooo  ooooo  00822  06352 

121  64510  04088  32OOO 

!9 

20 

.ooooo  ooooo  ooooo  00041  10318 

2432  90200  81766  40000 

20 

SMITHSONIAN  TABLES. 


48 


TABLE  19. 
EXPONENTIAL   FUNCTION. 


X 

log,0('*)      ex         e-x 

X 

logio(<?-O      ex        e-x 

0.00 
.01 
.02 

•03 
.04 

O.OOOOO     I  .OOOO     I  .OOOOOO 

.00434    .0101    0.990050 
.00869    .0202    .980199 

.01303   .0305   .970446 
.01737   .0408   .960789 

0.50 

•51 

.52 

•53 
•54 

0.21715    1.6487    0.606531 
.22149     -6653     .600496 
.22583     .6820     .594521 
.23018     .6989     .588603 
.23452     .7160     .582748 

0.05 
.06 
.07 
.08 
.09 

0.02171    I-°5I3   0.951229 
.02606'    .0618    .941765 
.03040    .0725    .932394 
.03474    .0833    .923116 
.03909    .0942    .9I3931 

•9 

:P 

•59 

0.23886    1.7333    0.576950 
.24320     .7507     .571209 
•-4755    -7683    -565525 
.25189    .7860    -559898 
.25623    .8040    .554327 

O.IO 

.11 

.12 

•r3 

.14 

0.04343   1.1052   0.904837 
.04777    .1163    .895834 
.05212    -1275    .886920 
.05646    .1388    -878095 
.06080    .1503    .869358 

0.60 
.61 
.62 

•63 
.64 

0.26058    1.8221    0.548812 
.26492    .8404    .5433  5  1 
.26926    .8589    -537944 
.27361    .8776    .532592 
•27795    -8965    -527292 

0.15 

3 

•19 

0.06514    1.1618   0.860708  • 
.06949    .1735    .852144 

•07383    -l853    -843665 
'.07817    .1972    .835270 
.08252    .2092    .826959 

0.65 
.66 
•67 
.68 
.69 

0.28229   1-9155   0.522046 
.28663    .9348    .516851 
.29098    .9542    .511709 
•29532    -9739    .506617 
.29966    .9937    .501576 

0.20 
.21 

.22 

•23 

.24 

0.08686    1.2214   0.818731 
.09120    -2337    .810584 
.09554    .2461    .802519 
.09989    .2586    -794534 
.10423    .2712    .786628 

0.70 
•71 
•72 
•73 
•74 

0.30401    2.0138   0.496585 
.30835    .0340    .49*644 
.31269    .0544    .486752 
.31707    .0751    .481909 
.32138    .0959    -477  "4" 

"S 

:S 

.29 

0.10857    1.2840   0.778801 
.11292    .2969    .771052 
.11726    .3100    .763379 
.12160    .3231    .755784 
•I2595    -3364    .748264 

0-75 
.76 

2 

•79 

0.32572    2.1170   0.472367 
.33006    .1383    .467666 
.33441    .1598    .463013 
•33875    -1815    .458406 
.34309    .2034    453845 

0.30 

•31 
•32 
•33 
•34 

0.13029   1.3499   0.740818 
.13463    -3634    -733447 
•13897    -3771    .726149 
.14332    .3910    .718924 
.14766    .4049    .711770 

0.80 
.81 
.82 

•83 
.84 

0.34744    2.2255    0.449329 
.35178    .2479    -444858 
.35612    .2705    .440432 
.36046    .2933    .436049 
.36481    .3164    .431711 

o-35 
•36 

$ 

•39 

0.15200    1.4191    0.704688 
•T5635    -4333    .697676 
.16069    .4477    .690734 
.16503    .4623    .683861 
.16937    .4770    -677057 

0.85 
.86 
.87 
.88 
.89 

0.36915    2.3396    0.427415 
•37349    -3632    .423162 
.37784    .3869    .418952 
.38218    .4109    .4147^3 
.38652    .4351    .410656 

0.40 
.41 

.42 
•43 

•44 

0.17372    1.4918   0.670320 
.17806    .5068    .663650 
.18240    .5220    -657047 
•18675    -5373    -650509 
.19109    .5527    .644036 

0.90 
.91 
.92 
•93 
•94 

0.39087    2.4596    0.406570 
.39521     .4843    .402524 
•39955    -5°93    •  3985r  9 
.40389    .5345    -394554 
.40824    .5600    .390628 

0-45 
.46 

•47 
.48 

•49 

0.19543    1.5683   0.637628 
.19978    .5841    .631284 
.20412    .6000    .625002 
.20846    .6161    .618783 
.21280    .6323    .612626 

°$ 

•97 
.98 

•99 

0.41258    2.5857    0.386741 
.41692    .6117    .382893 
.42127    .6379    -379083 
.42561    .6645    .37  5311 
.42995    .6912    .371577 

0.50 

0.21715    1.6487   0.606531 

1.  00 

0.43429   2.7183   0.367879 

SMITHSONIAN  TABLES. 


TABLE    19  (continued}. 
EXPONENTIAL    FUNCTION. 


49 


X 

logjo(^)     'x       '-* 

X 

l°g,o  (**  )      **         f~x 

1.  00 
.OI 
.02 

•03 
.04 

0.43429    2.7183    0.367879 
.43864    .7456    .364219 
.44298    .7732     .360595 
.44732    .8011     .357007 
.45167    .8292     -353455 

1.50 

•51 

•52 
•53 
•54 

0.65144    44817     0.223130 
•65578     -5267      .220910 
.66013      -5722     .218712 
.66447      .6182      .216536 
.66881      .6646     .214381 

1.05 
.OO 
.07 
.08 
.09 

0.45601    2.8577    0.349938 
.46035    .8864    .346456 
.46470    .9154    .343°°9 
.46904    .9447    .339596 
•47338    -9743    -336216 

•56 

:5^ 

•59 

0-67316    47II5    0.212248 
•  .67750     .7588     .210136 
.68184     .8066     .208045 
.68619     -8550     .205975 
•69053     .9037      .203926 

I.IO 

.11 

.12 

•13 

.14 

0.47772   3.0042   0.332871 
.48207    .0344    -.329559 
.48641    .0649    .326280 

•49075    -°957    -323033 
.49510    .1268    .319819 

i.  60 
.61 
.62 

•% 

0.69487     4.953O    0.201897 
.69921     5.0028     .199888 
•70356     -0531      .197899' 
.70790     .1039     .195930 
.71224     .1552      .193980 

•3 

•i? 
.18 

•T9 

0-49944   3-J582   0.316637 
.50378    .1899    -313486 
.50812    .2220    .310367 
.51247    .2544    .307279 
.51681    .2871    .304221 

•a 

•67 

.68 
.69 

0.71659    5.2070    0.192050 
•72093     .2593     .190139 
.72527      .3122      .188247 
.72961      .3656     .186374 
•73396     4195     .184520 

i.  20 

.21 
.22 

•23 
.24 

0.52115   3.3201    0.301194 
•52550    -3535    .298197 
.52984    .3872    .295230 
.53418    .4212    .292293 
•53853    4556    -289384 

1.70 

.71 

.72 

•73 
•74 

°-  7  3?  30   5-4739   0.182684 
.74264    .5290    .180866 
.74699    .5845    .179066 
•75T33    -6407    .177284 
•75567    -6973    .I75520 

1.25 
.26 

•2? 
.28 
.29 

0.54287    3-4903   0.286505 
.54721    .5254    .283654 
.55155    .5609    .280832 
•55590    .5966    .278037 
.56024    .6328    .275271 

31 

3 

•79 

0.76002   5.7546   0.173774 
.76436    .8124    .172045 
.76870    .8709    .170333 
.77304    .9299    .168638 
•77739    -9895    .166960 

I.30 

•31 

•32 

•33 
•34 

0.56458   3.6693   0.272532 
.56893    .7062    .269820 
•57327    -7434    -267135 
.57761    .7810    .264477 
.58195    .8190    .261846 

i.  80 
.81 
.82 

•l\ 

0.78173   6.0496   0.165299 
.78607    .1104    .163654 
.79042    .1719    .162026 
.79476    .2339    .160414 
.79910    .2965    .158817 

^ 

3 

•39 

0.58630   3.8574   0.259240 
.59064    .8962    .256661 
•59498    -9354    .254107 

•59933    -9749    -251579 
.60367   4.0149    .249075 

'II 

.87 
.88 
.89 

0.80344   6.3598  •  0.157237 
.80779    .4237    .155673 
.81213    .4883    .154124 
.81647    .5535    .152590 
.82082    .6194    .151072 

1.40 
.41 
.42 
•43 
•44 

0.60801    4-0552   0.246597 
.61236    .0960    .244143 
.61670    .1371    .241714 
.62104    .1787    -239309 
.62538    .2207    .236928 

1.90 
.91 
.92 
•93 
•94 

0.82516   6.6859   0.149569 
.82950    -7531    .148080 
•83385    .8210    .146607 
.83819    .8895    .145148 
•84253    -9588    -143704 

1.45 
.46 

•47 
.48 

•49 

0.62973   4.2631    0.234570 
.63407    .3060    .232236 
.63841    .3492    .229925 
.64276    .3929    .227638 
•64710    .4371    -225373 

i-95 
.96 

•97 
•98 
•99 

0.84687   7.0287   0.142274 
.85122    .0993    .140858 
.85556    .1707    .139457 
.85990    .2427    .138069 
•86425    -3155    -136695 

1.50 

0.65144   4-4817   0.223130 

2.OO 

0.86859   7.3891   0.135335 

SMITHSONIAN  TABLES. 


TABLE    19  (continued). 

EXPONENTIAL   FUNCTION. 


X 

logio  (*x)     «*       f~x 

X 

login  ('*)      «*        t-x 

2.OO 
.OI 
.02 

•03 

.04 

0.86859   7.3891   0.135335 
•87293   -4633   -133989 
•87727   .5383   -132655 

.88162    .6141    •I3I336 
.88596    .6906    .130029 

2.50 
•51 

•52 

•53 

•54 

1.08574    I2.I82      0.082085 
.09608      .305       .081268 
.09442      .429       .080460 

•09877    -554     -079659 
.10311    .680     .078866 

2.05 
.06 
.07 
.08 
.09 

0.89030   7.7679   0.128735 
.89465    .8460    .127454 
.89899    .9248    .126186 
•9°333   8.0045    -1  24930 
.90768    .0849    .123687 

2:^ 
:P 

•59 

1.10745   12.807    0.078082 
.11179    -936     -077305 
.11614   13.066     .076536 
.12048    .197     -075774 
.12482    .330     .075020 

2.IO 
.11 
.12 

•13 
•H 

0.91202   8.1662   0.122456 
.91636    .2482    .121238 
.92070    -3311    .120032 
.92505    .4149    .118837 
.92939    .4994    .117655 

2.60 
.6r 
.62 

% 

1.12917   13.464    0.074274 
•i335i    -599     -0/3535 
•13785    -736     .072803 
.14219    .874     .072078 
.14654   14.013     .071361 

2:ll 

•  17 
.18 
.19 

°-93373   8.5849   0.116484 
.93808    .6711    .115325 
•94242    .7583    .114178 
.94676    .8463    .113042 
.95110    .9352    .111917 

^ 

•67 

.68 
•69 

1.15088   14.154    0.070651 
.15522    .296     .069948 
.15957    .440     .069252 
.16391    .585     .068563 
.16825    .732     .067881 

2.20 
.21 

.22 

•23 
.24 

°-95545   9-0230   0.110803 
•95979    ."57    .109701 
.96413    .2073    -108609 
.96848    .2999    .107528 
•97282    .3933    .106459 

2.70 
•7i 
•72 
•73 
•74 

1.17260   14.880    0.067206 
.17694   15.029     .066537 
.18128    .180     -065875 
.18562    .333     .065219 
.18997    .487     -064570 

2.25 
.26 
.27 
.28 
.29 

0.97716   9.4877    0.105399 
.98151    .5831    -104350 
.98585    .6794    -103312 
.99019    .7767    .102284 
.99453    .8749    .101266 

2'75 
•76 
•77 
.78 

•79 

1.19431   15.643    0.063928 
.19865    .800     .063292 
.20300    .959     .062662 
.20734   16.119     .062039 
.21168    .281     .061421 

2.30 

•31 
•32 
•33 
•34 

0.99888   9.9742   0.100259 
1.00322   10.074     .099261 
.00756    .176     .098274 
.01191    .278     .097296 
.01625    .381     .096328 

2.80 
.81 
.82 
•83 
•84 

1.21602   16.445    0.060810 
.22037    .610     .060205 
.22471    .777     .059606 
.22905    .945     .059013 
.23340   17.116     .058426 

2:P 
3 

•39 

1.02059   10.486    0.095369 
.02493    -591     .094420 
.02928    .697     .093481 
.03362    .805     .092551 
•03796    .913     -091630 

2.85 
.86 

-87 
.88 
.89 

1.23774   17.288    0.057844 
.24208    .462     .057269 
.24643    .637     .056699 
.25077    .814     .056135 
•25511    -993     -055576 

2.40 
.41 
.42 
•43 
•44 

1.04231   11.023    0.090718 
.04665    .134     .089815 
.05099    .246     .088922 
•°5534    -359     .088037 
.05968    .473     .087161 

2.90 
.91 
.92 
•93 
-94 

1.25945   18.174    0.055023 
-26380    .357     .054476 
•26814    -541     -053934 
.27248    .728     -053397 
.27683    .916     .052866 

2.45 
.46 

•47 
.48 

•49 

1.06402   11.588    0.086294 
.06836    .705     .085435 
.07271    .82.2     .084585 
.07705    .941     .083743 
.08139   12.061     .082910 

'$ 

9 

-99 

1.28117   19.106    0.052340 
.28551    .298     .051819 
.28985    .492     -051303 
.29420    .688     -050793 
.29854    .886     .050287 

2.50 

1.08574   12.182    0.082085 

3.00 

1.30288   20.086    0.049787 

SMITHSONIAN  TABLES. 


TABLE    19  (contimtecT). 

EXPONENTIAL   FUNCTION. 


X 

Iog10(^')      ex        e—x 

X 

\oglo(ex)       ex        e—x 

3-0° 

.OI 

.02 

•03 
.04 

1.30288    20.086    0.049787 
.30723      .287     .049292 
.31157      .491     .048801 
.31591      .697     .048316 
.32026      .905     .047835 

3-50 

•51 

•52 
•53 
•54 

1.52003    33.115    0.030197 
•52437      448     .029897 
•52872      -784     -029599 
.53306    34-124     -029305 
.53740      .467     .029013 

3-05 
.06 
.07 
.08 
.09 

1.32460    21.115    0.047359 
.32894      -328     .046888 
.33328      .542     .046421 
.33763      .758     -045959 

•34197     -977    -045502 

•59 

I-54I75    34.8I3    0.028725 
.54609    35.163     .028439 

•55043     -5r7    .028156 
.55477     .874    .027876 
.55912   36.234    .027598 

3.10 
.11 
.12 

•13 

.14 

1.34631    22.198   0.045049 
.35066     .421    .044601 
.35500     .646    .044157 
•35934     -874    .043718 
.36368    23.104    .043283 

3.60 
.61 
.62 

1.56346   36.598   0.027324 
.56780     .966    .027052 
•57215   37-338    .026783 
•57649     -713    .026516 
•58083   38.092    .026252 

.16 

•T7 
.18 
.19 

1.36803    23.336   0.042852 
.37237     -571    .042426 
.37671     .807    .042004 
.38106   24.047    .041586 
.38540     .288    .041172 

•67 
.68 
.69 

1.58517   38.475   0.025991 
.58952     .861    -025733 
.59386   39.252    .025476 
.59820     .646    -025223 
.60255   40.045    .024972 

3-20 

.21 

.22 

•23 

.24 

1.38974   24.533   0.040762 
.39409     .779    .040357 
.39843    25.028    -039955 
.40277     .280    -039557 
.40711     .534    .039164 

3-70 

•7i 

.72 

•73 
•74 

1.60689   40.447   0.024724 
.61123     .854    .024478 
.61558   41.264    .024234 
.61992     .679    -023993 
.62426   42.098    .023754 

•27 
.28 
.29 

1.41146   25.790   0.038774 
.41580   26.050    .038388 
.42014     .311    .038006 
.42449     .576    .037628 
.42883     .843    .037254 

3-75 
.76 
•77 
-78 
•79 

1.62860   42.521    0.023518 
•63295     -948    .023284 
•63729   43-38o    -023052 
.64163     .816    .022823 
.64598   44-256    .022596 

3-30 
•31 
•32 

•33 
•34 

1-433*7    27.113   0.036883 
•43751     -385    -036516 
.44186     .660    .036153 
.44620     .938    .035793 
.45054   28.219    .035437 

3-8o 
.81 
.82 

•83 

.84 

1.65032   44.701    0.022371 
.65466   45^50    .022148 
.65900     .604    .021928 
.66335   46-063    .021710 
•66769     .525    .021494 

•39 

1.45489   28.503   0.035084 

•45923     -789    .034735 
.46357    29.079    .034390 
.46792     .371    .034047 
.47226     .666    -033709 

•87 
.88 

•89 

1.67203   46.993   0.021280 
.67638   47.465    .021068 
.68072     .942    .020858 
.68506   48.424    .020651 
.68941     .911    -020445 

3-40 
.41 
.42 
•43 
•44 

1.47660   29.964   0.033373 
.48094   30.265    .033041 
.48529     .569    .032712 
.48963     .877    .032387 
•49397    3I-l87    .032065 

CO 

1  -6937  5   49.402   0.020242 
.69809     .899    .020041 
.70243   50.400    .019841 
.70678     .907    .019644 
.71112   51.419    .019448 

3-45 
.46 

•47 
.48 

•49 

1.49832   31.500   0.031746 
.50266     .817    .031430 
.50700   32.137    .031117 
.51134     .460    .030807 
.51569     .786    .030501 

3-95 
.96 

•97 
.98 

•99 

1.71546   5*-935   0.019255 
.71981    52.457    .019063 
.72415     .985    .018873  . 
.72849   53.517    .018686 
.73283   54.055    .018500 

3-50 

1-52003   33.115   0.030197 

4.00 

1.73718   54-598   0.018316 

SMITHSONIAN  TABLES. 


TABLE     19    (continued). 

EXPONENTIAL    FUNCTION 


X 

log.o(^)    .           **                    e-x 

X 

logioC**)               e*                    e~x 

4.00 
.01 

.02 

•03 
.04 

1.73718          54-598          0.018316 
.74152           55.147             .018133 
.74586               .701             .017953 
.75021           56.261             -017774 
.75455               .826            .017597 

4.50 

•51 

•S2 
•53 
•54 

1  -95433        9°-or7        0.011109 
.95867            .922          .010998 
.96301        91.836          .010889 
.96735        92-759          .010781 
.97170        93.691          .010673 

4S 

•07 
.08 
.09 

1-75889        57-397        0.017422 
.76324            .974          .017249 
.76758        58.557          .017077 
.77192        59.  145          .016907 
.77626           .740          -016739 

4-55 
•56 

% 

•59 

1.97604        94.632        0.010567 
.98038        95.583          .010462 
.98473        96.544          .010358 
.98907        97-514          .010255 
.99341        98.494          .010153 

4.10 
.11 

.12 

•13 

.14 

1.78061        60.340        0.016573 
.78495            -947          .016408 
.78929        61.559          .016245 
.79364        62.178          .016083 
•79798            -803          -015923 

4.60 
.61 
.62 

•63 

.64 

1-99775        99-484        0.010052 

2.OO2IO         100.48                 .009952 
.00644          101-49                 .009853 
.OIO/8         IO2.5I                  .009755 
.01513         103.54                 .009658 

4-15 

•17 
.18 
.I9 

1.80232        63.434        0.015764 
.80667         64.072          .015608 
.81101             .715          .015452 
•8i535        65.366          .015299 
.81969        66.023          .015146 

4:66l 
% 

.69 

2.01947          104.58              0.009562 
.02381          105.64                 .009466 
.O28l6         IO6./O                 .009372 
.03250         107-77                  .009279 
.03684         108.85                 .009187 

4.20 
.21 

.22 

•23 
.24 

1.82404        66.686        0.014996 
.82838        67.357          .014846 
.83272        68.033          .014699 

•83707            -717          -OI4552 
.84141        69.408          .014408 

4.70 
•71 

.72 
-73 
•74 

2.O4II8         109.95              0.009095 

.04553      I:I-05           .009005 
.04987      112.17           .008915 
.05421       113-30           .008826 
.05856      114.43           -008739 

4.2| 
.26 

'.28 
.29 

^84575        70.105        0.014264 
.85009            .810          .014122 
.85444        71.522          .013982 
.85878        72.240          .013843 
.86312            .966          .013705 

4-75 
.76 

•77 
•78 
•79 

2.06290      115.58         0.008652 
.06724      116.75           .008566 
.07158      117.92           .008480 
.O7593      119.10           .008396 
.08027      120.30           .008312 

4-3° 
•3i 
•32 
•33 
•34 

1.86747        73.700        0.013569 
.87181        74-440          -013434 
.87615        75-189          .013300 
.88050            .944          .013168 
.88484        76.708          .013037 

4.80 
.81 
.82 

•83 
.84 

2.08461       121.51          0.008230 
.08896      122.73           .008148 
.09330      1  23.97           .008067 
.09764      125.21            .007987 
.10199      126.47           .007907 

4:^ 
% 

•39 

1.88918        77.478        0.012907 
.89352        78-257          .01.2778 
.89787        79-044          .012651 
.90221        79-838          .012525 
•90655        80.640          .012401 

4.85 
.86 
.87 
.88 
.89 

2.10633      127.74         0.007828 
.11067      129.02           .007750 
.11501       130-32           .007673 
.11936      131.63           -007597 
.12370      132.95           .007521 

4.40 
.41 
.42 
•43 
•44 

1.91090        81.451        0.012277 
.91524        82.269          -OI2I55 
.91958        83.096         .012034 
.92392           .931          .011914 
.92827        84.775          .011796 

4.90 
.91 
.92 
•93 
.94 

2.12804      134-29         0.007447 
•13239      I35-64           -007372 
•I3673       i37-oo            .007299 
.14107       138.38            .007227 
.14541       13977            -007155 

4-45 
.46 

•47 
.48 

•49 

1.93261        85.627        0.011679 
•93695        86.488          .011562 
.94130        87.357          .011447 
.94564        88.235          -011333 

.94998           89.121              .OII22I 

4-95 
.96 

•97 
.98 

•99 

2.14976       141.17          0.007083 
.15410       142.59            .007013 
.15844       144-03            .006943 
.16279       145-47            .006874 
.16713       146.94            .006806 

4-5° 

1  -95433        90.017        0.011109 

5.00 

2.17147       148.41           0.006738 

SMITHSONIAN  TABLES. 


TABLE   19  (continued). 

EXPONENTIAL    FUNCTION. 


53 


X 

logioC**)      «*        <r-x 

JC 

l°gio(*x)      ^        e-x 

5-oo 

.01 

.02 

.03 
.04 

2.17147    148.41    0.006738 
.17582    149.90     .006671 
.18016    I5I-4I     .006605 
.18450    152.93     -006539 
.18884    15447     .006474 

5-o 

sj 

•3 

•4 

2.17147    148.41    0.006738 
.21490    164.02     .006097 
.25833    181.27     .005517 
.30176    200.34     .004992 
.34519    221.41     .004517 

5:°J 
3 

.09 

2.19319    156.02    0.006409 

•'9753    J57-59    .006346 
.20187    I59«I7    .006282 
.20622    160.77    .006220 
.21056    162.39    .006158 

1 

•9 

2.38862    244.69    0.004087 
.43205    270.43     .003698 
.47548    298.87     .003346 
.51891    330.30     .003028 
.56234    365.04     .002739 

5.10 
.11 

.12 

•!3 
.14 

2.21490   164.02   0.006097 
.21924    165.67    .006036 
.22359   167.34    .005976 
.22793    169.02    .005917 
.23227    170.72    .005858 

6.0 
.1 

.2 

•3 

•4 

2.60577    403.43    0.002479 
.64920    445-86     .002243 
.69263    492.75     .002029  • 
.73606    544.57     .001836 
.77948    601.85     .001662 

5-l$ 
.16 

•  J7 

•19 

2.23662    172.43   0.005799 
.24096    174.16    .005742 
.24530   175.91    -005685 
.24965    177.68    .005628 
•25399    i  79-47    -005572 

"I 

'.8 
•9 

2.82291    665.14    0.001503 

.86634   735-10    .001360 
.90977   812.41    .001231 
.95320   897.85    .001114 
.99663   992.27    .001008 

5.20 

.21 

.22 

•23 

.24 

2.25833    181127   0.005517 
.26267    183.09    .005462 
.26702    184.93    .005407 
.27136    186.79-   -005354 
.27570    188.67    .005300 

7.0 
.1 

.2 

•3 

•4 

3.04006   1096.6    0.000912 

.08349    1  21  2.0       .000825 
.12092    1339.4       .000747 
.17035    1480.3       .000676 
.21378    1636.0       .0006ll 

5-2| 
.20 

.27 
.28 
•29 

2.28005    J90-57   0.005248 
.28439    192.48    .005195 
.28873    194-42    -005144 
.29307    196.37    .005092 
.29742    198.34    .005042 

7i 
•I 

•9 

3.25721   1808.0    0.000553 
.30064   1998.2     .000500 
.34407   2208.3     -000453 
•3875°   2440.6     .000410 
.43093   2697.3     .000371 

5-30 
•31 

1  -32 

•33 
•34 

2.30176   200.34   0.004992 
.30610   202.35    .004942 
.31045    204.38    -004893 
.31479  '  206.44    .004844 
.31913   208.51    .004796 

8.0 

.2 

•3 
•4 

3.47436   2981.0    0.000335 
•5J779   3294-5     .000304 
.56121   3641.0     .000275 
.60464   4023.9     .000249 
.64807   4447.1     .000225 

5-35 
•36 

% 

•39 

2.32348    210.61    0.004748 
.32782    212.72    .004701 
.33216   214.86    -004654 
.33650   217.02    .004608 
.34085    219.20    .004562 

8-5 
•9 

3.69150   4914.8    0.000203 
•73493   543!-7     .000184 
.77836   6002.9     .000167 
.82179   6634.2     .000151 
.86522   7332.0     .000136 

5-40 
.41 
.42 
•43 
•44 

2.34519   221.41    0.004517 
•34953   223.63    .004472 
.35388    225.88    .004427 
.35822    228.15    .004383 
.36256   230.44    -004339 

9.0 
.1 

.2 

•3 

•4 

3.90865   8103.1    0.000123 
.95208   8955.3     .000112 
.99551   9897.1     .000101 
4.03894  10938.      .000091 
.08237  12088.     .000083 

5-45 
.46 

•47 
.48 

•49 

2.36690   232.76   0.004296 
.37125   235.10    .004254 
•37559   237.46    .004211 
•37993   239-85    .004169 
.38428   242.26    .004128 

9-5 

! 

•9 

4.12580  13360.    0.000073 
.16923  14765.     .000068 
.21266  16318.      .000061 
.25609  18034.      .000055 
.29952  19930.      .000050 

5-50 

2.38862   244.69   0.004087 

IO.O 

4.34294  22026.    0.000045 

SMITHSONIAN  TABLES. 


54 


TABLE  2O. 
EXPONENTIAL   FUNCTIONS. 

Value  of  «•**  and  «—•*•*  and  their  logarithms. 


X 

9 

^' 

,-' 

log*-*' 

0.1 

l.OIOI 

0.00434 

0.99005 

1.99566 

2 

1  .0408 

oi737 

96079 

98263 

3 

1.0942 

03909 

91393 

96091 

4 

I-I735 

06949 

85214 

93°5  ! 

5 

1.2840 

10857 

77880 

89M3 

0.6 

M333 

0.15635 

0.69768 

1.84365 

7 

1.6323 

21280 

61263 

78720 

8 

1.8965 

27795 

52729 

72205 

9 

2.2479 

35178 

44486 

64822 

1.0 

2.7183 

43429 

36788 

56571 

1.1 

3-3535 
4.2207 

0.52550 
62538 

0.29820 
23693 

1.47450 
37462 

3 

5-4I95 

73396 

18452 

26604 

4 

7.0993 

85122 

14086 

14878 

5 

9-4877 

97716 

10540 

02284 

1.6 

1.2936  X  io 

1.11179 

0.77305  X  io-1 

2.88821 

7 

1.7993 

255" 

55576 

74489 

8 

2-5534   " 

40711 

39l64 

59289 

9 

3.6966   " 

56780 

27052 

43220 

2.O 

5-4598   " 

737i8 

18316   " 

26282 

2.1 

8.2269 

1.91524 

0.12155   " 

2.08476 

2 

1.2647  X  io2 

2.10199 

79071  X  'io-2 

3.89801 

3 

1.9834   " 

29742 

50418   || 

70258 

4 

3-1735   " 

5OI54 

49846 

5 

5.1801   " 

7H34 

19305   " 

28566 

2.6 

8.6264 

2.93583 

0.11592 

3.06417 

7 

i.  4656  X  io3 

3.16601 

68233  X  io~3 

4-83399 

8 

2.5402 

40487 

39367   " 

595  i  3 

9 

4.4918 

65242 

22263 

3475» 

3-° 

8.1031 

90865 

12341 

09135 

3.1 

1.4913  X  io4 

4.17357 

0.67055  X  io~4 

•  5-82643 

2 

2.8001 

44718 

35713 

55282 

3 

5.3637   " 

72947 

18644   " 

27053 

4 

1.0482  X  io5 

5.02044 

95402  X  io~5 

6.97956 

5 

2.0898 

32011 

47851 

67989 

3.6 

4.2507 

5.62846 

0.23526   " 

6.37154 

8 

8.8205 
1.8673  X  io6 

,  94549 
6.27121 

"337 
53553  X  10-6 

05451 
7.72879 

9 

4.0329 

60562 

24796 

39438 

4-0 

8.8861   « 

94871 

11254   " 

05129 

4.1 

1.9975  X  io7 

7.30049 

0.50062  X  io~7 

S.6995I 

2 

4-5809   " 

66095 

21830   " 

_  33905 

3 

1.0718  X  io8 

8.03010 

933°3  X  io~8 

9.96990 

4 

2.5582   " 

40794 

39089 

59206 

5 

6.2296   " 

79446 

16052 

20554 

4.6 

1.5476  X  io9 

9.18967 

0.64614  X  io—  9 

10.81033 

7 

3.9225   " 

59357 

25494   " 

40643 

8 

1.0142  X  io10 

10.00614 

98595  X  io-10 

1  1  .99386 

9 

2.6755 

42741 

37376   " 

57259 

7.2005 

85736 

13888   " 

14264 

SMITHSONIAN  TABLES. 


TABLE  21. 
EXPONENTIAL    FUNCTIONS. 

n  _w 

Values  ol  £  "«*  and  6     *    and  their  logarithms. 


55 


X 

7T 

log  i^ 

JT 

e  ~& 

3r* 

1 

2-1933 

0.34109 

0.45594 

1.65891 

2 

4.8105 

.68219 

.20788 

•3i78i 

3 

1.0551  X  io 

1.02328 

.94780  X  io-1 

2.97672 

4 

2.3141 

-36438 

•432I4 

.63562 

5 

5-0754 

•70547 

•19703 

•29453 

6 

1.1132  X  io2 

2.04656 

0.89833  X  io-2 

3-95344 

7 

2.4415 

.38766 

.40958 

.61234 

8 

5-3549 

•72875 

.18674       " 

.27125 

9 

10 

1.1745  X  io3 
2.5760 

3.06985 
.41094 

.85144  X  io~3 
.38820 

4-930I5 
.58906 

11 

12 

5.6498       " 
1.2392  X  io4 

3-75203  • 

4-093*3 

0.17700       " 
.80700  X  io~4 

4.24797 
5.90687 

T3 

2.7178       " 

.43422 

•36/94       " 

•56578 

14 

5.9610       " 

.77532 

.16776 

.22468 

*5 

1.3074  X  io5 

5.11641 

.76487  X  io-3 

6.88359 

16 

2.8675       " 

5-45751 

0.34873 

6.54249 

17 

6.2893       " 

.79860 

.15900 

.20140 

18 

1.3794  X  io6 

6.13969 

.72495  X  io-6 

7.86031 

19 

3.0254       " 

.48079 

•33°53 

.51921 

20 

6.6356       « 

.82188 

.15070 

.17812 

TABLE   22. 
EXPONENTIAL   FUNCTIONS. 

V^  _VE* 

Values  of  B  *  x  and  &     *     and  their  logarithms. 


aj 

V^ 

e~x 

VTT 
log  6  ** 

Vjr 

er-f 

w 
tog*--' 

1 

r-5576 

0.19244 

0.64203 

1.80756 

2 

2.4260 

.38488 

.41221 

.61512 

3 

3.7786 

•57733 

.26465 

.42267 

4 

5-8853 

.76977 

.16992 

.23023 

5 

9.1666 

.96221 

.10909 

•03779 

6 

14.277 

1-15465 

0.070041 

2-84535 

7 

22.238 

•34709 

.044968 

.65291 

8 

34-636 

•53953 

.028871 

.46047 

9 

53-948 

•73I98 

.018536 

.26802 

10 

84.027 

.92442 

.011901 

•07558 

11 

130.88 

2.11686 

0.0076408 

3.88314 

12 

203.85 

.30930 

.0049057 

.69070 

«3 

14 
15 

3I7-50. 
494.52 

770.24 

.50174 
.69418 
.88663 

.0031496 
.0020222 
.0012983 

.49826 
.30582 

•JI337 

16 

1199.7 

3.07907 

0.00083355 

4.92093 

\l 

19 

1868.6 
2910.4 
4533-1 

.27151 
•46395 
•65639 

•00053517 
.00034360 
.00022060 

.72849 
•53605 
•3436i 

20 

7060.5 

.84883 

.00014163 

•IS"7 

SMITHSONIAN  TABLES. 


TABLES  23  AND  24. 
EXPONENTIAL  FUNCTIONS  AND  LEAST  SQUARES. 

TABLE  23.— Exponential  Functions 
Value  of  e*  and  d~*  and  their  logarithms. 


X 

«• 

loge* 

e~x 

X 

ex 

log** 

e" 

1/64 

1.0157 

0.00679 

0.98450 

i/3 

I-3956 

0.14476 

0.71653 

1/32 

•03  »7 

•01357 

.96923 

1    1/2 

.6487 

.21715 

.60653 

1/16 

.0645        .02714 

•93941 

3/4 

2.1170 

•32572 

•47237 

I/IO 

.1052  ,     .04343 

.90484  ; 

i 

.7183 

•43429 

.36788 

i/9 

•1^75 

.04825 

.89484 

5/4 

3-49°3 

•54287 

.28650 

1/8 

I-I33I 

0.05429  |  0.88250 

3/2 

4.4817 

0.65144 

0.22313 

i/7 

•1536 

.06204 

.86688 

7/4 

5-7546 

.76002 

•!7377 

1/6 

.1814 

.07238 

.84648  : 

2 

7-3^91 

.86859 

•'3534 

i/S 

.2214 

.08686 

•81873  ; 

9/4 

9.4877 

.97716 

.10540 

i/4 

.2840 

.10857 

.77880 

5/2 

12.1825 

1.08574 

.08208 

TABLE   24.  —  Least   Squares. 


Values  of  P  = 


z  d  (hx). 


This  table  gives  the  value  of  P,  the  probability  of  an  observational  error  having  a  value  posi- 
tive or  negative  equal  to  or  less  than  x  when  h  is  the  measure  of  precision,  P  =  £_  C  h* e— ('<*)' 
d(hx}.  For  values  of  the  inverse  function  see  the  table  on  Diffusion. 


hx 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

.01128 

.02256 

•03384 

.04511 

•05637 

.06762 

.07886 

.09008 

.10128 

.1 

.11246 

.12362 

•13476 

.14587 

•T5695 

.16800 

.17901 

.18999 

.20094 

.21184 

.2 

.22270 

•23352 

.24430 

•25502 

.26570 

•27633 

.28690 

•29742 

•30788 

.31828 

•3 

.32863      .33891 

•349  »3 

•35928 

•36936 

37938 

•38933 

.39921 

.40901 

.41874 

•4 

.42839 

•43797 

•44747 

•45689 

.46623 

•47548 

.48466 

•49375 

•50275 

.51167 

0.5 

•52050 

.52924 

•53790 

.54646 

•55494 

•56332 

.57162 

.57982 

.58792 

•59594 

.6 

.60386 

.61168 

.61941 

.62705 

•63459 

.64203 

•64938 

•65663 

.66378 

.67084 

•7 

.67780 

.68467 

.69143 

.69810 

.70468 

.71116 

•71754 

-72382 

.73001 

.73610 

.8 

.74210 

.74800 

•7538i 

•75952 

•76514 

.77067 

.77610 

.78144 

.78669 

.79184 

•9 

.79691 

.80188 

.80677 

.81156 

.81627 

.82089 

.82542 

.82987 

•83423 

•83851 

1.0 

.84270 

.84681 

.85084 

.85478 

.85865 

.86244 

.86614 

.86977 

•87333 

.87680 

.1 

.88021 

-88353 

.88679 

.88997 

.89308 

.89612 

.89910 

.90200 

.90484 

.90761 

.2 

.91031 

.91296 

•91553 

.91805 

.92051 

.92290 

•92524 

•92751 

•92973 

.93190 

•3 

.93401 

.93606 

•93807 

.94002 

.94191 

•94376 

•94556 

•94731 

.94902 

•95067 

•4 

•95229 

•95385 

•95538 

.95686 

.95830 

•95970 

.96105 

.96237 

•96365 

.96490 

1.5 

.96611 

.96728 

.96841 

•96952 

.97059 

.97162 

.97263 

-9736o 

•97455 

•97546 

.6 

•97635 

•97721 

.97804 

.97884 

.97962 

.98038 

.98110 

.98181 

.98249 

•983,15 

•7 

•98379 

.98441 

.98500 

•98558 

.98613 

.98667 

.98719 

.98769 

.98817 

.98864 

1    -8 

.98909 

.98952 

.98994 

•99035 

•99074 

.99111 

.99147 

.99182 

.99216 

.99248 

•9 

.99279 

.99309 

•99338 

•99366 

•99392 

.99418 

•99443 

.99466 

.99489 

•995  " 

2.0 

•99532 

•99552 

-99572 

.99591 

.99609 

.99626 

.99642 

•99658 

•99673 

.99688 

.1 

.99702 

•997  i  5 

.99728 

.99741 

•99753 

•99764 

•99775 

•99785 

•99795 

•99805 

.2 

.99814 

.99822 

.99831 

.99839 

.99846 

.99854 

.99861 

.99867 

•99874 

.99880 

•3 

.99886 

.99891 

.99897 

.99902 

.99906 

.99911 

•999  '5 

.99920 

•99924 

.99928 

•4 

•9993  r 

•99935 

.99938 

.99941 

•99944 

•99947 

.99950  * 

•99952 

•99955 

•99957 

2.5 

.6 

•99959 
.99976 

.99961 

.99978 

•99963 
-99979 

•99965 
.99980 

•99967 
.99981 

•99969 
.99982 

•9997  i 
•99983 

•99972 
.99984 

•99974 
.99985 

•99975 
.99986 

•7 

•99987      -99987      -99988 

.99989 

.99989 

.99990 

•9999' 

.99991 

•99992 

•99992 

.8 

.99992      .99993      -99993 

•99994 

•99994 

•99994 

•99995 

•99995 

•99995 

.99996 

•9 

.99996 

.99996 

.99996 

•99997 

•99997 

•99997 

•99997 

•99997 

•99997 

.99998 

3.0 

.99998 

•99999 

•99999 

I.OOOOO 

Taken  from  a  paper  by  Dr.  James  Burgess  'on  the  Definite  Integral  y^/0  e~**  dt,  with  Ex. 
tended  Tables  of  Values.'     Trans.  Roy.  Soc.  of  Edinburgh,  vol.  xxxix,  1900,  p.  257. 
SMITHSONIAN  TABLES. 


TABLE  25. 
LEAST  SQUARES. 


57 


This  table  gives  the  values  of  the  probability  P,  as  defined  in  last  table,  corresponding  to  different  values  of 
x I  r  where  r  is  the  "  probable  error."     The  probable  error  r  is  equal  to  0.476947  h. 


» 

T 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

.00000 

.00538 

.01076 

.01614 

.02152 

.02690 

.03228 

.03766 

•04303 

.04840 

O.I 

•05378 

.05914 

.06451 

.06987 

•07523 

.08059 

•08594 

.09129 

.09663 

.10197 

0.2 

.10731 

.  1  1  264 

.11796 

.12328 

.12860 

J3391 

.13921 

•I4451 

.14980 

.15508 

o-3 

.16035 

.16562 

.17088 

.17614 

.18138 

.18662 

.19185 

.19707 

.20229 

.20749 

0.4 

.21268 

.21787 

.22304 

.22821 

•23336 

.23851 

•24364 

.24876 

.25388 

.25898 

0.5 

.26407 

.26915 

.27421 

.27927 

.28431 

.28934 

.29436 

•29936 

.30435 

•30933 

0.6 

•3r43° 

•3T925 

•32419 

.32911 

•33402 

.33892 

.34380 

.34866 

•35352 

•35835 

0.7 

•363  i  7 

.36798 

•37277 

•37755 

•38231 

•38705 

•39*78 

•39649 

.40118 

.40586 

o.S 

.41052 

•4i5I7 

.41979 

.42440 

.42899 

•43357 

.43813 

.44267 

.44719 

.45169 

0.9 

.45618 

.46064 

.46509 

.46952 

•47393 

.47832 

.48270 

.48705 

49139 

.49570 

1.0 

.50000 

.50428 

•50853 

•5I277 

•51699 

.52119 

.52537 

•52952 

•53366 

•53778 

i.i 

.54188 

•54595 

.55001 

.55404 

.55806 

•56205 

.56602 

.56998 

•57391 

.57782 

1.2 

.58171 

•58558 

.58942 

•59325 

.59705 

.60083 

.60460 

•60833 

.61205 

•61575 

r-3 

.61942 

.62671 

•63032 

•63391 

•63747 

.64102 

•64454 

.64804 

•651  S2 

1.4 

.65498 

.65841 

.66182 

.66521 

.66858 

•67193 

•67526 

.67856 

.68184 

.68510 

1.5 

.68833 

•69155 

.69474 

.69791 

.70106 

.70419 

.70729 

.71038 

.71344 

.71648 

1.6 

.71949 

.72249 

.72546 

.72841 

•73134 

•73425 

•737M 

.74000 

.74285 

•74567 

i-7 

.74847 

•75I24 

.75400 

•75674 

-75945 

.76214 

.76481 

•76746 

•77009 

.77270 

1.8 

.77528 

•77785 

.78039 

.78291 

•78542 

.78790 

.79036 

.79280 

•79522 

.79761 

1.9 

•79999 

.80235 

.80469 

.80700 

.80930 

.81158 

•81383 

.81607 

.81828 

.82048 

2.0 

.82266 

.82481 

.82695 

.82907 

.83117 

•83324 

•83530 

.83734 

•83936 

.84137 

2.1 

•84335 
.86216 

•84531 
.86394 

.84726 
.86570 

.84919 
.86745 

.85109 
.8691  7 

.85298 
.87088 

.85486 
.87258 

.85671 
•87425 

.85854 
•87591 

.86036 

•87755 

2-3 

.87918 

.88078 

.88237 

•88395 

.88550 

.88705 

.88857 

.89008 

.89157 

.89304 

2.4 

.89450      .89595 

.89738 

.89879 

.90019 

•90157 

•90293 

.90428 

.90562 

.90694 

2.5 

.90825 

.90954 

.91082 

.91208 

•9I332 

•91456 

•9*578 

.91698 

.91817 

•9I935 

2.6 

.92051 

.92166 

.92280 

.92392 

•92503 

.92613 

.92721 

.92828 

•92934 

-93038 

2.7 

•93  HI 

•93243 

•93344 

•93443 

•93541 

•93638 

•93734 

.93828 

.93922 

.94014 

2.8 

.94105 

•94195 

.94284 

•94371 

.94458 

•94543 

.94627 

.94711 

•94793 

.94874 

2.9 

•94954 

•95033 

.95111 

•95l87 

•95263 

•95338 

.95412 

.95484 

•95557 

.95628 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

.95698 

.96346 

.96910 

•97397 

.97817 

.98176 

.98482 

.98743 

.98962 

.99147 

4 

.99302    |  .9943  i 

•99539 

99627 

.99700 

.99760 

.99808 

.99848 

•998/9 

•99905 

5 

.99926      .99943 

.99956 

.99966 

•99974 

.99980 

•99985 

.99988 

.99991 

•99993 

TABLE  26. 
LEAST  SQUARES. 

Values  of  the  factor  0.6745  A/ ^-=. 

This  factor  occurs  in  the  equation  rs  =  0.6745-%  /       -    for  the  probable  error  of  a  single  observation,  and  other 

similar  equations. 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.6745 

0.4769 

0.3894 

0-3372 

0.3016 

0-2754 

0.2549 

0.2385 

10 

0.2248 

0.2133 

•2034 

.1947 

.1871 

.1803 

.1742 

.1686 

.1636 

.1590 

20 

•1547 

.1508 

.1472 

.1438 

.1406 

.1377 

•1349 

•1323 

.1298 

•1275 

30 

40 

.1252 
.1080 

!io66 

.1211 
•1053 

.1192 
.1041 

.1174 
.1029 

•"57 

.1017 

.1140 
.1005 

.1124 
.0994 

.1109 
.0984 

.1094 
.0974 

50 

0.0964 

0.0954 

0.0944 

0-0935 

0.0926 

0.0918 

0.0909 

0.0901 

0.0893 

0.0886 

60 
70 

.0878 
.0812 

.0871 
.0806 

.0864 
.0800 

•0857 
•0795 

.0850 
.0789 

.0843 
.0784 

•0837 
.0779 

.0830 
.0774 

.0824 
.0769 

.0818 
.0764 

80 

•°759 

•0754 

.0749 

•0745 

.0740 

.0736 

.07  1* 

.0727 

.0723 

.0719 

90 

•0715 

.0711 

.0707 

.0703 

.0699 

.0696 

.0692 

.0688 

.0685 

.0681 

SMITHSONIAN  TABLES. 


58  TABLE  27.- LEAST  SQUARES. 

Values  of  the  factor  0.6745A/   (><1_1)- 
This  factor  occurs  in  the  equation  r0=o.6745A/  — '         -  for  the  probable  error  of  the  arithmetic  mean. 


w  = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.4769 

0-2754 

0.1947 

o.  1  508 

0.1231 

o.  1  04  1 

0.090  1 

0.0795 

10 

0.0711 

0.0643 

.0587 

.0540 

.0500 

.0465 

•0435 

.0409 

.0386 

•0365 

20 

.0346 

.0329 

.0314 

.0300 

.0287 

.0275 

.0265 

•0255 

.0245 

.0237 

30 

.0229 

.0221 

.OJI4 

.0208 

.0201 

.0196 

.0190 

.0185 

.0180 

•0175 

40 

.0171 

.0167 

.0163 

.0159 

•O'SS 

.0152 

.0148 

.0145 

.0142 

.0139 

50 

0.0136 

0.0134 

0.0131 

0.0128 

0.0126 

0.0124 

O.OI22 

0.0119 

0.0117 

0.0115 

60 

.0113 

.Oil  I 

.01  10 

.0108 

.0106 

.0105 

.0103 

.0101 

.0100 

.0098 

?o 

.0097 

.0096 

.0094 

.0093 

.0092 

.0091 

.0089 

.0088 

.0087 

.0086 

80 

.0085 

.0084 

.0083 

.0082 

.0081 

.0080 

.0079 

.0078 

.0077 

.0076 

90 

.0075 

.0075 

.0074 

.0073 

.0072 

.0071 

.OO7I 

.0070 

.0069 

.0068 

TABLE  28. -LEAST  SQUARES. 

Values  of  the  factor  0.8453\/  y-1-— • 

\  ?i\?i — xj 


This  factor  occurs  in  the  approximate  equation  r  =0.8453  (• • for  the  probable  error  of  a  single  observation. 

•  « (« — /  ) 


n  = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.5978 

0-3451 

0.2440 

0.1890 

0.1543 

0.1304 

0.1130 

0.0996 

10 

0.0891 

0.0806 

.0736 

.0677 

.0627 

•05^3 

.0546 

•0513 

.0483 

•0457 

20 

•0434 

.O4I2 

•0393 

.0376 

.0360 

•°345 

•0332 

.0319 

.0307 

.0297 

30 

.0287 

.0277 

.0268 

.0260 

.0252 

.0245 

.0238 

.0232 

.0225 

.0220 

40 

.0214 

.0209 

.0204 

.0199 

.0194 

.0190 

.0186 

.0182 

.0178 

.0174 

50 

0.0171 

O.OI67 

0.0164 

0.0161 

0.0158 

0.0155 

0.0152 

o.oi  50 

0.0147 

0.0145 

60 

.0142 

.0140 

•0137 

•0135 

•0133 

.0131 

.0129 

.0127 

.0125 

.0123 

70 

.0122 

.0120 

.0118 

.0117 

.0115 

.0113 

.0112 

.0111 

.0109 

.0108 

80 

.OIO6 

.OIO5 

.0104 

.0102 

.OIOI 

.0100 

.OO99 

.0098 

.0097 

.0096 

90 

.0094 

.0093 

.0092    .0091 

.0090 

.0089 

.0089 

.0088 

.0087 

.0086 

TABLE  29.  -LEAST  SQUARES. 


Values  of  0.8453  —  r 

This  factor  occurs  in  the  approximate  equation  rn=:  0.8453 


n  —  1 

for  the  probable  error  of  the  arithmetical  mean. 


n  — 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

* 

0.4227 

0.1993 

0.1220 

0.0845 

0.0630 

0.0493 

0.0399 

0.0332 

10 

0.0282 

0.0243 

.0212 

.oiScS 

.0167 

.0151 

.0136 

.0124 

.01  14 

.0105 

20 

.0097 

.0090 

.0084 

.0078 

.0073 

.0069 

.0065 

.0061 

.0058 

•0055 

30 

.0052 

.0050 

.0047 

.0045 

.0043 

.0041 

.0040 

.0038 

.0037 

•0035 

40 

.0034 

.0033 

.0031 

.0030 

.0029 

.0028 

.0027 

.0027 

.0026 

.0025 

50 

0.0024 

0.002T 

0.0023 

O.OO22 

O.OO22 

O.OO2I 

0.0020 

O.OO2O 

0.0019 

0.0019 

60 

.0018 

.OOlS 

.0017 

.OOI7 

.OOI7 

.OOl6 

.OOl6 

.OOl6 

.0015 

.0015 

70 

.0015 

.OOI4 

.0014 

.0014 

.0013 

.0013 

.OOI3 

.OOI3 

.0012 

.0012 

80 

.0012 

.OOI2 

.0011 

.0011 

.OOI  I 

.OOI  I 

.OOI  I 

.0010 

.0010 

.OOIO 

90 

.0010 

.0010 

.0010 

.OOO9 

.OOO9 

.0009 

.0009 

.0009 

.0009 

.0009 

SMITHSONIAN  TABLES. 


TABLE  3O. 
LEAST  SQUARES. 


Observation  equations  : 

aizi  +  b!Z2  +  .  .  .    lizq  =  Mb  weight  pt 
a2zi  +  b2z2  +  .  .  .    I2zq  =  M2.  weight  p2 


anz!  +  bnz2  +  .  .  .    lnzq  =  Mn,  weight  pn. 

Auxiliary  equations : 

[paa]     =  piaf      +  P2af       +  •  •  •  pna^. 
[pab]     =  Piaib!   +  p2a2b2  +  .  .  .  pnanbn. 

[paM]  =  piaiMi  -f  p2a2M2  -f  .  .  .  pnanMn. 

Normal  equations  : 

fpaa]zi-f  [pab]z2  +  .  .  .  [pal]zq  =  [paM] 
pabJZl  +  [pbb]z2  +  .  .  .   [pbl]zq  =  [pbM] 

[pla]Zl  +  [plb]z2     +  .  .  .'  [plljzq  = 

Solution  of  normal  equations  in  the  form, 

Zl  =  AJpaM]  +  BifpbM]  -f  .  .  .  I 
z2  =  A2[paM]  +  B2[pbM]  +  .  .  .  I 

zq  =  An[paM]  +  Bn[pbMJ  +  .'.  .  Ln[plM], 
gives  : 

weight  of  zi  =  pzi  =  (Aj)— 1  ;  probable  error  of  zi  = — — - 


weight  of  z2  =  pz2  =  (B2)-1 ;  probable  error  of  z2  = — 

\/Pz2 

weight  of  zq  =  pZq  =  (Ln)"1;  probable  error  of  zq  = — — 

wherein 

r  =  probable  error  of  observation  of  weight  unity 

=  0.6745  -i/  —  • —  (q  unknowns.) 

Arithmetical  mean, n  observations:  _ 

r  =  0.6745 A/  —  (approx.)  =probable  error  of  ob- 

*  n  —  I       \/n(n  —  i)'  servation  of  weight  unity. 


/      S  V2         _  0.8453   2  V 

—      —   --         — 


V  _  0.453         V 

r0  =  0.67  45\/  —     —  :  --  7==.  —       (approx.)  =  probable  error 
\n(n-i)          nVn-i  of  mean. 


Weighted  mean,  n  observations: 

/Spv2  r 

r  =  0.6745  \   ~  — ;  r0  =  -==o. 


Probable  error  (R)  of  a  function  (Z)  of  several  observed  quantities  zi,  z2,  .  .  .  whose 

probable  errors  are  respectively,  i-i,  r.> 

Z'=  f  ("Zl,  z2,  .   .  .) 


Examples  : 

Z  --=  zi  ±  z2  +  .  .  .  R2  =  r\  +  r\ 

Z  =  Az!  ±  Bza  ±  .  .  .  R2  =A2  r\  + 

Z  =  zi  z2.  R-  =  zi2r!5-fj 


SMITHSONIAN  TABLES. 


6o 


TABLE  31  . 
DIFFUSION. 


Inverse  *  values  of  <•  /c  =  i  —  -77— 


log  x  =  log  (2y)  +  logx/Xtf.     t  expressed  in  seconds. 

=  log  6  +  logx/^A     /  expressed  in  days. 

=  log  7  +  log  \/kf.  "          «•  years. 

k  =  coefficient  of  diffusion.! 
c  =  initial  concentration. 
v  =  concentration  at  distance  x,  time  t. 


v/c 

log  2? 

2? 

logfi 

6 

log  y 

Y 

0.00 

+  00 

+  00 

+  00 

+  00 

oo 

oo 

.01 

0.56143 

3.6428 

!  3-02970 

1070.78 

4.31098 

20463. 

.02 

•S'719 

3.2900     ;  2.98545 

967.04 

.26674 

18481. 

•°3 

.48699     3.0690         .95525 

902.90 

•23654 

17240. 

.04 

.46366     2.9044 

.93132 

85373 

.21261 

16316. 

005 

0.44276     2.7718 

2.91102 

814.74 

4.19231 

r557i- 

.06 

.42486     2.6598 

.89311 

781.83 

.17440 

14942. 

.07 

.40865  i  2.5624 

.87691 

753-20 

.15820 

14395- 

.08 

•39372 

2.475» 

.86198 

727.75 

•M327 

13908. 

.09 

•37979 

2-3977 

.84804 

704.76 

•12933 

13469. 

0.10 

.1  1 

0.36664     2.3262 
.35414     2.2602 

2.83490 
.82240. 

66+36 

4.11619 
.10369 

13067. 
12697. 

.12 

.34218     2.1988 

.81044 

646.31 

.09173 

12352- 

•T3 

.33067     2.1413 

•79893 

629.40 

.08022      12029. 

.14 

.31954     2.0871 

.78780 

613.47 

.06909      11724. 

0.15 

0.30874     2.0358 

2.77699 

598.40 

4.05828      11436. 

.16 

.29821 

1.9871 

.76647 

584.08 

.04776      11162. 

•17 

.28793 

1.9406 

•75619 

57041 

.03748 

10901. 

.18 

.27786 

1.8961 

.74612 

557-34 

.02741 

10652. 

.19 

.26798 

1.8534 

.73624 

544.80 

•OI753 

10412. 

0.20 

0.25825 

1.8124 

2.72651 

532.73 

4.00780 

10181. 

.21 

.24866 

1.7728 

.71692 

521.10 

3.99821 

9958.9 

.22 

.23919 

1.7346 

.70745 

509.86 

.98874 

9744.1 

•23 

.22983 

1.6976 

.69808 

498.98 

•97937 

9536.2 

.24 

.22055 

i.  6617 

.68880 

488.43 

.97010 

9334-6 

025 

.26 

0.21134 
.20220 

1.6268 
I-593° 

2.67960 

.67046 

478.19 
468.23 

3.96089 
•95^75 

9138.9 
8948.5 

'   -27 

.19312 

1.5600         .66137 

458.53 

.94266 

8763-2 

.28 

.18407 

1.5278 

.65232 

449.08 

.93361       8582.5 

.29 

.17505 

1.4964 

.6433! 

439-85 

.92460 

8406.2 

0.30 

0.16606  |  1.4657 

2.63431 

430.84 

3.91560 

8233-9 

•31 

.15708      1.4357 

•62533 

422.02 

.90662 

8065.4 

•32 

.14810      1.4064 

.61636 

4I3-39 

•89765 

7900.4 

•33 

.13912      1.3776 

.60738 

404.93 

.88867 

7738.8 

•34 

•13014      1-3494 

.59840 

396.64 

.87969 

7580-3 

035 

0.12114 

1.3217 

2.58939 

388.50 

3.87068 

7424.8 

•36 

•37 

.11211 

.10305 

1.2945 
1.2678 

.58037 

•57I31 

38051 
372.66 

.86166 
.85260 

7272.0 
7122.0 

•38 

.09396        1.2415 

.56222 

364-93 

.8435' 

6974.4 

•39 

.08482        I.2I57 

•55308 

357-34 

.83437 

6829.2 

0.40 

.41 
.42 
•43 

0.07563        I.I9O2 
.06639        1.1652 
.05708        1.1405 

.04770      1.1161 

2-54389 
.53464 
•52533 
•5*595 

349.86 
342.49 
335-22 
328.06 

3.82518 

.81593 
.80662 

•79724 

6686.2 

6545-4 
6406.6 
6269.7 

•44 

.03824      1.0920 

.50650 

320.99 

.78779 

6134.6 

045 

002870      1.0683 

2.49696 

314.02 

3-77825 

6001.3 

.46 

.01907      1.0449 

•48733 

307-13 

.76862 

5869.7 

•47 

.00934      1.0217 

.47760 

300.33 

75889 

5739-7 

.48 

9.99951      0.99886 

•46776 

293.60 

•74905 

5611.2 

•49 

.98956     0.97624 

45782 

286.96 

•73911 

5484.1 

050 

9-97949  \  0.95387 

2-44775 

280.38 

3.72904 

5358.4 

t  Kelvin,  Mathematical  and  Physical  Papers,  vol.  III.  p.  428  ;  Becker,   Am.  Jour, 
of  Sci.  vol.  III.  1897,  p.  280*.  *For  direct  values  see  table  24. 

SMITHSONIAN  TABLES. 


TABLE   31    (continued). 

DIFFUSION. 


61 


vie 

log  2? 

2q 

log  6 

6 

logy 

Y 

0.50 

9-97949 

0.95387 

2-44775 

280.38 

3.72904 

5358.4 

•51 

.96929 

•93  '74 

•43755 

273-87 

.71884 

5234.I 

•52 

.95896 

.90983 

.42722 

26743 

.70851 

5  1  1  1  .0 

•53 

.94848 

.88813 

.41674 

261.06 

.69803 

4989.1 

•54 

•93784 

.86665 

.40610 

254-74 

.68739 

4868.4 

0.55 

9.92704 

0.84536 

2-3953° 

248.48 

3-67659 

4748.9 

•56 

.91607 

.82426 

•38432 

242.28 

.66561 

4630-3 

•57 

.90490 

•80335 

•373l6 

236.13 

•65445 

4512.8 

.58 

•89354 

.78260 

.36180 

230.04 

.64309 

4396.3 

•59 

.88197 

.76203 

•35023 

223.99 

.63152 

4280.7 

0.60 

9.87018 

0.74161       2.33843 

217.99 

3-6I973 

4166.1 

.61 

•85815 

•72135  !   -32640 

212.03 

.60770 

4052.2 

.62 

.84587 

.70124 

.31412 

2O6.  1  2 

•59541 

3939-2 

•63 

•83332 

.68126 

•3OI57 

200.25 

.58286 

3827.0 

.64 

.82048 

•66143 

. 

.28874 

194.42 

•57003 

37I5-6 

0.65 

9.80734 

0.64172 

2.27560 

I88.63 

3.55689 

3604.9 

.66 

.79388 

.62213 

.26214 

182.87 

•54343 

3494-9 

.67 

.78008 

.60266 

•24833 

I77.I5 

.52962 

3385.4 

.68 

.76590 

•58331 

.23416 

171.46 

•5I545 

3276.8 

.69 

•7  5  '33 

•56407 

.21959 

165.80 

.50088 

3168.7 

0.70 

9-73634 

0.54493 

2.20459 

160.17 

3.48588 

3061.1 

•7* 

.72089 

.52588 

.18915 

154.58 

•47044 

2954.2 

.72 

•70495 

.50694 

.17321 

I49.OI 

•4545° 

2847.7 

•73 

.68849 

.48808 

•15675 

143-47 

•43804 

2741.8 

•74 

.67146 

.46931 

.13972 

'37-95 

.42101 

2636.4 

0.75 

9.65381 

0.45062 

2.12207 

132.46 

340336 

25314 

•76 

•6355° 

.43202 

.10376 

126.99 

•38505 

2426.9 

•77 

.61646 

.41348     .08471 

121.54 

.36600 

2322.7 

.78 
•79 

.59662 
•57590 

•39502 
.37662 

.06487 
.04416 

1  1  6.  1  1 
110.70 

.34616 
•32545 

2219.0 
2115.7 

0.80 

9-55423 

0.35829 

2.02249 

105-31 

3-30378 

2012.7 

.81 

•53I5° 

.34001 

1-99975  1     99-943 

.28104 

1910.0 

.82 

•50758 

.32180 

.97584 

94.589 

•25713 

1807.7 

•83 

.84 

-48235 
•45564 

•30363 

.28552 

-95061 
.92389 

89.250 
83.926 

.23190 

.20518 

1705.7 
1603.9 

0.85 

9.42725 

0.26745 

I-8955I 

78.615 

3.17680 

1502.4 

.86 

•39695 

.24943 

.86521 

73-3I7 

.14650 

1401.2 

.87 

•36445 

•23*45 

.83271 

68.032 

.11400 

1300.2 

.88 

.32940 

•21350 

.79766 

62.757 

•07895 

1199.4 

.89 

•29!35 

•19559 

•7596i 

57492 

3.04090 

1098.7 

0.90 

9.24972 

0.17771 

1.71797 

52.236 

2.99926 

998.31 

.91 

.20374 

.15986 

.67200 

46.989 

•95329 

898.03 

.92 

•i5239 

.14203 

.62065 

41.750            .90194 

797.89 

•93 

.09423 

.12423 

.56249 

36.516            .84378 

697-88 

•94 

9.02714 

.10645 

•49539 

31.289 

.77668 

597.98 

0.95 

8.94783 

0.08868 

1.41609 

26.067 

2.69738 

498.17 

.96 

.85082 

•07093 

•3I9Q7 

20.848 

.60036 

398.44 

•97 

.72580       .05319 

.19406 

I5-633 

•47535 

298.78 

.98 

.54965       -03S45 

.01791 

10.421 

.29920 

199.16 

•99 

.24859       .01773 

0.71684 

5.21007 

1.99813 

99-571 

1.00 

—  oo      ;  o.ooooo 

—  00 

o.ooooo 

—  oo 

o.ooo 

il          1 

SMITHSONIAN  TABLES. 


62 


TABLE  32. 
GAMMA   FUNCTION, 


Value  of  log 


•JT- 


^dx  +  10. 

Values  of  the  logarithms  +  10  of  the  "  Second  Eulerian  Integral  "  (Gamma  function) 


S. 


log  n«)-|-ic 


for  values  of  «  between  i  and  2.     When  «  has  values  not  lying  between  i  and  2  the  value  of  the  ft  nction  can  be 
readily  calculated  from  the  equation  T(w-f-i)  =  «I\«)  =  «(»— i)  .  .  .  («— r)T(n— r). 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1OO 

9-99  

97497 

95001 

925*2 

90030 

87555 

85087 

82627 

80173 

77727 

I.OI 

75287 

72855 

7043° 

68011 

65600 

63*96 

60798 

58408 

56025 

53648 

1.02 

5I279 

48916 

46561 

44212 

41870 

39535 

37207 

34886 

32572 

30265 

1.03 
1.04 

27964 
05334 

25671 
03108 

23384 

21104 
98677 

18831 
9647* 

16564 
94273 

£4305 
92080 

12052 
89895 

09806 
87715 

07567 
§5544 

1.05 

9-9883379 

81220 

79068 

76922 

74783 

72651 

70525 

68406 

66294 

64188 

i.  06 

62089 

59996 

579*o 

55830 

5375,7 

5*690 

49630 

47577 

4553° 

43489 

1.07 

4M55 

39428 

37407 

35392 

33384 

3*382 

29387 

27398 

254*5 

23439 

i.  08 

21469 

19506 

17549 

*5599 

13655 

mn 

29785 

07860 

P.5M*. 

04029 

1.09 

02123 

00223 

98329 

96442 

9456i 

92686 

90818 

88956 

87100 

81256 

1.10 

9.9783407 

81570 

7973s 

779*4 

76095 

74283 

72476 

70676 

68882 

67095 

i.  n 

65313 

63538 

61768 

60005 

58248 

56497 

54753 

530*4 

51281 

49555 

1.  12 

47834 

46120 

44411 

42709 

4*013 

39323 

37638 

3596o 

34288 

32622 

1.13 

30962 

29308 

27659 

26017 

24381 

22751 

21126 

19508 

17896 

16289 

I.I4 

14689 

13094 

09922 

08345 

06774 

05209 

03650 

02096 

00549 

1.15 

9.9699007 

9747  i 

95941 

944*7 

92898 

9*386 

89879 

88378 

86883 

85393 

1.16 

83910 

82432 

80960 

79493 

78033 

76578 

75*29 

73686 

72248 

70816 

1.17 

.69390 

67969 

66554 

63742 

62344 

60952 

59566 

58*85 

56810 

l.lo 

55440 

54076 

52718 

5*366 

50019 

48677 

4734* 

46011  ' 

44687 

43368 

1.19 

42054 

40746 

39444 

38147 

36856 

35570 

34290 

33016 

3*747 

30483 

1.20 

9.9629225 

27973 

26725 

25484 

24248 

23017 

21792 

20573 

*9358 

18150 

1.  21 

16946 

15748 

14556 

'3369 

12188 

IIOI  I 

08675 

06361 

1.22 

05212 

04068 

02930 

01796 

00669 

99546 

98430 

973*8 

96212 

95*** 

1.23 

594015 

92925 

91840 

90760 

89685 

88616 

87553 

86494 

8544* 

84393 

1.24  ' 

83350 

82313 

81280 

80253 

79232 

78215 

77204 

76198 

74201 

1.25 

9.9573211 

72226 

71246 

70271 

69301 

68337 

67377 

66423 

65474 

6453° 

1.26 
1.27 

63592 
54487 

62658 
53604 

61730 

52727 

60806 
5*855 

59888 
50988 

58975 
50126 

58067 
49268 

57*65 
48416 

56267 

47570 

55374 
46728 

1.28 

45891 

45059 

44232 

434*0 

42593 

41782 

40975 

40173 

39376 

38585 

1.29 

37798 

37oi6 

36239 

35467 

347oo 

33938 

32429 

31682 

30940 

1.30 

9-9530203 

29470 

28743 

28021 

27303 

26590 

25883 

25180 

24482 

23789 

1.31 

23100 

22417 

21739 

21065 

20396 

19732 

19073 

18419 

17770 

17125 

1.32 

16485 

'5850 

15220 

*4595 

*3975 

*3359 

12748 

12142 

1  1  541 

10944 

i-33 

10353 

09766 

09184 

08606 

08034 

07466 

06903 

06344 

0579* 

05242 

i-34 

04698 

04158 

03624 

03094 

02568 

02048 

01532 

OIO2I 

00514 

00012 

1.35 

9-94995  *  5 

99023 

98535 

98052 

97573 

97100 

96630 

96166 

95706 

95251 

1.36 

94800 

94355 

939*3 

93477 

93044 

92617 

92*94 

9*776 

91362 

90953 

9°549 

90149 

89754 

89363 

88977 

88595 

88218 

87846 

874/8 

87II5 

I'js 

86756 

86402 

86052 

85707 

85366 

85030 

84698 

84371 

84049 

S373I 

i-39 

83417 

83108 

82803 

82503 

82208 

81916 

81630 

81348 

81070 

80797 

1.40 

9.9480528 

80263 

80003 

79748 

79497 

79250 

79008 

78770 

78537 

78308 

1.41 

78084 

77864 

77648 

77437 

7723° 

77027 

76829 

76636 

76446 

76261 

1.42 

76081 

75905 

75733 

75565 

75402 

75243 

75089 

74939 

74793 

74652 

i-43 

745'5 

74382 

74254 

74*30 

74010 

73894 

73783 

73676 

73574 

73476 

1.44 

73382 

73292 

73207 

73*25 

73049 

72976 

72908 

72844 

72784 

72728 

Legendre's  "Exercises  de  Calcul  Integral,"  tome 


SMITHSONIAN   TABLES. 


TABLE   &2  (continued). 

GAMMA    FUNCTION. 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.45 

9.9472677 

72630 

72587 

72549 

72514 

72484 

72459 

72437 

72419 

72406 

1.46 

72397 

72393 

72392 

72396 

72404 

72416 

72432 

72452 

72477 

72506 

1.47 

72539 

72576 

72617 

72662 

72712 

72766 

72824 

72886 

72952 

73022 

1.48 

73097 

73175 

73258 

73345 

73436 

73531 

73630 

73734 

73841 

73953 

1.49 

74068 

74188 

743  1  2 

74440 

74572 

74708 

74848 

74992 

75!4i 

75293 

1.50 

9.9475449 

75610 

75774 

75943 

76116 

76292 

76473 

76658 

76847 

77040 

l-5l 

77237 

774"- 

77642 

77851 

78064 

78281 

78502 

78727 

78956 

79189 

1.52 

79426 

79667 

79912 

80161 

80414 

80671 

80932 

81196 

81465 

81738 

i-53 

i-54 

82015 
84998 

82295 
85318 

82580 
85642 

82868 
85970 

83161 
86302 

83457 
86638 

83758 
86977 

84062 
87321 

84370 
87668 

84682 
88019 

1.55 

9.9488374 

88733 

89096 

89463 

89834 

90208 

90587 

90969 

9r355 

91745 

1.56 

92139 

92537 

92938 

93344 

93753 

94166 

94583 

95004 

95429 

95857 

l>57 

96289 

96725 

97165 

97609 

98056 

98508 

98963 

99422 

99885 

00351 

i-58 
i-59 

500822 
05733 

01296 
06245 

01774 
06760 

02255 
07280 

02741 
07803 

03230 
08330 

03723 
08860 

04220 
09395 

04720 
09933 

05225 
J0475 

1.60 

9.9511020 

11569 

I2I22 

12679 

13240 

13804 

M372 

14943 

J55T9 

16098 

1.61 

16680 

17267 

17857 

18451 

19048 

19649 

20254 

20862 

21475 

22091 

1.62 

22710 

23333 

23960 

24591 

25225 

25863 

26504 

27149 

27798 

28451 

1.63 

29107 

29766 

30430 

31097 

3*767 

32442 

33120 

338oi 

34486 

35X75 

1.64 

35867 

36563 

37263 

37966 

38673 

39383 

40097 

40815 

41536 

42260 

1.65 

9.9542989 

43721 

44456 

45*95 

4593s 

46684 

47434 

48187 

48944 

49704 

1.66 

50468 

5I236 

52007 

52782 

5356o 

54342 

55I27 

559*6 

56708 

575°4 

1.67 

58303 

59106 

59913 

60723 

61536 

62353 

63174 

63998 

64825 

65656 

1.68 

66491 

67329 

68170 

69015 

69864 

70716 

7i57i 

7243° 

73293 

74159 

1.69 

75028 

759oi 

/6777 

77657 

78540 

79427 

80317 

81211 

82108 

83008 

1.70 

9.9583912 

84820 

85731 

86645 

87563 

88484 

89409 

90337 

91268 

92203 

1.71 

93  HI 

94083 

95028 

95977 

96929 

97884 

98843 

99805 

00771 

01740 

1.72 

602712 

03688 

04667 

05650 

06636 

07625 

08618 

09614 

10613 

11616 

i-73 

12622 

13632 

14645 

15661 

16681 

17704 

18730 

19760 

20793 

21830 

1.74 

22869 

23912 

24959 

26009 

27062 

28118 

29178 

30241 

31308 

32377 

1.75 

9-963345I 

34527 

35607 

36690 

37776 

38866 

39959 

41055 

42155 

43258 

1.76 

44364 

45473 

46586 

47702 

48821 

49944 

51070 

52199 

53331 

54467 

i-77 

55606 

56749 

57894 

59043 

60195 

6135° 

62509 

63671 

64836 

66004 

1.78 

67176 

68351 

69529 

70710 

71895 

73082 

74274 

75468 

76665 

77866 

1.79 

79070 

80277 

81488 

82701 

83918 

85138 

86361 

87588 

88818 

90051 

1.80 

9.9691287 

92526 

93768 

95OI4 

96263 

975'5 

98770 

00029 

01291 

02555 

1.81 

703823 

05095 

06369 

07646 

08927 

IO2II 

11498 

12788 

14082 

15378 

1.82 

16678 

17981 

19287 

20596 

21908 

23224 

24542 

25864 

27189 

28517 

1.83 

29848 

31182 

32520 

33860 

35204 

36551 

379oo 

39254 

40610 

41969 

1.84 

43331 

44697 

46065 

47437 

48812 

50190 

5'57i 

52955 

54342 

55733 

1.85 

9.9757126 

58522 

59922 

61325 

62730 

64139 

65551 

66966 

68384 

69805 

1.86 

71230 

72657 

74087 

75521 

76957 

78397 

79839 

81285 

82734 

84186 

1.87 
1.88 

85640 
800356 

87098 
01844 

88559 
03335 

90023 
04830 

91490 
06327 

92960 

07827 

94433 
0933  i 

95909 
10837 

97389 
12346 

98871 
!3859 

1.89 

:5374 

16893 

18414 

J9939 

21466 

22996 

24530 

26066 

27606 

29148 

1.90 

9.9830693 

32242 

33793 

35348 

36905 

38465 

40028 

41595 

43l64 

44736 

1.91 

46311 

47890 

4947  i 

5I055 

52642 

54232 

55825 

5742i 

59020 

60621 

1.92 

62226 

63834 

65445 

67058 

68675 

70294 

71917 

73542 

75J7o 

76802 

i-93 
1.94 

78436 
9493s 

80073 
96605 

81713 
98274 

83356 
99946 

SJ002 

01621 

86651 
03299 

88302 
04980 

91614 
08350 

9J2U5 
10039 

1.95 

9.9911732 

13427 

!5I25 

16826 

18530 

20237 

21947 

23659 

25375 

27093 

1.96 

28815 

30539 

32266 

33995 

35728 

37464 

39202 

40943 

42688 

44435 

1.97 

46185 

47937 

49693 

5H51 

53213 

54977 

56744 

58513 

60286 

62062 

1.98 

63840 

65621 

67405 

69192 

70982 

72774 

7457° 

76368 

78169 

79972 

i-99 

81779 

83588 

85401 

87216 

89034 

90854 

92678 

945°4 

96333 

98165 

SMITHSONIAN  TABLES. 


64 


TABLE  33. 
ZONAL  SPHERICAL   HARMONICS. 


Degrees 

P, 

p, 

p, 

p. 

PS 

p. 

*  1 

O 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

I 

.9998 

•9995 

.9991 

•9985 

•9977 

.9968 

•9957 

2 

•9994 

.9982 

•9963 

•9939 

•9909 

.9872 

•9830 

3 

.9986 

•9959 

.9918 

•9863 

•9795 

.9714 

.9620 

4 

.9976 

•9927 

•9854 

•975» 

.9638 

•9495 

•9329 

's 

+  0.9962 

+  0.9886 

+  0.9773 

+  0.9623 

+  0.9437 

+  0.9216 

+  0.8962 

6 

•9945 

.9836 

.9674 

•9459 

.9194 

.8881 

.8522 

7 

•9925 

•9777 

•9557 

.9267 

.8911 

.8492 

.8016 

8 

•9903 

•9709 

•9423 

.9048 

.8589 

.8054 

•7449 

9 

.9877 

•9633 

•9273 

.8803 

.8232 

•7570 

.6830 

10 

+  0.9848 

+  0.9548 

+  0.9106 

+  0.8532 

+  0.7840 

+  0.7045 

+  0.6164 

ii 

.9816 

•9454 

•8923 

.8238 

•7417 

.6483 

.5462 

12 

.9781 

•9352 

.8724 

.7920 

.6966 

.5891 

•47  3  1 

13 

•9744 

.9241 

.8511 

.7582 

.6489 

•5273 

.3980 

14 

•9703 

.9122 

.8283 

.7224 

•5990 

•4635 

.3218 

15 

+  0.9659 

+  0.8995 

+  0.8042 

+  0.6847 

+  0.5471 

+  0.3983 

+  0.2455 

16 

.9613 

.8860 

•7787 

•6454 

•4937 

•3323 

.+  -1700 

«7 

•9563 

.8718 

•75T9 

.6046 

•4391 

.2661 

+  .0961 

18 

.9511 

.8568 

.7240 

.5624 

•3836 

.2002 

+  .0248 

19 

•9455 

.8410 

.6950 

.5192 

.3276 

•1353 

—  -°433 

20 

-f  0-9397 

+  0.8245 

+  0.6649 

+  0.4750 

+  0.2715 

+  0.0719 

—  0.1072 

21 

•9336 

.8074 

•6338 

.4300 

.2156 

+  .OI06 

.1664 

22 

.9272 

•7895 

.6019 

•3845 

.1602 

—  .0481 

.2202 

23 

.9205 

.7710 

.5692 

•3386 

.1057 

—  -1038 

.2680 

24 

•9I3S 

•75*8 

•5357 

.2926 

•0525 

-  -1558 

•3094 

25 

+  0.9063 

+  0.7321 

+  0.5016 

+  0.2465 

+  0.0009 

—  O.2O4O 

—  0.3441 

26 

.8988 

.7117 

.4670 

.2007 

—  .0489 

.2478 

•3717 

27 

.8910 

.6908 

•4319 

•*553 

—  .0964 

.2869 

.3922 

28 

.8829 

.6694 

•3964 

.1105 

—  -1415 

.3212 

•4053 

29 

.8746 

.6474 

.3607 

.0665 

-  -1839 

•3502 

30 

+  0.8660 

+  0.6250 

+  0.3248 

+  0.0234 

—  0.2233 

—  0.3740 

—  0.4102 

31 

•8572 

.6021 

.2887 

—  -0185 

•2595 

•3924 

.4022 

32 

.8480 

.5788 

•2527 

—  -059* 

.2923 

•4053 

.3877 

33 

.8387 

•5551 

.2167 

—  .0982 

.3216 

.4127 

.3671 

34 

.8290 

•5310 

.1809 

—  -1357 

•3473 

.4147 

.3409 

35 

+  0.8192 

+  0.5065 

+  0.1454 

—  0.1714 

—  0.3691 

—  0.4114 

—  0.3096 

36 

.8090 

.4818 

.1102 

.2052 

•3871 

.4031 

•2738 

37 

.7986 

•4567 

•0755 

.2370 

.4011 

.3898 

•2343 

38 

.7880 

•43I4 

.0413 

.2666 

.4112 

•3719 

.1918 

39 

•7771 

•4059 

.0077 

.2940 

.4174 

•3497 

.1470 

40 

+  0.7660 

+  0.3802 

—  0.0252 

—  0.3190 

—  0.4197 

—  0.3236 

—  0.1006 

41 

•7547 

•3544 

•0574 

.3416 

.4181 

•2939 

—  -0535 

42 

•743  1 

•3284 

.0887 

.3616 

.4128 

.2610 

—  .0064 

43 

•73H 

•3023 

.IIQI 

•3791 

.4038 

•2255 

+  .0398 

44 

•7193 

.2762 

.1485 

•3940 

•3914 

.1878 

+  .0846 

45 

+  0.7071 

+  0.2500 

—  0.1768 

—  0.4063 

—  0.3757 

—  0.1484 

+  0.1271 

46 

.6947 

•2238 

.2040 

.4158 

.3568 

—  .1078 

.1667 

47 

.6820 

•1977 

.2300 

.4227 

•335° 

—  .0665 

.2028 

48 
49 

.6691 
.6561 

.1716 
.1456 

•2547 
.2781 

.4270 
.4286 

•3105 
.2836 

—  -0251 
+  .0161 

•2350 
.2626 

50 

+  0.6428 

+  0.  1  1  98 

—  0.3002 

—  0.4275 

—  0.2545 

+  0.0564 

+  0.2854 

SMITHSONIAN  TABLES. 


*  Calculated  by  Mr.  C.  E.  Van  Orstrand  for  this  publication. 


TABLE  ^  (continued). 

ZONAL    SPHERICAL    HARMONICS. 


I  Degrees 

PI 

P2 

P3 

P4 

PS 

p« 

PT 

5° 

+  0.6428 

+  0.1198 

—  0.3002 

—  0.4275 

—0.2545 

+  0.0564 

+  0.2854 

51 

.6293 

.0941 

.3209 

•4239 

•2235 

•0954 

•3031 

52 

•6157 

.0686 

.3401 

.4178 

.1910 

.1326 

•3  '54 

53 

.6018 

.0433 

•3578 

.4093 

•1571 

.1677 

.3221 

54 

1 

•5878 

.0182 

•3740 

•3984 

.1223 

.2002 

•3234 

1   55 

+  0-5736 

—  0.0065 

—  0.3886 

-0.3852 

—  0.0868 

+  0.2297 

+  0.3191 

56 

•5592 

.0310 

.4016 

.3698 

—  .0509 

.2560 

•3095 

57 

•5446 

.0551 

•4I31 

•3524 

—  .0150 

.2787 

.2947 

58 

•5299 

,0788 

.4229 

•3331 

+  .0206 

.2976 

.2752 

59 

•S'S0 

.1021 

.4310 

•3"9 

+  .0557 

•3125 

.2512 

60 

+  0.5000 

—  0.1250 

—  0-4375 

—  0.2891 

+  0.0898 

4  0.3232 

+  0.2231 

61 

.4848 

.1474 

•4423 

.2647 

.1229 

.3298 

.1916 

62 

•4695 

.1694 

•4455 

.2390 

•1545 

•3321 

•1572 

63 

•4540 

.1908 

•447  1 

.2121 

.1844 

•33°2 

.1203 

64 

•4384 

.2117 

.4470 

.1841 

.2123 

.3240 

.0818 

65 

+  0.4226 

—  0.2321 

—  0.4452 

—  O.T552 

+  0.2381 

+  0.3138 

+  0.0422 

66 

.4067 

.2518 

.4419 

.1256 

.2615 

.2997 

+  .0022 

67 

•3907 

.2710 

•4370 

•0955 

.2824 

.2819 

—  -0375 

68 

•3746 

.2895 

•4305 

.  -0651 

•3005 

.2606 

—  -0763 

69 

•3584 

•3°74 

.4225 

•0344 

•3158 

.2362 

—  -"35 

70 

+  0.3420 

—  0.3245 

—  0.4130 

0.0038 

+  0.3281 

+  0.2089 

—  0.1485 

71 

•3256 

.3410 

.4021 

+  .0267 

•3373 

.1791 

.1808 

72 

.3090 

.3568 

.3898 

.0568 

•3434 

.1472 

.2099 

73 

.2924 

•3718 

.3761 

.0864 

•3463 

.1136 

•2352 

74 

.2756 

.3860 

.3611 

•"53 

.3461 

.0788 

•2563 

75 

+  0.2588 

—  0-3995 

—  0.3449 

+  0.1434 

+  0.3427 

+  0.0431 

—  0.2730 

76 

.2419 

4122 

•3275 

•1705 

•3362 

+  .0070 

.2850 

77 

.2250 

.4241 

.3090 

.1964 

.3267 

—  .0290 

.2921 

78 

.2079 

•4352 

.2894 

.2211 

•3143 

—  .0644 

.2942 

79 

.1908 

•4454 

.2688 

•2443 

.2990 

—  .0990 

.2913 

80 

4-0.1736 

—  0.4548 

—  0.2474 

+  0.2659 

+  0.2810 

—  0.1321 

—  0.2835 

Si 

.1564 

•4633 

.2251 

.2859 

.2606 

•1035 

.2708 

82 

.1392 

.4709 

.2020 

.3040 

•2378 

.1927 

•2536 

83 

.1219 

•4777 

•1783 

•3203 

.2129 

.2193 

.2321 

84 

.1045 

.4836 

•1539 

•3345 

.1861 

.2431 

.2067 

II 

+  0.0872 
.0698 

—  0.4886 
.4927 

—  0.1291 
.1038 

+  0.3468 

+  0.1577 
.1278 

—  0.2638 
.2810 

—  0.1778 
.1460 

87 

•0523 

•4959 

.0781 

.3648 

.0969 

.2947 

.1117 

88 
89 

•0349 
•0175 

.4982 
•4995 

.0522 
.0262 

•3704 
•3739 

.0651 
.0327 

•3°45 
•3105 

•0755 
.0381 

90 

+  o.oooo 

—  0.5000 

—  o.oooo 

+  0.3750 

+  o.oooo 

—  0.3125 

—  o.oooo 

SMITHSONIAN   TABLES. 


66 


TABLE  34. 

CYLINDRICAL   HARMONICS   OF   THE  OTH  AND   1ST  ORDERS 
Values  when  n  =  o  and  i  of  the  Bessel  function  Jn  (x) 

Ji(x) /„'(*)  = 


dJo(x) 
dx 


X 

/•(*) 

/i  00 

X 

/»<*) 

/»(*) 

X 

Jo(x) 

/!(*) 

X 

Jo(x) 

Ji(x) 

.00 

unity 

zero 

.50 

.938470 

.242268 

1.00 

.765198 

.440051 

1.60 

.511828 

•557937 

.01 

•999975 

.005000 

•5i 

.936024 

•246799 

.01 

.760781 

.443286 

•5i 

.506241 

•559315 

.02 

.999900 

.010000 

•52 

•933534 

.251310 

.02 

•756332 

.446488 

•52 

.500642 

•560653 

•03 

•999775 

.014998 

•53 

.930998 

•255803 

•03 

•751851 

.449658 

•53 

.495028 

•561951 

.04 

.999600 

.019996 

•54 

.928418 

.260277 

.04 

•747339 

•452794 

•54 

.489403 

.563208 

.05 

•999375 

.024992 

.55 

•925793 

.264732 

1.05 

.742796 

•455897 

1.55 

.483764 

.564424 

.06 

.999100 

.029987 

•56 

.923123 

.269166 

.06 

.738221 

.458966 

•56 

.478114 

.565600 

.07 

•998775 

•034979 

•57 

.920410 

•27358i 

.07 

•7336i6 

.462OOI 

•57 

•472453 

•566735 

.08 

.998401 

.039968 

•58 

.917652 

•277975 

.08 

.728981 

.465003 

•58 

.466780 

.567830 

.09 

.997976 

.044954 

•59 

.914850 

•282349 

.09 

.724316 

.467970 

•59 

.461096 

•568883 

.10 

.997502 

.049938 

.60 

.912005 

.286701 

1.10 

.719622 

.470902 

1.60 

•455402 

•569896 

.11 

.996977 

.054917 

.61 

.909116 

.291032 

.11 

.714898 

.473800 

.61 

.449698 

.570868 

.12 

.996403 

.059892 

.62 

.905184 

•295341 

.12 

.710146 

.476663 

.62 

•443985 

•571798 

•13 

•995779 

.064863 

•63 

.903209 

.299628 

•13 

•705365 

.479491 

•63 

.438262 

.572688 

.14 

.995106 

.069829 

.64 

.900192 

•303893 

.14 

.700556 

.482284 

.64 

•432531 

•573537 

.15 

•994383 

.074789 

.65 

.897132 

•308135 

1.16 

.695720 

.485041 

1.65 

.426792 

.574344 

.16 

.993610 

.079744 

.66 

.894029 

•312355 

.16 

.690856 

.487763 

.66 

.421045 

•575IH 

•  i? 

.992788 

.084693 

•67 

.890885 

•316551 

•17 

•685965 

.490449 

•67 

.415290 

•575836 

.18 

.991916 

.089636 

.68 

.887698 

.320723 

.18 

.681047 

.493098 

.68 

.409528 

.576520 

.19 

.990995 

.094572 

.69 

.884470 

.324871 

.19 

.676103 

.495712 

.69 

.403760 

•577163 

.20 

.990025 

.099501 

.70 

.881201 

.328996 

1.20 

.671133 

.498289 

1.70 

•397985 

•577765 

.21 

.989005 

.104422 

•7i 

.877890 

•333096 

.21 

.666137 

.500830 

•7i 

.392204 

.578326 

.22 

•987937 

.109336 

•72 

•874539 

•337170 

.22 

.661116 

.503334 

.72 

.386418 

•578845 

•23 

.986819 

.114241 

•73 

.871147 

.341220 

•23 

.656071 

.505801 

•73 

.380628 

•579323 

.24 

.985652 

.119138 

•74 

.867715 

•345245 

.24 

.651000 

.508231 

•74 

.374832 

•57976o 

.25 

.984436 

.124026 

.75 

.864242 

.349244 

1.26 

.645906 

.510623 

1.75 

•369033 

•580156 

.26 

.983171 

.128905 

•  76 

.860730 

•3532i6 

.26 

.640788 

.512979 

•76 

•363229 

•580511 

.27 

.981858 

•133774 

•77 

.857178 

•357i63 

•27 

•635647 

.515296 

•77 

•357422 

.580824 

.28 

.980496 

.138632 

.78 

•853587 

.361083 

.28 

.630482  .517577 

•78 

•351613 

.581096 

.29 

.979085 

.143481 

•79 

.849956 

•364976 

.29 

•625295  .519819 

•79 

.345801 

•581327 

.30 

.977626 

.148319 

.80 

.846287 

.368842 

1.30 

.620086  .522023 

1.80 

•339986 

•581517 

•3i 

.976119 

•153146 

.81 

.842580 

.372681 

•3i 

.614855  .524189 

.81 

•334170 

.581666 

•32 

•974563 

.157961 

.82 

.838834 

.376492 

•32 

.609602  .526317 

.82 

•328353 

•581773 

•33 

.972960 

.162764 

•83 

•835050 

•380275 

•33 

.604329  .528407 

•83 

•322535 

.581840 

•34 

.971308 

•167555 

•84 

.831228 

.384029 

•34 

.599034  .530458 

.84 

.316717 

•581865 

.35 

.969609 

•172334 

.85 

.827369 

.387755 

1.35 

•593720  .532470 

1.85 

.310898 

.581849 

•36 

.967861 

.177100 

.86 

•823473 

•391453 

•36 

.588385  .534444 

.86 

.305080 

•58i793 

•37 

.966067 

.181852 

•87 

.819541 

•395I2I 

•37 

•583031   -536379 

•87 

.299262 

.581695 

•38 

.964224 

.186591 

.88 

•8i557i 

.398760 

•38 

•577658  .538274 

.88 

.293446 

•58i557 

•39 

•962335 

.191316 

.89 

.811565 

.402370 

•39 

.572266  .540131 

.89 

.286631 

•58i377 

.40 

.960398 

.196027 

.90 

.807524 

•405950 

1.40 

.566855  .541948 

1.90 

.281819 

•581157 

.41 

.958414 

.200723 

.91 

.803447 

.409499 

.41 

.561427  .543726 

.91 

.276008 

.580896 

.42 

.956384 

.205403 

.92 

•799334 

.413018 

•42 

•55598i   -545464 

.92 

.270201 

.580595 

•43 

.954306 

.210069 

•93 

.795186 

.416507 

•43 

.550518  .547162 

•93 

.264397 

.580252 

•44 

.952183 

.214719 

•94 

.791004 

.419965 

•44 

.545038  .548821 

•94 

.258596 

.579870 

.45 

.950012 

•219353 

.95 

.786787 

•423392 

1.45 

•539541   .550441 

1.95 

.252799 

.579446 

.46 

•947796 

.223970 

.96 

•782536 

.426787 

.46 

.534029  .552020 

.96 

.247007 

•578983 

•47 

•945533 

.228571 

•97 

•778251 

•4,30151 

•47 

•528501   .553559 

•97 

.241220 

.578478 

•48 

.943224 

•233154 

.98 

•773933 

•433483 

.48 

.522958  .555059 

.98 

•235438 

•577934 

•49 

.940870 

.237720 

•99 

.769582 

•436783 

.49 

.517400  .556518 

•99 

.229661 

•577349 

.50 

.938470 

.242268 

1.00 

.765198 

.440051 

1.50 

.511828  .557937 

2.00 

.223891 

•576725 

SMITHSONIAN  TABLES. 


TABLE  34  (continued). 
CYLINDRICAL   HARMONICS  OF  THE  OTH  AND   IST  ORDERS- 

Ji(x)  =  —J<S(x).    Other  orders  may  be  obtained  from  the  relation,  Jn  +  i(x)   =  — Jn(x)  —  Jn-\(x). 

J-nM    =    (-!)»/„(*). 


67 


X 

Jo(x) 

Jl(X) 

X 

Jo(x) 

/!(*) 

X 

Jo(x) 

Jl(X) 

X 

Jo(x) 

/I  I*) 

2.00 

.223891 

•576725 

2.50 

-.048384 

.497094 

3.00 

-.260052 

•339059 

3.60 

-.380128 

•137378 

.01 

.218127 

.576060 

•51 

-.053342 

.494606 

.01 

-.263424 

•335319 

•5i 

-.381481 

•I33l83 

.02 

.212370 

•575355 

•S2 

-.058276 

.492086 

.02 

-.266758 

•331563 

•52 

-.382791 

.128989 

.03 

.206620 

.574611 

•53 

-.063184 

•489535 

.03 

-.270055 

.327789 

•53 

-.384060 

.124795 

.04 

.200878 

•573827 

•54 

-.068066 

•486953 

.o/ 

-.273314 

•323998 

•54 

-.385287 

.120601 

2.05 

•195143 

•573003 

2.55 

-.072923 

.484340 

3.05 

-.276535 

.320191 

3.55 

-.386472 

.116408 

.06 

.189418 

572139 

•56 

-•077753 

.481696 

06 

-.279718 

.316368 

•56 

-.387615 

.112216 

.07 

.183701 

.571236 

•57 

-.082557 

.479021 

.07 

-.282862 

.312529 

•57 

-.388717 

.108025 

.08 

•177993 

.570294 

•58 

-.087333 

.476317 

.08 

-.285968 

.308675 

•58 

-.389776 

.103836 

.09 

.172295 

•569313 

•59 

—.092083 

•473582 

.09 

-.289036 

.304805 

•59 

-•390793 

.099650 

2.10 

.166607 

.568292 

2.60 

-.096805 

.470818 

3.10 

—  .29206^ 

.300921 

3.60 

-.391769 

•095466 

.11 

.160929 

•567233 

.61 

-.101499 

.468025 

.11 

-.295054 

.297023 

.61 

-.392703 

.091284 

.12 

.155262 

.566134 

.62 

—.106165 

.465202 

.12 

-.298005 

.293110 

.62 

-.393595 

.087106 

•13 

.149607 

•564997 

•63 

—.110803 

.462350 

.13 

-.300916 

.289184 

•63 

-.394445 

.082931 

.14 

•143963 

•563821 

.64 

-.115412 

•459470 

.I/ 

-.303788 

.28524^ 

.64 

-•395253 

.078760 

2.15 

•138330 

.562607 

2.65 

-.119992 

.456561 

3.15 

—.306621 

.281291 

3.65 

-.396020 

•074593 

.16 

.132711 

•56i354 

.66 

-.124543 

•453625 

.16 

-.309414 

.277326 

.66 

-.396745 

.070431 

•17 

.127104 

.560063 

.67 

-.129065 

.450660 

.17 

—.312168 

•273348 

.67 

-.397429 

.066274 

.18 

.121509 

•558735 

.68 

-.133557 

.447668 

.18 

-.314881 

.269358 

.68 

-.398071 

.062122 

.19 

.115929 

•557368 

.69 

-.138018 

.444648 

.19 

-.317555 

•265356 

.69 

-.398671 

•057975 

2.20 

.110362 

•555963 

2.70 

-.142449 

.44I6OI 

3.20 

-.320188 

.261343 

3.70 

-.399230 

.053834 

.21 

.104810 

•554521 

•7i 

-.146850 

.438528 

.21 

-.322781 

•257319 

•7i 

-•399748 

.049699 

.22 

.099272 

•553041 

.72 

-.151220 

•435428 

.22 

-.325335 

.253284 

•72 

—.400224 

•045571 

•23 

•093749 

•551524 

•73 

-•155559 

.432302 

.23 

-.327847 

•249239 

•73 

-.400659 

.041450 

.24 

.088242 

•549970 

•74 

-.159866 

.429150 

.24 

-.330319 

.245184 

•74 

-.401053 

•037336 

2.25 

.082750 

.548378 

2.75 

—.164141 

.425972 

3.25 

-.332751 

241120 

3.76 

-.401406 

•033229 

.26 

.077274 

•546750 

•76 

-.168385 

422769 

.26 

-.335142 

237046 

.76 

—.401718 

.029131 

27 

.071815 

545085 

•77 

-.172597 

4I954I 

•27 

-.337492 

232963 

•77 

—.401989 

.025040 

.28 

•066373 

543384 

.78 

-.176776 

416288 

.28 

-.339801 

228871 

.78 

—.402219 

.020958 

.29 

.060947 

541646 

•79 

—  .180922 

4I30II 

.29 

-.342069 

224771 

•79 

—.402408 

.016885 

2.30 

•055540 

539873 

2.80 

-.185036 

409709 

3.30 

-.344296 

220663 

3.80 

-.402556 

.012821 

•3i 

.050150 

538063 

.81 

-.189117 

406384 

•3i 

-.346482 

216548 

.81 

—.402664 

.008766 

•32 

.044779 

536217 

.82 

-.193164 

403035 

•32 

-.348627 

212425 

.82 

-.402732 

.004722 

•33 

.039426 

534336 

•83 

-.197177 

399662 

•33 

-.35073! 

208296 

•83 

-.402759 

.000687 

•34 

.034092 

532419 

.84 

-.201157 

396267 

•34 

-•352793 

204160 

.84 

-.402746 

-•003337 

2.35 

.028778 

530467 

2.86 

—.205102 

392849 

3.35 

-.354814 

200018 

3.85 

—.402692 

-.007350 

•36 

.023483 

528480 

.86 

—.209014 

389408 

•36 

-•356793 

195870 

.86 

-.402599 

-.011352 

•37 

.018208 

526458 

.87 

—.212890 

385945 

•37 

-.358731 

191716 

.87 

-.402465 

-.015343 

•38 

.012954 

524402 

.88 

-.216733 

382461 

•38 

-.360628 

187557 

.88 

—.402292 

-.019322 

•39 

.007720 

522311 

.89 

-.220540 

378955 

•39 

-.362482 

183394 

.89 

-.402079 

-.023289 

2.40 

.002508 

520185 

2.90 

-.224312 

375427 

3.40 

-.364296 

179226 

3.90 

—.401826 

-.027244 

.41 

—  .002683 

518026 

.91 

-.228048 

371879 

.41 

-.366067 

175054 

.91 

-.401534 

—.031186 

.42 

-.007853 

515833 

.92 

-.231749 

3683II 

.42 

-.367797 

170878 

.92 

—.401202 

-•035H5 

•43 

—.013000 

513606 

•93 

-.235414 

364722 

•43 

-.369485 

166699 

•93 

-.400832 

-.039031 

•44 

-.018125 

5H346 

•94 

-.239043 

36III3 

•44 

-.371131 

162516 

•94 

—  .400422 

-.042933 

2.45 

-.023227 

509052 

2.95 

-.242636 

•357485 

3.45 

-.372735 

15833! 

3.95 

-.399973 

-.046821 

.46 

—.028306 

506726 

.96 

-.246193  .353837 

.46 

-.374297 

154144 

.96 

-.399485 

-.050695 

•47 

-.033361 

504366 

•97 

-.249713 

.350170 

•47 

-.375818 

149954 

•97 

-.398959 

-•054555 

.48 

-•038393 

501974 

.98 

-.253196 

.346484 

.48 

-.377296 

145763 

.98 

-.398394 

-.058400 

•49 

-.043401 

499550 

•99 

-.256643 

.342781 

•49 

-.378733 

141571 

•99 

-.397791 

-.062229 

2.50 

-.048384 

497094 

3.00 

-.260052 

•339059 

3.50 

-.380128 

137378 

4.00 

-.397150 

.066043 

SMITHSONIAN  TA.BLES. 


68 


TABLES  35-36. 
CYLINDRICAL   HARMONICS   OF  OTH  AND   1ST  ORDERS. 


TABLE  35.  —  4-place  Values  for  x 
to  15.0. 


4.0 


X 

/•(*) 

Jl(X) 

X 

MX) 

/'<*) 

4.0 

-•3972 

-.0660 

9-5 

-  •  J939 

+  .1613 

.  I 

-.3887 

~  •  1033 

.6 

—  .  2090 

•1395 

.2 

-.3766 

-  -  1386 

•  7 

-.2218 

.1166 

•3 

-.3610 

-.1719 

.8 

-.2323 

.0928 

-4 

-•3423 

-  .  2028 

•9 

-  •  2403 

.0684 

4-5 

-•3205 

-.2311 

IO.O 

-  •  2459 

•0435 

.6 

-  .  2961 

—  .2566 

.  i 

-  .  2490 

+  .0184 

•7 

-  •  2693 

-.2791 

.2 

-  .  2496 

-.0066 

.8 

-  .  2404 

-.2985 

•3 

-  -  2477 

-•°3I3 

•9 

-  .  2097 

-.3147 

•4 

-  •  2434 

-•0555 

5-o 

-.1776 

-.3276 

io-5 

-  .  2366 

-.0789 

.1 

--I443 

-•3371 

.6 

—  .  2276 

—  .  IOI2 

.2 

-.1103 

-•3432 

•7 

—  .2164 

—  .  1224 

•3 

-.0758 

-.3460 

.8 

-.2032 

—  .1422 

•4 

—  .0412 

-•3453 

•9 

-.1881 

-  •  1603 

5-5 

-.0068 

-•3414 

II.  0 

-.1712 

-.1768 

.6 

+  .0270 

-•3343 

.1 

-.1528 

-•i9J3 

•  7 

•0599 

-•3241 

.  2 

-•1330 

-  •  2039 

.8 

.0917 

-.3110 

•3 

—  .  II2I 

-•2143 

•9 

.1220 

-•2951 

•4 

—  .  O9O2 

-.2225 

6.0 

.1506 

-.2767 

n-5 

-.0677 

-.2284 

.1 

•1773 

-•2559 

.6 

—  .  0446 

-.2320 

.2 

.2017 

-•2329 

•7 

-.0213 

-  •  2333 

•3 

.2238 

-  .  2081 

.8 

+  .0020 

-.2323 

•  4 

•2433 

-.1816 

•9 

.0250 

—  .  2290 

6-5 

.2601 

-.1538 

12.  0 

.0477 

-•2234 

.6 

.2740 

-.1250 

.1 

.0697 

-•2157 

•  7 

.2851 

-•°953 

.2 

.0908 

—  .  2060 

.8 

.2931 

—  .0652 

•3 

.II08 

-  •  1943 

•9 

.2981 

-  •  0349 

•4 

.1296 

-.1807 

7.0 

.3001 

-.0047 

12.5 

.1469 

-•1655 

.1 

.2991 

+  .0252 

.6 

.1626 

-  -  1487 

.2 

.2951 

•0543 

•7 

.1766 

-  •  1307 

•3 

.2882 

.0826 

.8 

.1887 

—  .  1114 

•4 

.2786 

.1096 

•9 

.1988 

—  .0912 

7-5 

.2663 

•1352 

13-0 

.2069 

-.0703 

.6 

.2516 

•1592 

.  i 

.  2129 

—  .  0489 

•  7 

.2346 

.1813 

.2 

.2167 

—  .0271 

.8 

.2154 

.2014 

•3 

.2183 

-.0052 

•9 

.1944 

.2192 

•4 

.2177 

+.0166 

8.0 

.1717 

.2346 

13-5 

•  2I50 

.0380 

.  i 

•1475 

.2476 

.6 

.2IOI 

.0590 

.2 

.1222 

.2580 

•  7 

.2032 

.0791 

•3 

.0960 

.2657 

.8 

•1943 

.0984 

•4 

.0692 

.2708 

•9 

.1836 

.1165 

8-5 

.0419 

.2731 

14.0 

.1711 

•1334 

.6 

.0146 

.2728 

.1 

•1570 

.1488 

•  7 

—  .0125 

.2697 

.2 

.1414 

.1626 

.8 

-.0392 

.2641 

•3 

.1245 

•1747 

•9 

-•0653 

•2559 

•4 

.1065 

.1850 

9.0 

-.0903 

•2453 

14-5 

.0875 

•1934 

.1 

-.1142 

.2324 

.6 

.0679 

.1999 

.2 

-•1367 

•2174 

•7 

.0476 

•2043 

•3 

--I577 

.2004 

.8 

.O27I 

.  2066 

•4 

-.1768 

.1816 

•9 

.0064 

.  2069 

9-5 

--I939 

.1613 

15.0 

—  .OI42 

•  2051 

TABLE  36.  —  Roots. 

(a)   ist  10  roots  of  JQ(X)  =-•  o 

Higher  roots  may  be  calculated  to  better 
than  i  part  in  10,000  by  the  approximate 
formula 

Rm  =  Rm_!  +  TT 

RI  =    2.404826 

R2  =    5.520078 

^3     =       8.653728 

R*  =  11.791534 
R6  =  14.930918 
R6  =  18.071064 

J?7    =   21  .  2II637 

R&  =  24.352472 

Rg    =   27.493479 

Rw  =  30 .  634606 
(b)  ist  15  roots  of  Ji(x)  =      °       =  o 


dx 

with  corresponding  values  of  maximum  or 
or  minimum  values  of  Jc(x). 


No.  of 
root  («) 

Root  =  *». 

/<>(*„). 

I 

3.831706 

-.402759 

2 

7-OI5587 

+  .300116 

3 

10.173468 

-  .  249705 

4 

13.323692 

+.218359 

5 

16.470630 

-  .  196465 

6     19.615859 

+.180063 

7 

22  .760084 

-.167185 

8 

25.903672 

+  .156725 

9 

29.046829 

—  .  148011 

10 

32.189680 

+.  140606 

ii 

35.332308 

-.134211 

12 

38.474766 

+  .128617 

13 

41.617094 

-.123668 

14 

44-7593*9 

+.119250 

15 

47.901461 

-.115274 

Higher  roots  may  be  obtained  as  under  (a). 
NOTES,     y  =  Jn(x)    is    a    particular  solu- 
tion of  BessePs  equation, 


The  general  formula  for  Jn(x)  is 
^_(-i)^»-Mto 
o 


or 


when  »  is  an  integer  and 

T       fv\        2H  T  ( 
J  n+l\XJ  —         J  n\- 

and  7  T  /  \ 


SMITHSONIAN  TABLES 


^    ' 

J_n(^)=(-l)»/nW. 

Tables  35  to  36  are  based  upon  Gray  and 
Matthews'  reprints  from  Dr.  Meissel's 
tables.  See  also  Reports  of  British  Associa- 
tion, 1907-1916. 


TABLE  37. 
ELLIPTIC    INTEGRALS. 

*JT  IT 

Values  of   I  2(1—  sin20sin24>)±2"cty 


This  table  gives  the  values  of  the  integrals  between  o  and  n  /  2  of  the  function  (i—  sin20sin2<£) 
ues  of  the  modulus  corresponding  to  each  degree  of  6  between  o  and  90. 


d$  for  different  val- 


e 

n   d* 

£ir 
z(i—  sin20sin2<£)*aty 

e 

X7T          ,. 
2      d$ 

f  *(«  sin2*™  >»</ 

Jo 

Jo   (i—  sin*0sins$)* 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

0° 

;.57oS 

0.196120 

1.5708 

0.196120 

45° 

1.8541 

0.268127 

I  -35°6 

O.I3054I 

i 

5709 

I96I53 

5707 

196087 

6 

8691 

271644 

3418 

127690 

2 

5713 

196252 

5703 

195988 

7 

8848 

275267 

3329 

124788 

3 

5719 

196418 

5697 

195822 

8 

9011 

279001 

3238 

121836 

4 

5727 

196649 

5689 

*9559i 

9 

9180 

282848 

3H7 

118836 

5° 

1.5738 

0.196947 

1.5678 

0.195293 

50° 

I-9356 

0.2868II 

I-3055 

0.115790 

6 

5751 

I973I2 

5665 

194930 

i 

9539 

290895 

112698 

7 

5767 

197743 

5649 

194500 

2 

9729 

295101 

2870 

109563 

8 

5785 

198241 

5632 

194004 

3 

9927 

299435 

2776 

106386 

9 

5805 

198806 

5611 

193442 

4 

2.0133 

303901 

2681 

103169 

10° 

1.5828 

0.199438 

1.5589 

0.192815 

55° 

2.0347 

0.308504 

1.2587 

0.099915 

i 

5854 

200137 

5564 

192121 

6 

0571 

313247 

2492 

096626 

2 

5882 

200904 

5537 

191362 

7 

0804 

318138 

2397 

093303 

3 

5913 

201740 

55°7 

190537 

8 

1047 

323182 

2301 

089950 

4 

5946 

202643 

5476 

189646 

9 

1300 

328384 

2206 

086569 

15° 

1.5981 

0.203615 

1.5442 

0.188690 

60° 

2.1565 

0-333753 

I.2III 

0.083164 

6 

6020 

204657 

5405 

187668 

i 

1842 

339295 

2OI5 

079738 

7 

6061 

205768 

5367 

186581 

2 

2132 

345020 

I92O 

076293 

8 

6105 

206948 

5326 

185428 

3 

2435 

350936 

1826 

072834 

9 

6151 

2O82OO 

5283 

184210 

4 

2754 

357053 

1732 

069364 

20° 

1.6200 

0.209522 

1-5238 

0.182928 

65° 

2.3088 

0.363384 

1.1638 

0.065889 

i 

6252 

210916 

5191 

181580 

6 

3439 

369940 

1545 

062412 

2 

6307 

212382 

5141 

180168 

7 

3809 

376736 

1453 

058937 

3 

6365 

213921 

5090 

178691 

8 

4198 

383787 

1362 

055472 

4 

6426 

215533 

5°37 

177150 

9 

4610 

39III2 

1272 

052020 

25° 

1.6490 

0.217219 

1.4981 

0.175545 

70° 

2.5046 

0.398730 

I.II84 

0.048589 

6 

6557 

218981 

4924 

173876 

i 

5507 

406665 

1096 

045183 

7 

6627 

2208l8 

4864 

172144 

2 

5998 

4M943 

IOII 

041812 

8 

6701 

222732 

4803 

170348 

3 

6521 

423596 

0927 

038481 

9 

6777 

224723 

4740 

168489 

4 

7081 

432660 

0844 

035200 

30° 

i 

1.6858 
6941 

0.226793 
228943 

1.4675 
4608 

0.166567 
164583 

75° 

6 

2.7681 
8327 

0.442176 
452196 

1.0764 
0686 

0.031976 
028819 

2 

7028 

23H73 

4539 

162537 

7 

9026 

462782 

0611 

025740 

3 

7119 

233485 

4469 

160429 

8 

9786 

474008 

0538 

022749 

4 

7214 

235880 

4397 

158261 

9 

3.0617 

485967 

0468 

019858 

35° 

1.7312 

0.238359 

1.4323 

0.156031 

80° 

3.1534 

0.498777 

1.0401 

O.OI708I 

6 

7415 

240923 

4248 

1  53/42 

i 

2553 

5I2591 

0338 

014432 

7 

7522 

243575 

4171 

15*393 

2 

3699 

527613 

0278 

011927 

8 
9 

7633 
7748 

246315 
249146 

4092 
4013 

148985 
146519 

3 
4 

5004 
6519 

544120 
5625H 

0223 
0172 

009584 
007422 

40° 

1.7868 

0.252068 

i-393r 

0.143995 

85° 

3-8317 

0.583396 

1.0127 

0.005465 

I 

7992 

255085 

3849 

141414 

6 

4.0528 

607751 

0086 

003740 

2 

8122 

258197 

3765 

138778 

7 

3387 

637355 

0053 

0022/8 

3 

8256 

261406 

3680 

136086 

8 

7427 

676027 

0026 

OOII2I 

4 

8396 

264716 

3594 

1  33  340 

9 

5-4349 

735192 

0008 

OOO326 

45° 

1.8541 

0.268127 

1.3506 

0.130541 

90° 

oo 

co 

I.OOOO 



SMITHSONIAN  TABLES. 


7°  TABLE  38. 

MOMENTS  OF  INERTIA,   RADII   OF  GYRATION,  AND  WEIGHTS. 

In  each  case  the  axis  is  supposed  to  traverse  the  centre  of  gravity  of  the  body.     The  axis  is 
/>ne  of  symmetry.     The  mass  of  a  unit  of  volume  is  w. 


Body. 

Axis. 

Weight. 

Moment  of  Inertia  Io. 

Square  of  Ra- 
dius of  Gyra- 
tion pj. 

Sphere  of  radius  r 

Diameter 

4«v,r* 

8*wr& 

2^2 

3 

15 

5 

Spheroid  of  revolution,  po- 
lar axis  2a,  equatorial  di- 

Polar axis 

4*war* 

Sirwar* 

2r2 

ameter  2r 

3 

5 

5 

Ellipsoid,  axes  2^,  2b,  2c 

Axis  2a 

4-irwabc 

4-irwabc  (£2-f  c2-  ) 

^2-ff2 

3 

?S 

5 

Spherical  shell,  external  ra- 
dius r,  internal  r' 

Diameter 

^Tn^r*  —  r'8) 

STTIV^  —  r'&) 

fl^j 

3 

IS 

Ditto,  insensibly   thin,  ra- 
dius r,  thickness  dr 

Diameter 

,^-dr 

8mvr*dr 

2r2 

3 

3 

Circular  cylinder,  length  20, 
radius  r 

Longitudinal 
axis  2a 

2wr* 

irwar* 

^2 

2 

Elliptic  cylinder,  length  2a, 

Longitudinal 

inua6c(P+t?) 

32+r2 

transverse  axes  2b,  2c 

axis  2a 

2 

4 

Hollow    circular    cylinder, 
length    2a,  external    ra- 
dius r,  internal  r' 

Longitudinal 
axis  20. 

2irwa(r2—r"2) 

m^ 

r2+rv 

2 

Ditto,  insensibly  thin,  thick- 

Longitudinal 

Axwardr 

49Va**tfr 

r2 

ness  dr 

axis  20 

Circular  cylinder,  length  2a, 
radius  r 

Transverse 
diameter 

2-jrwar2 

ra/^2(3r2+402) 

rz      a2 
4+3 

6 

Elliptic  cylinder,  length  2a, 

Transverse 

-> 

mva&f(yz-}-4az) 

<r2      a2 

transverse  axes  2a,  2b 

axis  2b 

6 

4+  3 

Hollow    circular    cylinder, 
length    2a,   external    ra- 
dius r,  internal  r' 

Transverse 
diameter 

,™,<r*-o 

irwa  j  3(r*  —  r'*)           ) 
6     (    -f~4^2(r2  —  r>i^  £ 

4       *~  3 

Ditto,  insensibly  thin,  thick- 

Transverse 

4  2 

r2      a2 

ness  dr 

diameter 

4-mvar  r 

3a  ' 

2+   3 

Rectangular  prism,  dimen- 
sions 2a,  2b,  2c 

Axis  20. 

Swabc 

8zvat><:(t>'2-\-c2) 

b2+c2 

3 

3 

Rhombic  prism,  length  2a, 
diagonals  2b,  2c 

Axis  2a 

Afivabc 

z-wabc^+c1} 
3 

b2+c2 

6 

Ditto 

Diagonal  2b 

qwabc 

2wabc(c'i-\-2a'i) 

c2      a2 

3 

6  +  3 

(Taken  from  Rankine.) 

For  further  mathematical  data  see  Smithsonian  Mathematical  Tables,  Becker  and  Van  Orstrand 
(Hyperbolic,  Circular  and  Exponential  Functions);  Functionentafeln,  Jahnke  und  Emde  (xlgx, 
Roots  of  Transcendental  Equations,  a  -j-  bi  and  re1**,  Exponentials,  Hyperbolic  Functions, 


/x    •  f*oo  t*~x 

—  du,    I  -  du,    I         —  du,   Fresnel    Integral,   Gamma    Function,    Gauss    Integral 

0  J     X  J       Oo 

-^=  I      f-x^dx,  Pearson  Function  e-^v  I     si 


,  Elliptic  Integrals  and  Functions,  Spherical 


and  Cylindrical  Functions,  etc.).  For  further  references  see  under  Tables,  Mathematical,  in  the 
nth  ed.  Encyclopaedia  Britannica.  See  also  Carr's  Synopsis  of  Pure  Mathematics  and  Mellor's 
Higher  Mathematics  for  Students  of  Chemistry  and  Physics. 


SMITHSONIAN  TABLES- 


TABLE  39.  yj 

INTERNATIONAL  ATOMIC  WEIGHTS.      VALENCIES. 

The  International  Atomic  Weights  are  quoted  from  the  report  of  the  International 
Committee  on  Atomic  Weights  (Journal  American  Chemical  Society,  39.42,  p.  9,  1920). 


Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =  16. 

Valency. 

Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =16. 

Valency. 

Aluminum 

Al 

27.1 

3- 

Mercury 

Hg 

200.6 

I,  2. 

Antimony 

Sb 

1  20.  2 

3>5- 

Molybdenum 

Mo 

96.0 

4,6. 

Argon 

A 

39-9 

o. 

Neodymium 

Nd 

144-3 

3- 

Arsenic 

As 

74.96 

3'  5- 

Neon 

Ne 

2O.2 

o. 

Barium 

Ba 

J37-37 

Nickel 

Ni 

58.68 

2,3- 

[ation^ 

Bismuth 

Bi 

208.0 

3>  5- 

Niton  (Raeman- 

Nt. 

222.4 

— 

Boron 

B 

10.9 

3- 

Nitrogen 

N 

14.008 

3.  5- 

Bromine 

Br 

79.92 

i. 

Osmium 

Os 

190.9 

6,8. 

Cadmium 

Cd 

112.40 

2. 

Oxygen 

O 

16.00 

2. 

Caesium 

Cs 

132.81 

I. 

Palladium 

Pd 

106.7 

2,4- 

Calcium 

Ca 

40.07 

2. 

Phosphorus 

P 

31.04 

3,5- 

Carbon 

C 

12.005 

4- 

Platinum 

Pt 

195.2 

2,  4- 

Cerium 

Ce 

140.25 

3'  4- 

Potassium 

K 

39.10 

I. 

Chlorine 

Cl 

35-46 

Praseodymium 

Pr 

140.9 

3- 

Chromium 

Cr 

52.0 

2,  3,  6. 

Radium 

Ra 

226.0 

2. 

Cobalt 

Co 

58-97 

2,  3- 

Rhodium 

Rh 

102.9 

3. 

Columbium 

Cb 

93-1 

5. 

Rubidium 

Rb 

85-45 

I. 

Copper 

Cu 

63-57 

I,  2. 

Ruthenium 

Ru 

101.7 

6,8. 

Dysprosium 

Dy 

162.5 

3- 

Samarium 

Sa 

150.4 

3- 

Erbium 

Er 

167.7 

3- 

Scandium 

Sc 

3- 

Europium 

Eu 

152.0 

3- 

Selenium 

Se 

79-2 

2,  4,  6. 

Fluorine 

F 

19.0 

i. 

Silicon 

Si 

28.3 

4- 

Gadolinium 

Gd 

3. 

Silver 

Ag 

107.88 

i. 

Gallium 

Ga 

70.1 

3. 

Sodium 

Na 

23.00 

i. 

Germanium 

Ge 

72-5 

4- 

Strontium 

Sr 

87.63 

2. 

Glucinum 
Gold 

Gl 
Au 

9.1 
197.2 

2.    e 
I,  3. 

Sulphur 
Tantalum 

S 
Ta 

32.06 
181.5 

2,  4,  6. 

5. 

Helium 

He 

4.00 

O. 

Tellurium 

Te 

127-5 

2,  4,  6. 

Holmium 

Ho 

l63-5 

3- 

Terbium 

Tb 

159.2 

3- 

Hydrogen 

H 

1.008 

Thallium 

Tl 

204.0 

1.3- 

Thorium 

Th 

232.15 

4- 

Indium 

In 

114.8 

3- 

Iodine 

I 

126.92 

I. 

Thulium 

Tm 

168.5 

3- 

Iridium 

Ir 

I93-1 

4- 

Tin 

Sn 

118.7 

2,  4- 

Iron 

Fe 

2,  3. 

Titanium 

Ti 

48.1 

" 

4- 

Krypton 

Kr 

8^92 

*    O 
0. 

Tungsten 

W 

184.0 

6. 

Uranium 

U 

238.2 

4,6. 

Lanthanum 

La 

139.0 

3- 

Lead 

Pb 

207.20 

2,  4. 

Vanadium 

V 

51.0 

3'  5- 

Lithium 

Li 

6.94 

I. 

Xenon 

Xe 

130.2 

0. 

Lutecium 

Lu 

175-° 

3. 

Ytterbium 

Yb 

I73-'5 

3- 

Magnesium 
Manganese 

Mg 
Mn 

24.32 

54-93 

2 

2,  3.  7- 

Yttrium 
Zinc 

Yt 

Zn 

89-33 
65-37 

3- 

Zirconium 

Zr 

90.6 

4- 

SMITHSONIAN  TABLES. 


7 '2  TABLE  40. 

VOLUME   OF  A  CLASS  VESSEL   FROM   THE  WEIGHT  OF  ITS  EQUIVALENT 
VOLUME    OF    MERCURY    OR    WATER. 

If  a  glass  vessel  contains  at  /°  C,  P  grammes  of  mercury,  weighed  with  brass  weights  in  air  at 
760  mm.  pressure,  then  its  volume  in  c.  cm. 

at  the  same  temperature,  /,  :    V=  PR    =  P^> 
at  another  temperature,  /lf  :    V  =  PA\  =  P  pjd  1 1  +  7  (*i  —  /)  } 
p  =  the  weight,  reduced  to  vacuum,  of  the  mass  of  mercury  or  water  which,  weighed  with  brass 

weights,  equals  i  gram  ; 
d  =  the  density  of  mercury  or  water  at  /°C, 
and  7  =  o.ooo  025,  is  the  cubical  expansion  coefficient  of  glass. 


Temper- 
ature 
t 

WATER. 

MERCURY. 

R. 

Rlt  ^  =  10°. 

Rl,  *,  =  20°. 

R. 

*^=,0o. 

Rltti  =  20°. 

0° 

1.001192 

I.OOI443 

I.OOI693 

0.0735499 

0.0735683 

0.0735867 

I 

"33 

1358 

I6O9 

5633 

5798 

5982 

2 

1092 

1292 

1542 

5766 

59*4 

6098 

3 

1068 

1243 

H93 

5900 

6029 

6213 

4 

1060 

I2IO 

I46O 

6033 

6144 

6328 

5 

1068 

"93 

1443 

6l67 

6259 

6443 

6 

1.001092 
1131 

1.001192 
1206 

I.OOI442  ' 

0.0736301 
6434 

0.0736374 
6490 

0.0736558 

8 

1184 

1234 

M85 

6568 

6605 

6789 

9 

1252 

1277 

6702 

6720 

6904 

10 

'333 

1584 

6835 

6835 

7020 

ii 

1.001428 

i.oor4O3 

I.OOI653 

0.0736969 

0-0736951 

0.0737135 

12 

1536 

1486 

1736 

7103 

7066 

7250 

13 

1657 

1582 

I832 

7236 

7181 

7365 

14 

1790 

1690 

1940 

7370 

7297 

7481 

IS 

J935 

1810 

2060 

75°4 

7412 

7596 

16 

1.002092 

1.001942 

I.OO2I93 

0.0737637 

0.0737527 

0.0737711 

17 

2261 

2086 

2337 

•   7771 

7642 

7826 

18 

2441 

2241 

2491 

79°5 

7757 

7941 

19 

2633 

2407 

2658 

8039 

7872 

8057 

20 

2835 

2584 

2835 

8172 

7988 

8172 

21 

1.003048 

1.002772 

1.003023 

0.0738306 

0.0738103 

0.0738288 

22 

3271 

2970 

3220 

8440 

82  1  S 

8403 

23 

35°4 

3178 

3429 

8573 

8333 

8518 

24 

3748 

3396 

3647 

8707 

8449 

8633 

25 

4001 

3624 

3875 

8841 

8564 

8748 

26 

1.004264 

1.003862 

I.004II3 

0.0738974 

0.0738679 

0.0738864 

27 
28 

4537 
4818 

41  10 
4366 

4361 
46l6 

9108 
9242 

8794 
8910 

8979 

9094 

29 

5110 

4632 

4884 

9376 

9025 

9210 

30 

54io 

4908 

5159 

9510 

9140 

9325 

Taken  from  Landolt,  Bornstein,  and  Meyerhoffer's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  41-42. 

REDUCTIONS  OF  WEIGHINGS  IN  AIR  TO  VACUO. 

TABLE  41. 


73 


When  the  weight  M  in  grams  of  a  body  is  determined  in  air,  a  correction  is  necessary  for  the 
buoyancy  of  the  air  equal  to  M  S  (i/d — i/d,)  where  5  =  the  density  (vvt.  of  i  ccm  in  grams 
=  0.0012)  of  the  air  during  the  weighing,  d  the  density  of  the  body,  dt  that  of  the  weights. 
5  for  various  barometric  values  and  humidities  may  be  determined  from  Tables  153  to  155.  The 
following  table  is  computed  for  8  =  0.0012.  The  corrected  weight  =  M  +  kM/iooo. 


Density 
of  body 
weighed 
d. 

Correction  factor,  k. 

Density 
of  body 
weighed 
d. 

Correction  factor,  k. 

Pt.  Ir.                Brass              Quartz  or 
weights             weights         Al.  weights 
d1=2i.s.               8.4.                    2.65. 

Pt.  Ir.               Brass 
weights             weights 
^•=21.5.               8.4. 

Quartz  or 
Al.  weights 
2.65. 

.5 

4-2-34 

+  2.26 

4-  i-95 

1.6 

+  0.69 

+  0.61 

4-0.30 

.6 

4-  .94 

+  1.86 

4-  1-55 

1.7 

+     -65 

4-  -56. 

4-   -25 

•7 

4-    .66     i     +I.S7 

+  1.26 

1.8 

+     .62 

4-  -52 

+     .21 

•75 

4-    -55 

+  1.46 

4-I-I5 

1.9 

4-  .58 

4-    -49 

+     .18 

.80 

+    .44         +  1.36 

4-1-05 

2.O 

4-  -54 

+    .46 

+     .15 

.85 

+    .36         +  1.27 

+  0.96 

2-5 

4-  -43 

+    .34 

+     .03 

.90 

+    .28 

4-I-I9 

+    .88 

3-° 

4-    -34 

+    .26 

.05 

•95 

+     .21 

+  1.12 

+     .8! 

4.0 

+    .24 

+    .16 

—     .15 

1.  00 

+     .14 

+  1.  06 

4-  -75 

6.0 

+    .14 

+    .06 

—     -25 

.1 

+  1.04             +0.95 

+    -64 

8.0 

+    .09 

+     .01 

—     -30 

.2 

+  0.94 

+    .86 

4-    -55 

1  0.0 

+    .06 

—   .02 

—   -33 

•3 

4-  -87 

+    .78 

4-    -47 

15.0 

4-   -03 

—    .06 

—  -37 

•4 

•5 

+  .80 

+    -75 

4-  -71 

+    .66 

+    .40 

4-  -35 

2O.O 
22.0 

+  .004 

.001 

—   .08 
—    .09 

—   -39 
—   .40 

TABLE   42.-  Reductions  of  Densities  in  Air  to  Vacuo. 

(This  correction  may  be  accomplished  through  the  use  of  the  above  table  for  each  separate 
weighing.) 

If  s  is  the  density  of  the  substance  as  calculated  from  the  uncorrected  weights,  S  its  true  den- 
sity, and  L  the  true  density  of  the  liquid  used,  then  the  vacuum  correction  to  be  applied  to  the 
uncorrected  density,  s,  is  0.0012  (i  — s/L). 

Let  Ws  =  uncorrected  weight  of  substance,  Wi  =  uncorrected  weight  of  the  liquid  displaced 
by  the  substance,  then  by  definition,  s  =  LWs/Wi.  Assuming  D  to  be  the  density  of  the 
balance  of  weights,  Ws  {i  +0.0012  (i/S  —  i/D)}and  Wi  {i  +0.0012  (i/L  — i/D)}are  the 
true  weights  of  the  substance  and  liquid  respectively  (assuming  that  the  weighings  are  made 
under  normal  atmospheric  corrections,  so  that  the  weight  of  i  cc.  of  air  is  0.0012  gram). 

Ws{r  +  0.0012  (i/S  —  i/D)  } 

Then  the  true  density  S  =  —  —  L. 

Wl  {i  +  0.0012  (i/L—  i/D)  } 

But  from  above  Ws/WTj  =  s/L,  and  since  L  is  always  large  compared  with  0.0012, 

S  —  5  =  0.0012(1 — s/L). 

The  values  of  0.0012  (i — s/L)  for  densities  up  to  20  and  for  liquids  of  density  I  (water), 
0.852  (xylene)  and  13.55  (mercury)  follow  : 

(See  reference  below  for  discussion  of  density  determinations). 


Density  of 
substance 
s. 

Corrections. 

Density  of 
substance 

s 

Corrections. 

WaTer. 

L  =  0.852 
Xylene. 

L=  '3-55 
Mercury. 

L=i 
Water. 

L='S.SS 

Mercury. 

0.8 

+  O.OO024 

_ 

II. 

—  O.OI2O 

+  0.0002 

0.9 

+     .OOOI2 

_ 

12. 

—     .0132 

+     .OOOI 

i. 

O.OOOO                —  O.OOO2 

+  O.OOII 

T3- 

—     .0144 

O.OOOO 

2. 

—     .OOI2 

—    .OOl6 

+     .0010 

14. 

—    .01  s6 

O.OOOO 

3- 
4- 

—     .OO24 
.0036 

—    .0030           +     .0009 
—    .0044           +     .0008 

g 

—    .0168 
—    .0180 

—     .OOOI 
—     .0002 

5- 

—     .0048 

—    .0058           +     -0008 

17. 

—    .0192 

—     .0003 

6. 

.OO6O 

—    .0073           +     .0007 

18. 

—    .0204 

.OOO4 

7. 

—     .OO72 

—    .0087 

+  .0006 

19. 

—    .0216 

.OOO5 

8. 

—     .0084 

—     .OIOI 

+  .0005 

20. 

—    .0228 

—     .OOO6 

9- 

.0096 

—     .0115 

+     .0004      ; 

10. 

—     .0108 

—     .0129 

+     .0003 

SMITHSONIAN  TABLES. 


Johnston  and  Adams,  J.  Am.  Chem.  Soc.  34,  p.  563,  1912. 


J  A  TABLE  43. 

MECHANICAL   PROPERTIES.  • 

*  Compiled  from  various  sources  by  Harvey  A.  Anderson,  C.E.,  Assistant  Engineer  Physicist,  U.  S.  Bureau 
of  Standards. 

The  mechanical  properties  of  most  materials  vary  between  wide  limits;  the  following  figures  are  given  as 
being  representative  rather  than  what  may  be  expected  from  an  individual  sample.  Figures  denoting  such 
properties  are  commonly  given  either  as  specification  or  experimental  values.  Unless  otherwise  shown,  the 
values  below  are  experimental.  Credit  for  information  included  is  due  the  U.  S.  Bureau  of  Standards;  the 
Am.  Soc.  for  Testing  Materials;  theSoc.  of  Automotive  Eng.;  the  Motor  Transport  Corps,  U.  S.  War  Dept.; 
the  Inst.  of  Mech.  Eng.;  the  Inst.  of  Metals;  Forest  Products  Lab.;  Dept.  of  Agriculture  (Bull.  556);  Moore's 
Materials  of  Engineering;  Hatfield's  Cast  Iron;  and  various  other  American,  English  and  French  authorities. 
The  specified  properties  shown  are  indicated  minimums  as  prescribed  by  the  Am.  Soc.  for  Testing  Materials, 
U.  S.  Navy  Dept.,  Panama  Canal,  Soc.  of  Automotive  Eng.,  or  Intern.  Aircraft  Standards  Board.  In  the 
majority  of  cases,  specifications  show  a  range  for  chemical  constituents  and  the  average  value  only  of  this 
range  is  quoted.  Corresponding  average  values  are  in  general  given  for  mechanical  properties.  In  gen- 
eral, tensile  test  specimens  were  12.8  mm  (0.505  in.)  diameter  and  50.8  mm  (2  in.)  gage  length.  Sizes  of 
compressive  and  transverse  specimens  are  generally  shown  accompanying  the  data. 

All  data  shown  in  these  tables  are  as  determined  at  ordinary  room  temperature,  averaging  20°  C  (68°  F.). 
The  properties  of  most  metals  and  alloys  vary  considerably  from  the  values  shown  when  the  tests  are  con- 
ducted at  higher  or  lower  temperatures. 

The  following  definitions  govern  the  more  commonly  confused  terms  shown  in  the  tables.  In  all  cases  the 
stress  referred  to  in  the  definitions  is  equal  to  the  total  load  at  that  stage  of  the  test  divided  by  the  original 
cross-sectional  area  of  the  specimen  (or  the  corresponding  stress  in  the  extreme  fiber  as  computed  from  the 
flexure  formula  for  transverse  tests). 

Proportional  Limit  (abbreviated  P-limit).  —  Stress  at  which  the  deformation  (or  deflection)  ceases  to  be 
proportional  to  the  load  (determined  with  extensometer  for  tension,  compressometer  for  compression  and 
deflectometer  for  transverse  tests). 

Elastic  Limit.  —  Stress  which  produces  a  permanent  elongation  (or  shortening)  of  o.ooi  per  cent  of  the 
gage  length,  as  shown  by  an  instrument  capable  of  this  degree  of  precision  (determined  from  set  readings  with 
extensometer  or  compressometer).  In  transverse  tests  the  extreme  fiber  stress  at  an  appreciable  permanent 
deflection. 

Yield  Point.  —  Stress  at  which  marked  increase  in  deformation  (or  deflection)  of  specimen  occurs  without  in- 

crease in  load  (determined  usually  by  drop  of  beam  or  with  dividers  for  tension,  compression  or  transverse  tests). 

Ultimate  Strength  in  Tension  or  Compression.  —  Maximum  stress  developed  in  the  material  during  test. 

Modulus  of  Rupture.  —  Maximum  stress  in  the  extreme  fiber  of  a  beam  tested  to  rupture,  as  computed 

by  the  empirical  application  of  the  flexure  formula  to  stresses  above  the  transverse  proportional  limit. 

Modulus  of  Elasticity  (Young's  Modulus).  —  Ratio  of  stress  within  the  proportional  limit  to  the  corre- 
sponding strain,  —  as  determined  with  an  extensometer.  Note:  All  moduli  shown  are  obtained  from  tensile 
tests  of  materials,  unless  otherwise  stated. 

Brinell  Hardness  Numeral  (abbreviated  B.  h.  n.).  —  Ratio  of  pressure  on  a  sphere  used  to  indent  the 
material  to  be  tested  to  the  area  of  the  spherical  indentation  produced.  The  standard  sphere  used  is  a  10- 
mm  diameter  hardened  steel  ball.  The  pressures  used  are  3000  kg  for  steel  and  500  kg  for  softer  metals,  and 
the  time  of  application  of  pressure  is  30  seconds.  Values  shown  in  the  tables  are  based  on  spherical  areas 
computed  in  the  main  from  measurements  of  the  diameters  of  the  spherical  indentations,  by  the  following 
formula: 

B.  h.  n.  =  P  -f-  irtD  =  P  -h  irD(D/2  - 


P  =  pressure  in  kg,  /  =  depth  of  indentation,  D  =  diameter  of  ball,  and  d  =  diameter  of  indentation,  —  all 
lengths  being  expressed  in  mm.  Brinell  hardness  values  have  a  direct  relation  to  tensile  strength,  and  hardness 
determinations  may  be  used  to  define  tensile  strengths  by  employing  the  proper  conversion  factor  for  the  ma- 
terial under  consideration. 

Shore  Scleroscope  Hardness.  —  Height  of  rebound  of  diamond  pointed  hammer  falling  by  its  own  weight 
on  the  object.  The  hardness  is  measured  on  an  empirical  scale  on  which  the  average  hardness  of  martensitic 
high  carbon  steel  equals  100.  On  very  soft  metals  a  "  magnifier"  hammer  is  used  in  place  of  the  commonly 
used  "universal"  hammer  and  values  may  be  converted  to  the  corresponding  "universal"  value  by  multi- 
plying the  reading  by  $.  The  scleroscope  hardness,  when  accurately  determined,  is  an  index  of  the  tensile 
elastic  limit  of  the  metal  tested. 

Erichsen  Value.  —  Index  of  forming  quality  of  sheet  metal.  The  test  is  conducted  by  supporting  the 
sheet  on  a  circular  ring  and  deforming  it  at  the  center  of  the  ring  by  a  spherical  pointed  tool.  The  depth  of 
impression  (or  cup)  in  mm  required  to  obtain  fracture  is  the  Erichsen  value  for  the  metal.  Erichsen  standard 
values  for  trade  qualities  of  soft  metal  sheets  are  furnished  by  the  manufacturer  of  the  machine  corresponding 
to  various  sheet  thicknesses.  (See  Proc.  A.  S.  T.  M.  17,  part  2,  p.  200,  1917.) 

Alloy  steels  are  commonly  used  in  the  heat  treated  condition,  as  strength  increases  are  not  commensurate 
with  increases  in  production  costs  for  annealed  alloy  steels.  Corresponding  strength  values  are  accordingly 
shown  for  annealed  alloy  steels  and  for  such  steels  after  having  been  given  certain  recommended  heat  treat- 
ments of  the  Society  of  Automotive  Engineers.  The  heat  treatments  followed  in  obtaining  the  properties 
shown  are  outlined  on  the  pages  immediately  following  the  tables  on  steel.  It  will  be  noted  that  considerable 
latitude  is  allowed  in  the  indicated  drawing  temperatures  and  corresponding  wide  variations  in  physical  prop- 
erties may  be  obtained  with  each  heat  treatment.  The  properties  vary  also  with  the  size  of  the  specimens 
heat  treated.  The  drawing  temperature  is  shown  with  the  letter  denoting  the  heat  treatment,  wherever  the 
information  is  available. 


TABLE  44. 

MECHANICAL   PROPERTIES. 
TABLE  44.  —  Ferrous  Metals  and  Alloys  —  Iron  and  Iron  Alloys. 


75 


Metal.                          Grade. 

14 

£1 

Ultimate  1 
strength.  1  1 

Sjj 

sa 

Ultimate  1 
strength.  I 

.sE^ 

fciE.S 
o°9  M 

wS,^ 

Reduct.  1 
in  area.  I 

Hardness. 

Brinell 
at  3000 
kg 

Sclero- 
scope. 

Tension- 

kg/mm2 

Tension 

lb/in2 

Per  cent. 

Iron: 

Electrolytic*  (remelt)  :  as  forged  .  .  . 
annealed  900°  C. 
Gray  castt(i9  mm  diam.  bars)  .... 

Malleable   cast,    American     (after 
Hatfield) 

34-o 
12.5 
indet. 

fi4-o 

<3i-5 
,19:0 
{28.0 

fiQ-5 
122.5 

29-5 

II.O 

48.0 
25.0 
66.0 
5i-o 
35-5 
12.5 

48.0 
22.5 
54-5 
37-5 

38.5 
27.0 

{17.5 
120.5 

(24-5 
(40.0 

|29-5 
145-5 
40.8 
(34-o 
(37.0 
3i-5 
24-5 

53-5 
38.0 
74.0 
64-5 
38.5 
24-5 

54-5 
37-5 
60.5 
49.0 

48,500 
l8,OOO 
indet. 

|  20,000 

(45,000 
,27,000 
{40,000 

(  28,000 
(32,000 
41,800 
16,000 

68,100 
35,800 
94,000 
72,900 
50,700 
17,600 

68,200 
31,800 
77,700 
53,4oo 

55,ooo 

38,000 
(  25,000 
(38,000 

(35,000 
(57,000 
,42,000 
{65,000 
58,000 
(  48,000 
(53,000 
45,200 
34,900 

76,300 
54,2oo 
105,000 
91,600 
54,7oo 
34,900 

77,5oo 
53,4oo 
86,000 
69,800 

33-0 
520 
negh 

M5-0 
<   4-5 
/   6.0 

{     2.0 
21.6 

(40.0 
(30.0 

35-o 
53-o 

37-o 
50.0 
6.0 
24.0 
26.0 
60.0 

2I.O 
51.0 
28.0 
27.0 

83.0 
87.0 
gible 

{15-0 
t   4-5 

e     6.O 
\     2.0 

U5-o 
^35-0 
78.0 
81.5 

82.0 
90.6 

7-5 
25.1 

84-3 
93-5 

76.4 
85-3 
74-7 
55-5 

95  t 

75  t 

(  100 

(150 

~ 

18 
{24 

1  40 

{25 

(30 

European  (after   Am.  Malleable 
Castings  Ass.)  
(run  of  24  successive  heats,  1919)1 
Commercial  wrought   .  . 

Silicon  alloys  |!  Si  0.01:  as  forged.  .  . 
(Melted  in  vacuo)  ann.  970°  C 
(Note:  C  max.  o.oi  per  cent) 
Si  1.71  :  as  forged  
annealed  970°  C  
Si  4.40  1  as  forged 

annealed  970°  C  
Aluminum  alloy  s^  Al  0.00  :  as  forged 
(Melted  in  vacuo)  ann.  1000°  C 
(Note:  C  max.  o.oi  per  cent) 
Al  3.08  :  as  forged  
annealed  1000°  C  
Al  6.24  I  as  forged  

annealed  1000°  C  

.6.7 


0.204 


Composition,   approximate: 

Electrolytic,  C  0.0125  per  cent;    other  impurities  less  than  0.05  per  cent. 

Cast,  gray:  Graphitic,  C  3.0,  Si  1.3  to  2.0,  Mn  0.6  to  0.9,  S  max.  o.i,  P  max.  1.2. 

A.  S.  T.  M.  Spec.  A48  to  18  allows  S  max.  o.io,  except  S  max.  0.12  for  heavy  castings. 
Malleable:  American  "  Black  Heart,"  C  2.8  to  3.5,  Si  0.6  to  0.8,  Mn  max.  0.4,  S  max.  0.07,  P  max.  0.2. 

European  "  Steely  Fracture,"  C  2.8  to  3-5,  Si  p.6  to  0.8,  Mn  0.15,  S  max.  0.35,  P  max.  0.2. 
Compressive  Strengths  [Specimens  tested:  25.4  mm  (i  in.)  diam.  cylinders  76.2  mm  (3  in.)  longj. 
Electrolytic  iron  56.5  kg/mm2  or  80,000  lb/in2. 

Gray  and  malleable  ca^t  iron  56.5  to  84.5  kg/mm2  or  80,000  to  120,000  lb/in2. 
Wrought  iron,  approximately  equal  to  tensile  yield  point  (slightly  above  P-limit). 
Density: 

Electrolytic  iron 7.8  g/cm3  or  487  lb/ft3     Malleable  iron 7.6    g/cm3  or  474  lb/ftj 

Cast  iron 7.2  g/cm3  or  449  lb/ft3     Wrought  iron 7.85  g/cm3  or  490  lb/ft3 

Ductility:  —  Normal  Erichsen  values  for  good  trade  quality  sheets,  0.4  mm  (0.0156  in.) 

Thickness,  soft  annealed.  Depth. 

mm  in. 

Sheet  metal  hoop  iron,  polished 9.5  0.374 

Charcoal  iron  tinned  sheet 7.5  0.295 

Second  quality  tinned  sheet 

Modulus  of  elasticity  in  tension  and  compression: 

Electrolytic  iron ....    17,500  kg/mm2  or  25,000,000  lb/in2 

Cast  iron 10,500  kg/mm2  or  15,000,000  lb/in2 

Modulus  of  elasticity  in  shear: 

Electrolytic  iron 7030  kg/mm2  or  10,000,000  lb/in2 

Wrought  iron 

Scleroscope  hardness  values  shown  are  as  determined  with  the  Shore  Universal  hammer. 
Strength  in  Shear: 

Electrolytic  (remelt)  Commercial  wrought 

P-limit 8.4  kg/mm2  or  12,000  lb/in2         P-limit 

Ultimate  strength 21.1  kg/mm2  or  30,000  lb/in2         Ultimate  strength. , 

Transverse  strength,  from  flexure  formula: 
Gray  cast  iron 

Modulus  of  rupture,  33.0  kg/mm2  or  47,000  lb/in2 

"Arbitration  Bar,"  31.8  mm  (ij  in.)  diameter,  or  304.8  mm  (12  in.)  span;  minimum  central  load  at  rup- 
ture 1130  to  1500  kg  (2500  to  3300  lb.);  minimum  central  deflection  at  rupture  2.5  mm  (o.i  in.),  (A.  S.  T. 
M.  Spec.  A  48-18). 

*  Properties  of  Swedish  iron  (impurities  less  than  i  per  cent)  approximate  those  of  electrolytic  iron, 
t  These  two  values  of  B.  h.  n.    only  are  as  determined  at  500  kg  pressure, 
t  U.  S.  Navy  specifies  minimum  tensile  strength  of  14.1  kg/mm2  or  20,000  lb/in2. 
§  Averages  for  a  U.  S.  foundry. 

[|  From  T.  D.  Yensen,  University  of  Illinois,  Engr.  Exp.  Station,  Bulletin  No.  83,  1915  (shows  Si  4.40  as  alloy  of 
maximum  strength). 

^  From  T.  D.  Yensen,  University  of  Illinois,  Engr.  Exp.  Station,  Bulletin  No.  95,  1917. 
SMITHSONIAN  TABLES. 


Malleable  iron.. 
Wrought  iron. . . 


17,500  kg/mm2  or  25,000,000  lb/in2 
17,500  kg/mm2  or  25,000,000  lb/in2 


Cast  iron 8450   .kg/mm2  or  12,000,000  lb/in2 

7030  kg/mm2  or  10,000,000  lb/in2 


2 1. 1  kg/mm2  or  30,000  lb/in2 
35.0  kg/mm2  or  50,000  lb/in2 


jfo  TABLES  45-46. 

MECHANICAL   PROPERTIES  OF   MATERIALS- 
TABLE  45.  —  Carbon  Steels  '—  Commercial  Experimental  Values. 

S.  A.  E.  (Soc.  of  Automotive  Eng..  U.  S.  A.)  classification  scheme  used  as  basis  for  steel  groupings.  First 
two  digits  S.  A.  E.  Spec.  No.  show  steel  group  number,  and  last  two  (or  three  in  case  of  five  figures)  show 
carbon  content  in  hundredths  of  one  per  cent. 

The  first  lines  of  properties  for  each  steel  show  values  for  the  rolled  or  forged  metal  in  the  annealed  or  nor- 
malized condition.  Comparative  heat-treated  values  show  properties  after  receiving  modified  S.  A.  E.  heat 
treatment  as  shown  below  (Table  46).  The  P-limit  and  ductility  of  cast  steel  average  slightly  lower  and  the 
ultimate  strength  10  to  15  per  cent  higher  than  the  values  shown  for  the  same  composition  steel  in  the  annealed 
condition.  Tiie  properties  of  rolled  steel  (raw)  are  approximately  equal  to  those  shown  for  the  annealed  con- 
dition, which  represents  the  normalized  condition  of  the  metal  rather  than  the  soft  annealed  state. 

The  data  for  heat-treated  strengths  are  average  values  for  specimens  for  heat  treatment  ranging  in  size 
from  £  to  i£  in.  diameter.  The  final  drawing  or  quenching  temperature  for  the  properties  shown  is  indicated 
in  degrees  C  with  the  heat  treatment  letter,  wherever  the  information  is  available.  In  general,  specimens 
were  drawn  near  the  lower  limit  of  the  indicated  temperature  range. 


Metal. 

S.A.E. 
spec. 
no. 

Nominal 
contents 
per  cent. 

S.A.E. 
heat 
treat- 
ment. 

I 

p!< 

Ultimate  1 
strength.  1 

J 

PH 

Ultimate  1 
strength.  1 

'SH 

31" 

Reduct.  1 
in  area. 

Hardness. 

Brinell 
(5)  3000  kg. 

o  <o 
»§• 
£« 

Tension 
kg/  mm2 

Tension 

lb/in2 

Per  cent 

Steel,  carbon 

1010  ) 
1010  ) 
1020  ) 
1020  ) 
1045) 
1045  ) 
1095  J 

See  Spec. 
No 

(Mn  0.45) 
(Mn  0.65) 
(Mn  0.35) 

Ann. 
A 
Ann. 
H  230°  C 
Ann. 
H  260°  C 
Ann. 
F  510°  C 

24.0 
27*0 
28.0 
35-o 
40.0 
62.0 
42.0 
84.0 

32.0 
42.0 
38.0 
56.0 
50.0 
86.0 
56.0 
123.0 

34,500 
39,ooo 
39,5oo 
49,500 
57,5oc 
88,000 
59,5oo 

120,000 

46,000 
60,000 
54,400 
79,500 
71,300 
123,000 
79,000 
175,000 

37-0 
30.0 
32-0 

20.0 
23-0 

13-5 

21  .0 

6.0 

72.0 
62.0 
68.0 
59-0 
54-0 
36.0 

iS'.o 

120 
100 

176 
1  68 
290 

187 

18 
24 
17 
35 
27 
45 
29 
75 

Specification  values:  Steel,  castings,  Ann.  A.S.T.M.  A27~i6,  Class  B;*  P  max.  0.06;  S  max.  0.05. 

Grade.                         Yield  point. 

Ultimate  tensile  strength 

Per  cent 
elong. 
50.8  mm 
or  2  in. 

Per  cent 

reduct. 
area. 

kg/mm2 

Ib/im 

Hard                                  O.AZ 

ultimate                  56.2 
49-2 

42.  2 

80,000 
70,000 
60,000 

ii 

22 

20 
25 
30 

Medium  . 
Soft 

0    AS 

0.45 

Structural  Steel:    Rolled:    S  max.  0.05;    P-Bess.  max.  o.io;  -O-H.  max.  0.06. 

Tension:  Yield  Point  min.  =  0.5  ultimate;  ultimate  =  38.7  to  45.7  kg/mm2  or  55,000  to  65,000  Ib/in* 
with  22%  min.  elongation  in  50.8  mm  (2  in.). 

*  Average  carbon  contents:  steel  castings,  C  0.30  to  0.40;  structural  steel,  C  0.15  to  0.30  (mild  carbon  or  medium 
hard  steel). 

TABLE  46.  —  Explanation  of  Heat  Treatment  Letters  used  in  Table  of  Steel  Data, 

Motor  Transport  Corps  Modified  S.  A.  E.  Heat  Treatments  for  Steels.  (S.  A.  E.  Handbook,  Vol.  i,  pp. 
gd  and  90,  1915,  q.  v.  for  alternative  treatments.) 

Heat  Treatment  A.  —  After  forging  or  machining  (i)  carbonize  at  a  t°mperature  between  870  and  930°  C. 
(1600  and  1700°  F.);  (2)  cool  slowly;  (3)  reheat  to  760  to  820  C.  (1400  to  1500°  F.)  and  quench  in  oil. 

Heat  Treatment  D.  —  After  forging  or  machining:  (i)  heat  to  820  to  840°  C.  (1500  to  1550°  F.);  (2)  quench; 
(3)  reheat  to  790  to  820°  C.  (1450  to  1500°  F.);  (4)  quench;  (5)  reheat  to  320  to  650°  C.  (600  to  1200°  F.) 
and  cool  slowly. 

Heat  Treatment  F.  —  After  shaping  or  coiling:  (i)  heat  to  775  to  800°  C.  (1425  to  1475°  F.);  (2)  quench; 
(3)  reheat  to  200  to  480°  C.  (400  to  900°  F.)  in  accordance  with  degree  of  temper  required  and  cool  slowly. 

Heat  Treatment  H.  —  After  forging  or  machining:  (i)  heat  to  820  to  840°  C.  (1500  to  1550°  F.); 
(2)  quench;  (3)  reheat  to  230  to  650°  C.  (450  to  1200°  F.)  and  cool  slowly. 

Heat  Treatment  L.  —  After  forging  or  machining:  (i)  carbonize  at  a  temperature  between  870  and 
050°  C.  (1600  and  1750°  F.),  preferably  between  900  and  930°  C.  (1650  and  1700  F.);  (2)  cool  slowly  in  car- 
bonizing material;  (3)  reheat  to  790  to  820°  C.  (1450  to  1500°  F.);  (4)  quench;  (5)  reheat  to  700  to  760°  C. 
(1300  to  1400°  F.);  (6)  quench;  (7)  reheat  to  120  to  260°  C.  (250  to  500  F.)  and  cool  slowly. 

Heat   Treatment   M.  —  After   forging   or   machining:     (i)   heat   to    790  to   820°  C.    (1450   to    1500    F.); 

(2)  quench;    (3)   reheat  to  between  260  and  680°  C.  (500  and  1250°  F.)  and  cool  slowly. 

Heat  Treatment  P.  —  After  forging  or  machining:  (i)  heat  to  790  to  820°  C.  (1450  to  1500  F.);  (2) 
quench;  (3)  reheat  to  750  to  770°  C.  (1375  to  i425*F.);  (4)  quench;  (5)  reheat  to  260  to  650  C.  (500  to 
I200°F.)  and  cool  slowly. 

Heat  Treatment  T.  —  After  forging  or  machining:  (i)  heat  to  900  to  950'  C.  (1650  to  1750    F.);  (2)  quench; 

(3)  reheat  to  260  to  700°  C.  (500  to  1300°  F.)  and  cool  slowly. 

Heat  Treatment  U.  —  After  forging:  (i)  heat  to  830  to  870"  C.  (1525  to  1600°  F.),  hold  half  an  hour; 
(2)  cool  slowly;  (3)  reheat  to  900  to  930°  C.  (1650  to  1700°  F.);  (4)  quench;  (5)  reheat  to  180  to  290  C. 
(350  to  550°  F.)  and  cool  slowly. 

Heat  Treatment  V.  —  After  forging  or  machining,  (i)  heat  to  900  to  950'  C.  (1650  to  1750  *.); 
(2)  quench;  (3)  reheat  to  between  200  and  650°  C.  (400  and  1200°  F.)  and  cool  slowly. 

EDITOR'S  NOTE:    Oil  quenching  is  recommended  wherever  the  instructions  specify  "quench,"  inasmuch  as 
the  data  in  the  table  are  taken  from  tests  of  automobile  parts  which  must  resist  considerable  vibration  and 
which  are  usually  small  in  section.     The  quenching  medium  must  always  be  carefully  considered. 
SMITHSONIAN  TABLES. 


TABLE  47. 

MECHANICAL   PROPERTIES. 
TABLE  47.  —  Alloy  Steels  —  Commercial  Experimental  Values. 


77 


Metal. 

S.  A.  E. 
spec, 
no. 

Nominal 
contents, 
per  cent. 

S.  A.  E. 
heat 
treat- 
ment. 

i 

Ultimate  1 
strength.  1 

i 

Ultimate  1 
strength.  1 

•9  5 

Reduct. 
in  area.  1 

Hard- 
ness. 

Brinell 
C"  3000  kg. 

it 

Tension 
kg/  mm2 

Tension 

Ib/in' 

Per  cent. 

Steel,  nickel  .  . 

2315 

_ 

Ann. 

30.0 

38.0 

42,500 

54,000 

32.0 

6o.O 

138 



2315 

— 

H 

53-0 

76.0 

75,000 

107,500 

18.0 

55-o 

321 

43 

2335 

. 

Ann. 

39-o 

48.0 

55,000 

68,000 

24.0 

53-o 

165 

2335 

JNi  3.50 

H 

106.0 

131.0 

151,000 

186,000 

15.0 

51.0 

465 

62 

2345 
2345 

(Mn  0.65) 

Ann. 
H 

44-o 
136.0 

55-o 
149.0 

62,500 
193,000 

78,000 
212,000 

2I.O 

I2.O 

48.0 
45-o 

172 
570 

76 

Invar 

Ni  36.0 

C  0.40 

Ann. 

50.0 

77-5 

71,000 

110,000 

30.0 

50.0 

— 

— 

nickel 

chrome.  .  .  . 

3120 

/Ni    1.25 

Ann. 

34-o 

44.0 

49,000 

62,000 

23.0 

53-0 

155 

22 

3120 

\Cr    0.60 

H45o°C 

60.0 

82.0 

85,000 

116,000 

23.0 

48.0 

270 

36 

3135 

Ann. 

40.0 

50.0 

57,000 

71,300 

2O.O 

46.0 

182 

30 

3135 

(Mn  0.65) 

HorD 

88.0 

I2I.O 

125,000 

172,000 

18.0 

43-o 

330 

44 

3220 

Ann. 

39-° 

49-o 

55,ooo 

69,000 

21.0 

50.0 

170 

— 

3220 

/Nii.75 

HorD 

77.0 

106.0 

1  10,000 

151,000 

23.0 

48.0 

375 

So 

3250 

1  Cr  1.  10 

Ann. 

44.0 

55-o 

62,000 

78,000 

I9.O 

42.0 

1  80 

— 

3250 

(Mn  0.45) 

M 

134.0 

183.0 

190,000 

260,000 

16.0 

32.0 

480 

64 

3320 

Ann. 

32.0 

42.0 

46,000 

59,500 

2I.O 

50.0 

— 

— 

3320 

/  Ni  3.50 

L 

77.0 

105.0 

110,000 

1  50,000 

23.0 

48.0 

375 

50 

3340 

\  Cr  1.50 

Ann. 

39-o 

52.0 

56,000 

74,000 

18.0 

45-o 

3340 

(Mn  0.45) 

P 

I2O.O 

163.0 

1  70,000 

232,000 

18.0 

42.0 

479 

64 

chromium. 

51120 

Cr     i.  oo 

Ann. 

44.0 

58.0 

62,000 

82,000 

16.0 

31.0 

— 

51120  ' 

(Mn  0.35) 

MorP 

144.0 

193.0 

205,000 

275,000 

7.0 

26.0 

500 

66 

52120 

Cr     1.20 

Ann. 

44.0 

58-0 

62,000 

82,000 

13.0 

24.0 

— 

52120 

(Mn  0.35) 

MorP 

I4I.O 

178.0 

200,000 

253,000 

7.0 

25-0 

524 

70 

chrome 

y-                      "\ 

vanadium 

6l30  1 
f.,  -_    f 

(Mn  0.65) 

Ann. 

43-o 

59-o 

61,500 

84,500 

23-0 

51.0 

152 

—  . 

0130  J 

/  Cr  0.95 

T 

84.0 

115.0 

120,000 

163,000 

16.0 

43-o 

432 

59 

\V    0.18 

6l95/ 

(Mn  0.35) 

Ann. 
U 

48.0 
176.0 

63.0 
232.0 

68,200 
250,000 

90,000 
330,000 

16.0 
8.c 

38.0 
24.0 

562 

75 

silico- 

manganese 

9250 

/Si     1.95 

Ann. 

42.0 

54-0 

60,000 

77,000 

16.0 

28.0 

— 

— 

9250 

\  Mn  0.70 

V 

91.0 

122.0 

130,000 

174,000 

14.0 

24.0 

441 

59 

9X30 

/Si     0.85 

Ann. 

48.0 

6l.O 

68,000 

87,000 

13.0 

22.O 

— 

9x30 

\  Mn  1.75 

V 

113.0 

148.0 

160,000 

211,000 

I2.O 

2I.O 

470 

63 

tungsten  .  . 

(C-73 

W    2.4 

Ann. 

34-o 

59.0 

48,100 

84,2OO 

20.5 

31-5 

(C-7Q) 

W    9-7 

Ann. 

63.0 

89.0 

90,000 

126,000 

14.0 

22.1 

— 

— 

(C-47) 

Wi5.6 

Quench 

1065° 

158-5 

175-0 

225,000 

248,OOO 

6.0 

43-o 

520 

64 

Draw 

205°  C 

GENERAL  NOTE.  —  Table  on  steels  after  Motor  Transport  Corps,  Metallurgical  Branch  of  Engineering  Division, 
Table  No.  88. 

Maximum  allowable  P  0.045  or  less,  maximum  allowable  S  0.05  or  less. 

Silicon  contents  were  not  determined  by  Motor  Transport  Corps  in  preparing  table,  except  for  silico-manganese  steels. 
Compressive  strengths: 

For  all  steels  approx.  equal  to  yield  point  in  tension  (slightly  above  P-limit). 
Density: 

Steel  weighs  about  7.85  g/cm3  or  490  lb/ft3 
Ductility,  Erichsen  values: 

0.75  mm  (0.029  in.)  thick,  low  carbon  soft  annealed  sheet  (B.  S.),  depth  of  indentation  12.0  mm  or  0.472  in. 
1.30  mm  (0.050  in.)  thick,  low  carbon  soft  annealed  sheet  (B.  S.),  depth  of  indentation  12.5  mm  or  0.492  in. 
Modulus  of  elasticity  in  tension  and  compression: 

For  all  steels  approx.  21,000  kg/mm2  =  30,000,000  lb/in2. 
Modulus  of  elasticity  in  shear: 

For  all  steels  approx.  8400  kg/mm2  =  12,000,000  lb/in2. 

Scleroscope  hardness  values  shown  are  as  determined  with  the  Shore  Universal  hammer. 
Strength  in  shear: 

P-Iimit  and  ultimate  strength  each  about  70  per  cent  corresponding  tensile  values. 

SMITHSONIAN  TABLES. 


78  TABLES  48-50. 

MECHANICAL   PROPERTIES. 

TABLE  48.  —  Steel  Wire  —  Specification  Values. 

(After  I.  A.  S.  B.  Specification  3812,  Sept.,  1917,  for  High-strength  Steel  Wire.) 

S.  A.  E.  Carbon  Steel,  No.  1050  or  higher  number  specified  (see  Carbon  steels  above).    Steel  used  to  be  manufac- 
tured by  acid  open-hearth  process,  to  be  rolled,  drawn,  and  then  uniformly  coated  with  pure  tin  to  solder  readily. 


American 
or 
B.  and  S. 
wire  gage. 

Diameter. 

Req'd 
twists  in 
203.2  mm 
or  8  in. 

Weight. 

Req'd 
bends 
thru  90' 

Spec,  minimum  tensile  strength. 

mm 

in. 

kg/ioo  m 

lb/IOO 

ft. 

kg 

Ib. 

kg/mm2 

lb/in2 

6 

4-II5 

0.162 

16 

10.44 

7.01 

5 

2040 

4500 

154 

219,000 

7 

3-665 

.144 

19 

8.28 

5.56 

6 

1680 

37oo 

161 

229,000 

8 

3.264 

.129 

21 

6-55 

4.40 

8 

1360 

3000 

164 

233,000 

9 

2.906 

.114 

23 

5-21 

3-50 

9 

H35 

2500 

172 

244,000 

10 

2.588 

.IO2 

26 

4.12 

2-77 

ii 

910 

2OOO 

172 

244,000 

ii 

2.305 

.091 

30 

3-28 

2.  2O 

14 

735 

l62O 

179 

254,000 

12 

2-053 

.081 

33 

2.60 

i-74 

17 

590 

1300 

177 

252,000 

13 

1.828 

.072 

37 

2.06 

i-38 

21 

470 

IO4O 

179 

255,000 

14 

1.628 

.064 

42 

1.64 

I  .  IO 

25 

375 

830 

181 

258,000 

15 

i-45° 

•057 

47 

1.30 

o.  57 

29 

300 

660 

182 

259,000 

16 

1.291 

.051 

53 

1.03 

0.69 

34 

245 

540 

186 

264,000 

I? 

1.150 

•045 

60 

0.81 

0.55 

42 

195 

425 

188 

267,000 

18 

1.024 

.040 

67 

0.65 

0.43 

52 

155 

340 

190 

270,000 

iQ 

0.912 

•036 

75 

0-51 

0.34 

70 

125 

280 

193 

275,000 

20 

0.812 

.032 

85 

0.41 

0.27 

85 

IOO 

225 

197 

280,000 

21 

0.723 

.028 

96 

0.32 

O.  22 

105 

80 

175 

200 

284,000 

NOTE.  —  Number  of  90°  bends  specified  above  to  be  obtained  by  bending  sample  about  4.76  mm  (0.188  in.)  radius, 
alternately,  in  opoosite  directions. 

(Above  specification  corresponds  to  U.  S.  Navy  Department  Specification  22W6,  Nov.  i,  1916,  for  tinned,  galvan- 
ized or  bright  aeroplane  wire.) 

TABLE  49.  — Steel  Wire  —  Experimental  Values. 

(Data  from  tests  at  General  Electric  Company  laboratories.)    "  Commercial  Steel  Music  Wire  (Hardened).' 


Diameter. 

Ultimate  strength. 

mm 

in. 

kg/mm2  tension  lb/in2 

12.95 

0.051 

226.0 

321,500 

11.70 

.046 

249.0 

354,000 

9-iS 

.036 

253-0 

360,000 

7.60 

.030 

260.0 

370,000 

6.  35 

.025 

262.0 

372,500 

4-55 

.018 

265.5 

378,000 

2-55* 

.010 

386.5 

550,000 

1.65* 

.0065 

527.0 

750,000 

4-55t 

.018 

49.2 

70,000 

*  For  4.55  mm  wire  drawn  cold  to  indicated  sizes.       t  For  4.55  mm  (0.018  in.)  wire  annealed  in  Hz  at  850°  C. 

TABLE  50.  —  Semi-steel. 

Test  results  at  Bureau  of  Standards  on  iss-mm  shell,  Jan.  1919. 

Microstructure  —  matrix  resembling  pearlitic  steel,  embedded  in  which  are  flakes  of  graphite. 

Composition-Comb.  Co.6o  100.76,  Mno.88,  P  0.42  100.43,  80.077  to  0.088,  Si  1.22  to  1.23,  graphitic  C  2. 84  to  2.94. 


Metal. 

.ti 
£ 

£M 

P-limit. 

Ultimate  1 
strength.  1 

| 

Ultimate  1 
strength.  1 

P-limit.  1 

*>^ 

§•§ 

Hardness. 

PH 

£3  *"* 

PH 

Brinell 
(0)3000 
kg 

Sclero- 
scope. 

Tension 

kg/mm2 

Tension 
lb/in2 

Compression 

kg/  mm2 

Compression 
Ib/in2 

Semi-steel: 
Graph.  C  2.  85        \ 
Comb.  C  o.  76         / 

Graph.  C  2.  92        \ 
Comb.  Co.  60        j 

7-9 

4-2 

19.8 
14.9 

11,200 
6,000 

28,200 
21,200 

24-3 
18.3 

72.6 
61.4 

34,500 
26,000 

103,000 
87,300 

176 
170 

- 

Tension   specimens   12.7   mm    (0.5   in.)   diameter,  50.8  mm  (2   in.)   gage  length;     elongation  and   reduction  of 
area  negligible. 

Compression  specimens  20.3  mm  (0.8  in.)  diameter,  61.0  mm  (2.4  in.)  long;   failure  occurring  in  shear. 

Tension  set  readings  with  extensometer  showed  elastic  limit  of  2.1  kg/mm2  or  3000  lb/in2. 

Modulus  of  elasticity  in  tension  —  9560  kg/mm2  or  13,600,000  lb/in2. 
SMITHSONIAN  TABLES. 


TABLE  51. —  Steel-wire  Rope  —  Specification  Values.  79 

Cast  steel  wire  to  be  of  hard  crucible  steel  with  minimum  tensile  strength  of  155  kg/mm2  or  220,000  Ib/in* 
and  minimum  elongation  of  2  per  cent  in  254  mm  (10  in.). 

Plow  steel  wire  to  be  of  hard   crucible  steel  with  minimum  tensile  strength  of  183  kg/mm2  or  260,000 
lb/in2  and  minimum  elongation  of  2  per  cent  in  254  mm  (io  in.). 

Annealed  steel  wire  to  be  of  crucible  cast  steel,  annealed,  with  minimum  tensile  strength  of  77  kg/mm2  or 
110,000  lb/in2  and  minimum  elongation  of  7  per  cent  in  254  mm  (io  in.). 

Type  A:    6  strands  with  hemp  core  and  19  wires  to  a  strand  (=  6  X  19),  or  6  strands  with  hemp  core  and 

18  wires  to  a  strand  with  jute,  cotton  or  hemp  center. 

Type  B:    6  strands  with  hemp  core,  and  12  wires  to  a  strand  with  hemp  center. 
Type  C:    6  strands  with  hemp  core,  and  14  wires  to  a  strand  with  hemp  or  jute  center. 
Type  AA:   6  strands  with  hemp  core,  and  37  wires  to  a  strand  (=  6  X  37)  or  6  strands  with  hemp  core  and 
36  wires  to  a  strand  with  jute,  cotton  or  hemp  center. 


Description. 

Diameter. 

Approx.  weight. 

Minimum  strength. 

mm 

in. 

kg/m 

Ib/ft 

kg 

Ib. 

Galv.  cast  steel,  Type  A  .... 

9-5 
12.7 

25-4 
38.i 
9-5 
12.7 

25-4 
38.1 

9-5 
12.7 

25-4 
38.i 
25-4 
41-3 
9-5 
12.7 

25-4 
36.5 
9-5 

T2.7 

25-4 
4i-3 

f 

I 

l£ 

I 

I 

If 

J 

I 

l| 

I 

if 

1 

I 
If 

0.31 

0-55 
2.23 
5.06 

0-35 
0.58 
2-23 
5-28 
0.25 
0.42 

1.68 
3-94 
i-59 
4-35 
0.31 

o-55 
2-23 
4.66 

o-33 
0.58 

2-35 
6.18 

O.  21 

0-37 
I.SO 
3-40 
O.  22 

°-39 

1.50 

3-55 
0.17 
0.28 

1-13 
2.65 
1.07 
2.92 

0.21 

0-37 

1-50 

3-i3 

O.  22 

°-39 

1.58 
4-15 

3,965 
6,910 
27,650 
63,485 
3,840 
7,410 
27,650 
59,735 
2,995 
5,210 
20,890 

47,965 
18,825 

5i,575 
4,690 
8,165 

32,675 
69,140 
4,540 
8,750 
32,250 
83,010 

8,740 
15,230 
60,960 
139,960 
8,460 
16,330 
60,960 
131,690 
6,600 
11,500 
46,060 
105,740 
41,500 
113,700 
10,340 
18,000 
72,040 
152,430 
10,000 
19,300 
71,100 
183,000 

u               a               a               a        a 
a            a            a             a       a 
a             n             a             it       n 

Galv.  cast  steel,  Type  A  A  

it           a           n            t(          a 

Galv.  cast  steel,  Type  B  

u            a            a             a        n 

Galv.  cast  steel,  Type  C  

Galv.  plow  steel,  Type  A  

a            a            a             u         a 

a            a            a             a         a 

Galv.  plow  steel,  Type  AA.  . 

a            a            a             a           a 
a           a           tt            a           a 

•  .... 

TABLE  52.  — Plow  Steel  Hoisting  Rope  (Bright). 

(After  Panama  Canal  Specification  No.  302,  1912.) 

Wire  rope  to  be  of  best  plow  steel  grade,  and  to  be  composed  of  6  strands,  19  wires  to  the  strand,  with  hemp  center. 
Wires  entering  into  construction  of  rope  to  have  an  elongation  in  203.2  mm  or  8  in.  of  about  2?  per  cent. 


Diameter.^ 

Spec,  minimum  strength. 

Diameter. 

Spec,  minimum  strength. 

mm 

in. 

kg 

Ib. 

mm 

in. 

kg 

Ib. 

9-5 

f 

5,215 

11,500 

38.1 

if 

74,390 

164,000 

12.7 

^ 

9,070 

20,000 

50.8 

2 

127,000 

280,000 

19.0 

f 

20,860 

46,000 

63.5 

** 

207,740 

458,000 

25-4 

I 

34,470 

76,000 

69.9 

2f 

249,350 

550,000 

TABLE  53.  —  Steel-wire  Rope  —  Experimental  Values. 

(Wire  rope  purchased  under  Panama  Canal  Spec.  302  and  tested  by  U.  S.  Bureau  of  Standards,  Washington,  D.  C.) 


Description  and  analysis. 

Diameter. 

Ultimate  strength. 

Ultimate  strength 
(net  area). 

mm 

in. 

kg 

Ib. 

kg/mm2 

lb/in2 

Plow  Steel,  6  strands  x  19  wires 
C  0.90,  S  0.034,  P  0.024,  Mn 
0.48,  Si  0.172  .  .  .  . 

50.8 
69.9 
82.6 
82.6 

2 

2f 

3l 
3* 

137,900 
314,800 
392,800 
425,000 

304,000 
694,000 
866,000 
937,ooo 

129.5 
I5I.2 
132.2 
142.5 

184,200 
214,900 
187,900 
202,400 

Plow  Steel,  6  strands  X  25  wires 
C  0.77,  S  0.036,  P  0.027,  Mn 
0.46,  Si  0.152  .  .  . 

Plow  Steel,  6  x  37  plus  6  x  19 
C  0.58,  S  0.032,  P  0.033,  Mn 
0.41,  Si  0.160 

Monitor  Plow  Steel,  6  x  61  plus 
6  x  19,  C  0.82,  80.025,  P  0.019, 
Mn  0.23,  Si  0.169  

Recommended  allowable  load  for  wire  rope  running  over  sheave  is  one  fifth  of  specified  min.  strength. 
SMITHSONIAN  TABLES. 


So 


TABLES  54-55. 
TABLE  54.  —  Aluminum. 


Density 

1& 

E 

Z^ 
JM 

1 

2jS 

II 

'"I- 

te  C  c 

tjd 

Hardness. 

Metal,  approx. 
composition, 

Condition. 

or  weight. 

PH 

g| 

A 

§§ 

S°°'« 
J2  6^ 
W  ft 

*C 

«^ 

®*n 

per  cent. 

gm 
per 
cm? 

Ib.per 
ft* 

Tension, 
kg/mm2 

Tension, 
lb./in2 

Per  cent. 

|8 
«  ^ 

OQ    «« 

ALUMINUM: 

Av.  Al  99.3 

Imp.,  Fe  and  Si.  .  . 

Cast,    sand    at 

700°  C  

2-57 

160.5 

6.0  to 

8.0  to 

8,500  to 

12,000  to 

29  to 

36  to 

25  to 

4  to 

Cast,  sand  and 

7-0 

9.8 

10,000 

14,000 

15 

22 

26 

5 

heat  treated 
Ann.  500°  C,  air 

— 

— 

— 

8.  9  to 

— 

12,600  to 

28  to 

30  to 

25  to 

4  to 

cooled  
Cast,  chill  

Sheet,  ann 

2-57 
2.69 
2.70 
2.70 
2.70 

160.5 
168.0 
168.5 
168.5 
168.5 

6.0 
6.0 
14.0 
15.0 

21.0 

9-6 
9.0 
9-0 

21.0 

23-0 

28.0 

9,000 
8,500 

20,000 
22,000 
30,000 

13,600 
13,000 
13,500 
30,000 
33,000 
40,000 

18 

20.0 

23-0 
4.0 

6.0 

22 

25.  c 

25.0 

35-0 
50.0 

27 
26 

S 

5 

14 

Sheet,  hard  
Bars,  hard  
Wire,  hard  

Compressive  strength:  cast,  yield  point  13.0  kg/mm2  or  18,000  lb/in2;  ultimate  strength  47.0 
kg/mm2  or  67,000  lb/in2. 

Modulus  of  elasticity:  cast,  6900  kg/mm2  or  9,810,000  lb/in2  at  17°  C. 


TABLE  55. —  Aluminum  Sheet. 

(a)  Grade  A  (Al  min.  99.0)  Experimental  Erichsen  and  Scleroscope  Hardness  Values. 
[From  tests  on  No.  18  B.  &  S.  Gage  sheet  rolled  from  6.3  mm  (0.25  in.)  slab.    Iron  Age  v.  101,  page  950]. 


Heat  treatment 
annealed. 

Thickness, 
mm 

Indentation, 
mm 

Scleroscope 
hardness. 

None  (as  rolled) 

08 

6  83 

@  200°  C,  2  hours  
@  300°  C,  2  hours  
@  400°  C,  2  hours  
@  200°  C,  30  min 

.09 

.07 
.08 

8.86 
10.  17 
9.40 

8.0 
4-5 
4-5 
ii  8 

@  400°  C,  30  min  

.08 

9.80 

4-5 

(6)  Specification  Values.  —  (i)  Cast:  U.  S.  Navy  49  Al,  July  i,  1915;  Al  min.  94,  Cu  max. 
6,  Fe  max.  0.5,  Si  max.  0.5,  Mn  max.  3. 

Minimum  tensile  strength  12.5  kg/mm2  or  18,000  lb/in2  with  minimum  elongation  of  8  per 
cent  in  50.8  mm  (2  in.). 

(2)  Sheet,  Grade  A:  A.  S.  T.  M.  25  to  i8T;  Al  min.  99.0;  minimum  strengths  and  elongations. 


Gage,  sheet  thicknesses. 

Temper,  No. 

Tensile  strength. 

Elong.  in  50.8 
mm  or  2  in. 

(B.&S.) 

mm 

in. 

kg/mm2 

lb/in2 

per  cent. 

12  tO 

.052  to 

0.0808  to 

i  Soft,  Ann. 

8.8 

12,500 

30 

Sheets  of  temper  No. 

1  6  incl. 

•  293 

.0509 

2  Half-hard 

12.5 

18,000 

1 

i    to    withstand    being 

3  Hard 

15.  5 

22,000 

4 

bent  double  in  any  di- 

17 to 

.152  to 

.0453  to 

i  Soft,  Ann. 

8.8 

12,500 

20 

rection  and   hammered 

22  incl. 

•  643 

.0253 

2  Half-hard 
3  Hard 

12.5 

17-5 

18,000 

2^,000 

5 

2 

flat;     temper  No.   2  to 
bend  180°  about  radius 

23  to 
26  incl. 

•574  to 
.404 

.0226  to 

.0159 

• 

i  Soft,  Ann. 
2  Half-hard 

8.8 
12.5 

12,500 
18,000 

10 

5 

equal  to  thickness  with- 
out cracking. 

I  3  Hard 

21.0 

30,000 

2 

NOTE.  —  Tension  test  specimen  to  be  taken  parallel  to  the  direction  of  cold  rolling  of  the  sheet. 
SMITHSONIAN  TABLES. 


TABLE  66. 
ALUMINUM    ALLOY. 


8l 


Density 

~ 

If 

S1*' 

p 

dbEi 

a 

Hardness. 

or  weight. 

^3 

,S    K 

'S  v 

c  oo  *~ 

Alloy,  approx. 

Condition, 

£ 

5* 

PH 

5~ 

3  2>^" 

P4*o 

composition 

per  cent 

per  cent. 

reduction. 

—  ^ 

£  cL 

gm/ 
cm3 

ft' 

Tension, 
kg/mm2 

Tension, 
lb/in2 

per  cent. 

|8 

t/2  <" 

Aluminum  —  Copper  . 

Cast,  chill.... 



_ 

5-3 

10.5 

7,5oo 

15,000 

24.0 

34-0 

_ 

_ 

Al  98  Cu  i  Imp.  max.  i 

Rolled,  70%  .  . 

— 

— 

19.0 

21.0 

27,000 

30,000 

4.0 





Al  96  Cu  3  Imp.  max.  i 

Cast,  chill.... 
Rolled,  70%.. 

~ 

~ 

8.1 

25-0 

HI 

11,500 

35,ooo 

19,500 
41,000 

I2.O 

5-5 

2I.O 





Al  94  Cu  5  Imp.  max.  i 

Cast,  chill  
Rolled,  70%  .  . 

— 

IO.O 

23-0 

15-0 
27.0 

14,500 
33,ooo 

21,500 
38,000 

7-o 
6.0 

14.0 





A192  Cu8:  Alloy  No. 

Cast,  sand  

2.88 

1  80 

7-7  to 

10.5  to 

1  1  ,OOO  tO 

1  5  ,000  to 

4.0  to 

3-5  to 

50  to 

13  to 

12  

— 

— 

10.5 

16.2 

15,000 

23,000 

None 

None 

65 

18 

Al  90-92     Cu     7-8.5 

Imp.  max.  1.7  

Cast*  

2.9 

181 

— 

12.7 

— 

18,000 

I.O 

— 



— 

Copper,  Magnesium.. 

Cast  at  700°  C. 

— 

3-  2  tO 

9.6  to 

4,500  to 

13,600  to 

2.0  to 

0.5  to 

74  to 

17  tc 

Al  9.52  Cu  4.2  Mg  0.6 

4.6 

13.3 

6,500 

18,900 

o 

o 

74 

18 

Ann.  500°  C..  . 

— 

— 

4-6 

17.3 

6,500 

24,900 

3-0 

I.O 

80 

21 

Duralumin      or      178    f  Ann  

2.8 

174 

25-0 

42.0 

35,100 

59,500 

21.  1 

29-5 

— 



Alloy  Al  94  Cu  4  Mg   \  Rolled  70%.  .  . 

— 

53-o 

56.0 

75,400 

79,600 

4-0 

13-2 

—  • 



0.5  

1  Rolled  heat 

tr'd  t 





23.4 

39-O 

33,400 

55,300 

25.5 

26.0 

. 



Copper,  Manganese  .  . 
Al  96  Cu  2  Mn  2  

Cast,  chill  
Rolled,  20  mm 

- 

— 

IO.O 

19.0 

14.0 
27.0 

14,300 
27,100 

20,300 
38,200 

5-o 
16.0 

28.0 

— 

~ 

Al96Cu3Mni  Cast,  chill.  ... 

— 

— 

H-3 

19.0 

16,200 

27,000 

14.0 

— 

— 



Naval  Gun  Factory.  .  .    (  Cast,  sand.  .  .  . 

2.8 

I75 

14.0 

20,000 

12.0 

— 

— 



Al  97  Cu  1.5  Mn  i..  .  .     (Forged  

— 

— 

14.0 

19.0 

i9,5oo 

27,800 

I2.O 

47-o 

— 



Al  94  Cu  max.  6  Mn 

max.  3  

Minimum  J.  .  . 

— 

— 

— 

12.7 

— 

l8,OOO 

8.0 

— 

— 



Copper,  Nickel,  Mg 

Cast  at  700°  C. 

3-5  to 

17.9  to 

5,000  to 

25,500  to 

6.0  to 

8.5  to 

54  to 

9  to 

Al  93-5  Cu  3.5  Ni  1.5 

Mg  i  Mn  0.5  
Copper,  Nickel  Mn... 

Cast  at  700°  C. 



~ 

9-8 

23.2 

14-5  tO 

14,000 

33,000 
20,600  to 

i-S 
6.0  to 

I.O 
II.O  tO 

86 
50  to 

25 
9  to 

Al  94.2  Cu  3  Ni  2  Mn 

0.8  

21.4 

30,500 

I.O 

2.0 

91 

27 

Magnesium: 

Magnalium  Al  95  Mg  5 

Cast,  sand  

2.5 

156 

5-6 

15-5 

8,000 

22,000 

7.0 

8-5 

— 

— 

Al  77-98,  Mg  23-2..  . 

Cast,  chill  

2.410 

1  50  to 

—      29.5  to 

— 

42,000  to 

— 

— 

2.57 

160 

145-0 

64,000 

Cast,  chill.  ... 

— 

4.0 

II.O 

5,8oo 

14,900 

21.0 

36.0 

— 

— 

Nickel  Al  97  Ni  2  

Drawn,  cold  .  . 

— 

— 

14.0 

16.0 

19,700 

22,700 

13-0 

37-0 

— 

— 

Rolled,  hot.  .  . 

— 

— 

8.0 

13.0 

1  1  ,900 

18,200 

28.0 

52.0 

— 

— 

Cast,  chill  

— 

— 

6.0 

15.0      j  9,000 

21,700 

9-0 

II.O 

— 

— 

Al95NiS  

Drawn,  cold.  . 

— 

— 

16.0 

20.0         22,90O 

27,000 

8.0 

24.0 

— 

— 

Rolled,  hot  .  .  . 

— 

—       9.0 

16.0      13,500 

22,300 

22.0 

36.0 

— 

— 

Nickel  Copper: 

Al  93.5  Ni  5.5  Cu  i  .  . 

Cast,  chill  

— 

—        7.0 

17.0 

10,700 

24,800 

6.0 

8.0 

— 

— 

Al  91.5  Ni  4.5  Cu  4.  . 

Cast,  chill  

— 

7.0      18.0 

9,900 

25,200 

4.0 

5-o 

— 

— 

Al  92  Ni  5.5  Cu  2  

/  Drawn,  cold.  . 
\Rolled,  hot... 

~ 

~ 

22.0 
13-0 

27.0 

22.0 

31,700 
18,200 

37,800 
31,500 

8.0 
16.0 

15-0 
24.0 

~ 

~ 

Zinc,  Copper: 

Al  88.6  Cu  3  Zn  8.4.  . 

Cast  at  700°  C. 

— 

— 

4-7 

I8.5 

6,700 

26,300 

8.0 

7-5 

So 

10 

Ann.  500°  C.  . 



_  _ 

4-4 

20.2 

6,200 

28,800 

8.0 

7-5 

50 

IO 

Al  81.1  Cu  3  Zn  15.9. 

Cast  at  700°  C. 

3-1 

193 

9.8 

24.7 

14,000 

35,ioo 

2.O 

2.0 

74 

15 

Ann.  500°  C... 

9.8 

29.0 

14,000 

41,200 

4.0 

4.0 

70      US 

*  Specification  Values:  Alloy  "  No.  12":  A.  S.  T.  M.  B26-i8T,  tentative  specified  minimums  for  aluminum,  copper, 
t  Quenched  in  water  from  475°  C.  after  heating  in  a  salt  bath.      Modulus  of  elasticity  for  Duralumin  averages 
7000  kg/mm2  or  10,000,000  lb/in2. 

t  Specification  values:  Aluminum  castings;  U.  S.  Navy  49  Al,  July  i,  1915  (Impurities:  Fe  max.  0.5,  Si  max.  0.5). 

SMITHSONIAN   TABLES. 


82 


TABLES  57-59 

MECHANICAL   PROPERTIES. 
TABLE  57.  —  Copper. 


Metal  and 
approx. 
composition. 
Per  cent. 

Condition. 

Density 
or  weight. 

P-limit.  1 

Ultimate  1 
strength.  1 

1 

Ultimate  I 
strength.  1 

.a  g^ 
bis'i 

!«« 

ssr 

Reduct.  I 
in  area. 

Hardness. 

& 

is 

si 

gm/ 
cm8 

lb/ 
ft* 

Tension, 
kg/mm2 

Tension,  lb/in2 

Per  cent. 

Copper: 
00.9:  electrolytic 
Cu  99.6  

Ann.  2oc3  C. 

8.89 
8.85 
8.89 
8.90 

555 
552 

m 

6.0 
7.0 
14.0 
mdet. 

26.0 

27.0 
18.0 
35-o 
25.0 

35-0 
47-3 
21.9 
33-0 

8,500 
10,000 
20,000 
indet. 

37,000 

38.000 
25,000 
50,000 
35,000 

50,000 
67,400 
31,200 
46,800 

50.0 

20.O 

5-0 
50.0 

9.0 

0.8 
24-5 
4-3 

50.0 
60.0 
8.0 
60.0 

64.5 
76.0 
70.5 

40 
so 

94 
42 

l 

6 
18 

Cast  
f  Hard,  40%  reduct 
\  Ann.  at  500°  C.  .  . 
Drawn  cold,  50% 
reduct 

Rolled  .  . 

Cu  99.6  

No  Ann.  (96%  re- 
duction). ....  .  . 
Ann.  750°  C  after 
drawing  cold  .  .  . 
Drawn  hot  (64% 
reduction)  

Cu  99.9  1  • 

*  Wire  drawn  cold  from  3.18  mm  (0.125  in.)  to  0.64  mm  (0.025  in.)  Bull.  Am.  Inst.  Min.  Eng.,  Feb.,  1919. 
t  Wire  drawn  at  150°  C  from  0.79  mm  (0.031  in.)  to  0.64  mm  (0.025  in.)  (Jeffries,  loc.  cit.). 
Compression,  cast  copper,  Ann.  15.9  mm  (0.625  in.)  diam.  by  50.8  mm  (2  in.)  long  cylinders. 
Shortened    5  per  cent  at  22.0  kg/mm2  or  31,300  lb/in2  load. 
10   "  "    29.0  kg/mm2  "  41,200  lb/in2 

20   "  "    39.0  kg/ mm2  "   55,400  lb/in2     ' 

Shearing  strength,  cast  copper  21.0  kg/mm2  or  30,000  lb/in2 

Modulus  of  elasticity,  electrolytic  12,200  kg/mm2  or  17,400,000  lb/in2 

cast  7,700  kg/ mm2  or  11,000,000  lb/in2 
"          "         drawn,  hard  12,400  kg/mm2  or  17,600,000  lb/in2 

TABLE  58.  —  Rolled  Copper  —  Specification  Value. 

Specification  values:  U.  S.  Navy  Dept.,  4?C2,  minimums  for  rolled  copper,  —  Cu  min.  99.5 


Description,  temper  and  thickness. 

Tensile  strength. 

Elong.  in  50.8 
or  2  in.  —  per  cent. 

kg/mm2 

lb/in2 

Rods,  bars,  and  shapes: 
Soft  
Hard:  to  9.  5  mm  (f  in.)  incl  

21.0 

35-0 
31-5 
28.0 

24-5 

21.0  tO  28.O 
24-5 

30,000 
50,000 
45,ooo 
40,000 
35,ooo 

30,000  to  40,000 
35,ooo 

25 

10 
12 
IS 
20 

25  to  25 
18 

Hard:  9.5  mm  to  25.4  mm  (i  in.)  
Hard:  25  .  4  mm  to  50.  8  mm  (2  in.)  
Hard:  over  50  8  mm  (2  in  ) 

Sheets  and  plates: 
Soft 

Hard  

TABLE  59.  —  Copper  Wire  —  Specification  Values. 

Specific  Gravity  8.89  at  20°  C  (68°  F). 

Copper  wire  :  Hard  Drawn  (and  Hard-rolled  flat  copper  of  thicknesses  corresponding  to  diameters  of  wire) 
Specification  values.     (A.  S.  T.  M.  BI-IS,  and  U.  S.  Navy  Dept.,  22\V3,  Mar.  i,  1915-) 


Diameter. 

Minimum  tensile  strength. 

Maximum  elongation, 
per  cent  in 
254  mm  (10  in.). 

mm 

in. 

kg/mm2 

lb/W 

11.68 

.460 

34-5 

49,000 

2-75 

10.41 
9.27 

.410 
•  365 

35-9 
37-1 

51,000 
52,800 

3-25 
.80 

8.25 

.325 

38.3 

54,5oo 

.40 

7-34 

.289 

39-4 

56,100 

•  17 

6.55 

.258 

40-5 

57,600 

.98 

5-82 

.229 

41-5 

59,000 

•79 

in  1524  mm  (60  in.) 

5.18 

.204 

42.2 

60,100 

•24 

.62 

.182 

43-0 

61,200 

.18 

i  .12 

.162 

43-7 

62,100 

.14 

.66 

.144 

44-3 

63,000 

.09 

•25 

.128 

44.8 

63,700 

.06 

.90 

.114 

45-2 

64,300 

.02 

•59 

.102 

45-7 

64,900 

.00 

•  3i 

.091 

46.0 

65,400 

•97 

.06 

.O8l 

46.2 

65,700 

•95 

•  83 

.072 

46.3 

65,900 

.92 

.63 

.064 

46.5 

66,200 

.00 

•45 

•057 

46.7 

66,400 

.89 

•  30 

.051 

46.8 

66,600 

•  87 

.14 

•045 

47-0 

66,800 

.86 

.02 

.040 

47-1 

67,000 

•  85 

P-limit  of  hard-drawn  copper  wire  must  average  55  per  cent  of  ultimate 
in  table,  and  60  per  cent  of  tensile  strength  for  smaller  sizes. 


tensile  strength  for  four  largest  sized  wires 


SMITHSONIAN  TABLES. 


TABLES  60-63. 

MECHANICAL   PROPERTIES. 
TABLE  60.  —  Copper  Wire  —  Medium  Hard-drawn. 

(A.  S.  T.  M.  62-15)  Minimum  and  Maximum  Strengths. 


Tensile  strength. 

Minimum. 

Maximum. 

minimum  per  cent 

mm 

in. 

kg/mm2 

lb/in» 

kg/mm2 

lb/in» 

II  .70 

0.460 

29-5 

42,000 

34-5 

49,OOO 

3-75 

6-55 

.258 

33-o 

47,000 

38.0 

54,000 

2.50 

in  i524mm  (60  in.) 

4.12 

.162 

34-5 

49,000 

39-5 

56,000 

«  -is 

2-59 

.  IO2 

35-5 

50,330 

40.5 

57,330 

1.04 

1.02 

.040 

37-o 

53,ooo 

42.0 

60,000 

0.88 

Representative  values  only  from  table  in  specifications  are  shown  above. 
P-limit  of  medium  hard-drawn  copper  averages  50  per  cent  of  ultimate  strength. 

TABLE  61.  —  Copper  Wire  —  Soft  or  Annealed. 

(A.  S.  T.  M.  83-15)  Minimum  Values. 


Diameter. 

Minimum  tensile 
strength. 

Elongation 
in  254  mm 
(10  in.), 
per  cent. 

mm 

ill. 

kg/mm2 

lb/h* 

n.  70  to  7.37 

0.460  to  0.290 

25-5 

36,000 

35 

7  .  34  to  2  .  62 

0.289  to  o.  103 

26.0 

37,000 

30 

2-  59  to  0.53 

O.IO2  tO  O.  02  1 

27.0 

38,500 

25 

0.51  to  o  .  08 

O.O2O  tO  O.OO3 

28.0 

40,000 

2O 

NOTE.  —  Experimental  results  show  tensile  strength  of  concentric-lay  copper  cable  to  approximate  90  per  cent  of 
combined  strengths  of  wires  forming  the  cable. 

TABLE  62.  —  Copper  Plates. 

(A.  S.  T.  M.  Bn-i8)  for  Locomotive  Fire  Boxes.    Specification  Values. 


Minimum  requirements. 

Tensile  strength. 

Elong.  in 
203.2  mm 
(8  in.), 
per  cent. 

kg/mm* 

lb/in« 

Copper,  Arsenical,  As  0.25-0.50 
Impurities,  max.  0.12  

22.0 
21  .O 

31,000 
30,000 

35 
30 

Copper,  Non-arsenical: 
Impurities,  max.  0.12  

NOTE.  —  Copper  to  be  fire-refined  or  electrolytic,  hot-rolled  from  suitable  cakes. 
TABLE  63.  —  Copper  Alloys. 


The  general  system  of  nomenclature  employed  has  been  to  denominate  all  simple  copper- 
zinc  alloys  as  brasses,  copper-tin  alloys  as  bronzes,  and  three  or  more  metals  alloys  composed 
primarily  of  either  of  these  two  combinations  as  alloy  brasses  or  bronzes,  e.g.,  "Zinc  bronze" 
for  T.I.  S.  Government  composition  "  G  "  Cu  88  per  cent,  Sn  10  per  cent,  Zn  2  per  cent.  Alloys 
of  the  third  type  noted  above,  together  with  other  alloys  composed  mainly  of  copper,  have 
been  called  copper  alloys,  with  the  alloying  elements  other  than  minor  impurities  listed 
as  modifying  copper  in  the  order  of  their  relative  percentages. 

In  some  instances,  the  scientific  name  used  to  denote  an  alloy  is  based  upon  the  deoxidizer 
used  in  its  preparation,  which  may  appear  either  as  a  minor  element  of  its  composition  or 
not  at  all,  e.g.,  phosphor  bronze. 

Commercial  names  are  shown  below  the  scientific  names.  Care  should  be  taken  to  specify 
the  chemical  composition  of  a  commercial  alloy,  as  the  same  name  frequently  applies  to 
widely  varying  compositions. 


SMITHSONIAN  TABLES. 


TABLE  64. 

MECHANICAL   PROPERTIES  OF   MATERIALS- 
TABLE  64.  —  Copper-zinc  Alloys  or  Brasses;  Tin  Alloys  or  Bronzes. 


Metal  and 

Density 
or  weight. 

j 

|| 

1 

|| 

fj3 

IS 

Hardness. 

composition, 

Condition. 

* 

5ts 

* 

11 

ssr 

K.£ 

M 

O    QJ 

gm 
cm3 

Ib 
ft3 

Tension, 
kg/mm2 

Tension  , 
lb/in2 

Per  cent. 

la 

If 

Brass  : 

Sand  cast  

— 

— 



20.0 



29,000 

22 







Cu  90  Zn  iof.  . 

Cold  rolled,  hard 
Cold  rolled,  soft. 

8.7 

543 



39-0 
26.0 

— 

55,000* 
37,000* 

4: 

70 

60 

47 

20 
10 

Cu  80,  Znao  {. 

Cu  70,  Zn  30.  . 
Cu66Zn34Std. 
sheet  

Sand  cast  
Cold  rolled,  hard 
Cold  rolled,  soft. 
Sand  cast  
/  Cold  rolled,  hard 
\  Cold  rolled,  soft. 

8.6 
8.4 
8.5 
8.4 

537 
524 
530 
524 

— 

25-0 
53-0 
29.0 
28.0 
42.0 
34-0 

— 

35,000 
75,ooo* 
42,000* 
40,000 
60,000 
48,000  * 

3l> 

50* 

32 

85 
85 

75 
46 

45 

28 
12 

26 
12 

Cu  60,  Zn  40..  . 
Muntz  metal.  .  . 

Sand  cast  
Cold  rolled,  hard 

U« 

522 

15-5 

32.2 
49.0 

21,800 
45,000 

45,8oo 
70,000 

15 
30 

22 

50 

— 



Bronze  : 

Cu  97.7,  Sn  2.3. 

/Cast  
\Rolled  

— 

— 

6.0 
7.6 

19-5 
34-° 

8,500 
10,800 

28,000 
48,000 

20 

55 

75 

— 

— 

ICast      or      gun 

Cu  90,  Sn  10.  .  . 

bronze    or  bell 

8.78 

548 

7-2 

23.0 

10,300 

33,ooo 

10 

— 

— 

23 

metal  

Cu  80  Sn  20 

Cast 

881 

Cu  70,  Sn  30.  .  . 

Cast  

8.84 

552 

1-4 

5-o 

2,000 

7,000 

o.S 

— 

— 



Compressive  Strengths,  Brasses: 

Cu  90,  Zn  10,  cast  21.0  kg/mm2  or  30,000  lb/in2 
Cu  80,  Zn  20,  cast  27.4  kg/mm2  or  39,000  lb/in2 
Cu  70,  Zn  30,  cast  42.0  kg/mm2  or  60,000  lb/in2 
Cu  60,  Zn  40,  cast  52.5  kg/mm2  or  75,000  lb/in2 
Cu  50,  Zn  50,  cast  77.0  kg/mm2  or  110,000  lb/in2 

Modulus  of  elasticity,  —  cast  brass,  —  average  9100  kg/mm2  or  13,000,000  lb/in2 

Erichsen  values:  Soft  slab,  1.3  mm  (0.05  in.)  thick,  no  rolling,  depth  of  impression  13.8  mm  (0.55  in.). 

Hard  sheet,  1.3  mm,  rolled  38%  reduction,  depth  of  impression  7.3  mm  (0.29  in.). 

Hard  sheet,  0.5  mm,  rolled  60%  reduction,  depth  of  impression  3.7  mm  (0.15  in.). 

Compressive  Ultimate  Strengths,  Cast  Bronzes: 

Cu  97.7,  Sn  2.3  to  24.0  kg/mm2  or  34,000  lb/in2 
Cu  90,  Sn  10  to  39.0  kg/mm2  or  56,000  lb/in2 
Cu  80,  Sn  20  to  83.0  kg/ mm2  or  118,000  lb/in2 
Cu  70,  Sn  30  to  105.0  kg/mm2  or  150,000  lb/in2 

Specification  value,  A.  S.  T.  M.,  B  22-18  T,  for  specimen  =  cylinder  645  sq.  mm  (i  sq.  in.)  area,  25.4  mm  (i  in.  > 
long. 

Cu  80,  Sn  20:   minimum  Compressive  elastic  limit  =  17.0  kg/mm2  or  24,000  lb/ina 

Modulus  of  elasticity  for  bronzes  varies  from  7000  kg/mm2  or  10,000,000  lb/in2  to  10,000  kg/mm2  or  15,500,00^ 
lb/in2 

*  Values  marked  thus  are  S.  A.  E.  Spec,  values.     (See  S.  A.  E.  Handbook,  Vol.  I,  p.  i3a,  rev.  December,  1913. 
t  Red  metal.  t  Low  brass  or  bell  metal. 

§  A.  S.  T.  M.  Spec.  Big-iST  requires  B.h.n.  of  51-65  kg/mm2  @  5000  kg  pressure  for  70:  30  annealed  sheet 
brass. 


FOOT  NOTES  TO  TABLE  65,  PAGE  85. 

*Tensilite,  Cu6?,  Zn  24,  Al  4.4,  Mn  3.8,  P  o.oi  compressive  P-limit:    42.2  kg/mm2  or  60,000  lb/in2  and  1.33  per 
cent  set  for  70.3  kg/mm2  or  100,000  lb/in2  load. 

t  Compressive  P-limit  20.0  to  28.2  kg/mm2  or  28,500  to  40,000  lb/in2 

t  Compressive  ultimate  strength  54.5  kg/mm2  or  77,500  lb/in2 

§  Compressive  P-limit  4.2  kg/mm2  or  6000  lb/in2  and  40  per  cent  set  for  70.3  kg/mm2  or  100,000  lb/in2 

^  Modulus  of  elasticity  9840  kg/mm2  or  14,000,000  lb/in2 
,  ||  Values  are  for  yield  point.  **  Minimum  values  for  ingots. 

ft  Rolled  manganese  bronze  (U.  S.  N.)  Cu  57  to  60,  Zn  40  to  37,  Fe  max.  2.0,  Sn  0.5  to  1.5;    2.9  per  cent  increase 
for  thickness  25.4  mm  (i  in.)  and  under. 

it  Ni  9  per  cent,  B.h.n.  =  130  as  rolled;  B.h.n.  =  50  as  annealed  at  930°  C. 

U.  S.  Navy  Dept.  Spec.  468  3a,  June  i,  1917:   German  silver  Cu  60  to  67,  Zn  18  to  22,  Ni  min.  15,  no  mechanical 
requirements. 

For  list  of  30  German  silver  alloys,  see  Braunt,  "  Metallic  Alloys,"  p.  314,  —  "best"  (Hiorns),  "  hard  Sheffield," 
Cu  46,  Zn  20,  Ni  34. 

§§  Platinoid  Cu  60,  Zn  24,  Ni  14,  W  i  to  2;  high  electric  resistance  alloy  with  mechanical  properties  as  nickel  brass. 

HII  Specification  Values,  Naval  Brass  Castings,  U.  S.  Navy,  466  lob,  Dec.  i,  1917  for  normal  proportions  Cu  62,  Zn 
37,  Sn  i,  min.  tensile  strength  17.5  kg/mm2  or  25,000  lb/in2  with  15  per  cent  elongation  in  50.8  mm  (3  in.). 

SMITHSONIAN  TABLES. 


TABLE  65. 

MECHANICAL   PROPERTIES. 
TABLE  65.  —  Copper  Alloys  —  Three  (or  more)  Components. 


•tf 

J 

If 

I 

.1  0 

•pi 

Jg 

Hardness. 

Alloy  and  approx. 
composition 

Condition. 

V    £ 

* 

If 

PH 

SI 

5  S)^' 

OS'o 

(§) 

per  cent. 

it 

to 

O  4> 

gm 
per 
cm 

ID 
per 
ft* 

Tension, 
kg/  mm2 

Tension, 
lb/in2 

Per  cent. 

1! 

PQ 

1! 

Brass,  Aluminum.  . 

Cast 

Cu  57,Zn42,  Al  i  .  . 

— 

— 

— 

40.0 

— 

57,000 

50.0 

— 

— 

— 

Cu  s  S  Zn  41  Al  4. 

— 

-  — 

— 

6o.O 

— 

85,400 

16.5 







Cu62'.9,  Zn  33.3,'A 

3.8.1 

— 

— 

— 

56.2 

— 

80,000 

— 

— 

— 

Cu  70.5,  Zn  26.4,  Al 
Alum.,  Manganese.. 

3.lJ 

Cast,  tensilite* 

— 

13-4 

33-0 

19,000 

47,000 

50.0 

— 

— 

Cu64,  Zn  29,  Al3.i 

Mn  2.5,  Fe  1.2..  . 

— 

— 

21.  1 

68.8 

30,000 

98,000 

16.0 

17.0 

130 



Alum.,  Vanadium..  . 

Cu  58.5,  Zn  38.5,  Al 

1.5,  V  0.03  

Cold  drawn  .  .  . 

— 

— 

35-6 

57-0 

50,600 

81,400 

12.0 

14.0 

— 

— 

Iron: 

Cu  56,  Zn  41.5,  Fe  i. 

Cast  

— 

— 

— 

50.7  to 

— 

72,000  to 

35-o  to 

35-0  to 

109  to 

— 

59-2 

84,000 

22.O 

25-0 

119 

Aich's  Metal 

Cu6o,Zn38.2,Fei.8 

Cast  

8.42 

526 

— 

40.3 

— 

57,300 

— 

— 

— 

— 

Delta  Metal 

r       7       F 

f  Cast,  sand..  . 

— 

— 

— 

31-7 

— 

45,ooo 

10.0 

— 

— 

— 

CU  57,  ^n  42,  re  i.. 

\  Rolled,  hard  .  . 

— 

— 

— 

42.2 

— 

60,000 

17.0 

— 

— 

— 

Cu6s,Zn30,  Fes.. 

Rolled  hard... 

— 

— 



45-5 

— 

65,000 

— 



— 

Iron,  Tin: 

Cu56.s,Zn40,Fei.5, 

Cast  

— 

— 

23.2  to 

49-  2  tO 

33,  ooo  to 

70,000  to 

35-0  to 

35-o  to 

104  to 

— 

Sn  i.of  

— 

— 

26.0 

52.8 

37,ooo 

75,ooo 

20.0 

22.0 

119 

— 

Sterro  metal: 

Cu  55,  Zn  42.4  Fe 
1.8,  Sn  0.8  

f  Cast  
<  Forged  
(  Hard  drawn  .  . 

8.4 

525 

— 

42.5 

53-6 
58.5 

- 

60,500 
76,200 
83,100 

- 

= 

— 

= 

Lead  or  Yellow  brass 

Cast 

8-5 

53i 



23.2  to 



33,000  to 

30.0  to 

35-O  tO 



___ 

27-5 

39,ooo 

26.0 

30.0 

Cu  60  to  63.5,  Zn  35 

/  Sheet  ann  

— 

•  — 

— 

25-5 

— 

42,000 

50.0 

— 

— 

— 

to  33-5,  Pb  5  to  3. 
Lead,  Tin  or 

\Sheethard.... 

— 

— 

42.9 

— 

61,000 

30.0 

— 

— 

— 

Red  brass  

Cast  

8.6 

535 

II.  0 

21.0 

16,000 

30,000 

17.0 

19.0 

— 

7-o 

Cu83,Zn7,Pb6,Sn4 

Cu  78,Zn9.s,  Pb  10, 

Sn  2  .... 

Cast  

8.87 

554 

8.4 

18.6 

12,000 

26,500 

22.  0 

24.9 



Yellow  brass: 

Cu  70,  Zn  27,  Pb  2, 

Sn  i  

Cast§  

8.4 

524 

7-4 

20.7 

10,500 

29,500 

25-0 

28.5 

53-0 

— 

Manganese  or  Man- 

ganese bronze 

Cu  58,  Zn  39,   Mn 

Cast,  sand  U  .  . 

8.3 

520 

21.  1  tO 

49.2  to 

30,000  to 

70,000  to 

30.0  to 

3  2.0  to 

109  to 

i8to 

0.05 

24-6 

52.7 

35,000!  1 

75,ooo 

22.0 

25.0 

119 

19 

(Sn,  Fe,  Al,  Pb.) 

Cast,  chill  .... 

— 

— 

22-5  tO 

26.0|  | 

52.7  to 
563 

32,000  to 
3  7,  oool  | 

75,  ooo  to 

80,000 

32.0  to 

25-0 

34.0  to 

28.0 

119  to 
130 

i8to 

22 

Cu  60,  Zn   39    Mn, 

Rolled  

8.3 

520 

31-5 

52-5 

45,000 

75,ooo 

25-0 

28.0 

3O 

tr 

Specification  values: 

U.  S.  Navy,  46  B 

i6a**  

— 

— 



49.2 

— 

70,000 

20.O 

— 

— 



U.S.N.,46B  i5a 

Rolledft  

— 

— 

24.6 

49-2 

?5,ooo 

70,000 

3O.O 

— 

— 



Manganese     Vana- 

dium: 

Cu  58.6,  Zn  38.5,  Al 

Cold  drawn  .  .  . 

— 

— 

5-6 

57-0 

50,600 

81,400 

I2.O 

14.0 

— 



1.5  Mn  0.5,  V  0.03. 

Nickel:    Nickel    sil- 

ver, Cu  60.4,  Zn 

31.8,  Ni  7.7  

Cast 

1.5 

53° 

0.8 

25.3 

15,400 

36,000 

.O.5 

,2.0 

46 



German  silver, 

Cu   61.6,  Zn  17.2, 

Ni  21.  i  

8.7 

544 

3-2 

28.8 

18,800 

40,900 

28.5 

25.1 

80 



Cu  60.6,  Zn   11.8, 

Ni  27.3  

8.8 

547 

16.7 

37-6 

23,700 

53,500 

32.O 

31.4 

67 



Fine  wire: 

CusS.Zn  24,Nii8 

Drawn  hard  .  . 

8-5 

530 

— 

105.5 

— 

50,000 



— 

— 



Nickel  silver  tt 

Nickel  Tungsten  :§§ 

Tin: 

Cu6i,Zn38,Sni... 
Naval  brass,  as  above 

Cast,  sand  
Ann.  after  roll- 

— 

— 

II.  0 

30.0 

15,700 

42,600 

29-6 

32.0 

— 



ing  

— 

— 

26.0 

43-5 

37,000 

62,000 

25.0 

37-0 

— 



Tobin  bronze:  as  be- 

Cast   

.8.3 

518 

17.6 

42.2 

25,000 

60,000 

— 



low 

Cu   58.2,  Zn  39.5 

Sn  2.3. 

Rolled  .  . 

8.4 

524 

38.0 

56.0 

54,000 

79,000 

35.O 

40.0 





Cus5,Zn43,  Sn  2 

Castllll  .... 

48.4 

68,900 

48.0 

70.0 

"""" 

For  Footnotes  see  page  84. 
SMITHSONIAN  TABLES. 


86 


TABLE  65  (continued). 

MECHANICAL    PROPERTIES. 

TABLE  65.  —  Copper  Alloys  —  Three  (or  more)  Components. 


Alloy  and  approx. 
composition 
per  cent. 

Condition. 

Density 
or  weight.  1 

.d 
J 

fc 

Ultimate  1 
strength.  1 

d 

H 

eu 

l! 

S^ 
tifc  c 

Coo"" 

Iff 

Reduct.  I 
of  area.  1 

Hard- 

• 

Sfi 

Brinell(oi 
500  kg. 

%  "> 

gm 
per 
cm3 

8.8 

9.1 
8.9 

8.6 

Ib. 

!?r 

Tension, 
kg/mm* 

Tension, 
Ib/in2 

Per  cent. 

Brass,  Tin  —  (continued): 
Rods:*  o  to  12.7  mm  ($  in.) 
12.7   to   25.4  mm   (i   in.) 

over  25.4  mm  (in.)  diam.. 
Shapes,  all  
Plates  to   12.7   mm   (i  in.) 
over  12.7  mm  (£  in.)  thick 
Tubing  (wall  thickness)  o  to 
3.2  mm  (1  in.)  
3.2  to  6.4  mm  (J  in.)  

Cold  drawn 

See  Cu.  Al 

Castt  
Cast§  

/  Cast,  sand  . 
\Cast,  chill.. 

Cast  

CastH  
CastU  

Cast 

549 

570 
555 

535 

19.0 

18.3 

17.6 
iS-7 
19-3 
17.6 

21.  1 
19-7 
I8.3 

56.5 
15.8 

13-4  to 
16.2 
10.9 

12.8 
I  I.O 

13.8 

13-4  tO 

14.1 

10.5 
9.0 

9.2 
8.1 

28.0 

II.  2  tO 
I4.I 

4a.»IHl 

28.I|||| 

ax.zlHI 

17-6111! 

42.2 
40.8 

38.0 
39-4 
38.7 
39-4 

42.2 
38.7 
35-1 

64.5 
38.7 

IS-S 

21.  1  tO 
24.6 
22.1 
24.7 

21.0 

18.8 

21.  1  tO 
24.6 
21.8  tO 

26.0 

21.4 
19.1 

28.6 
27.9 

46.0 
21.8  to 

24.6 
56.2 

42.2 

38.7 
63.2 

3S-i 

27,000 
26,000 

25,000 
22,400 
27,500 
25,000 

30,000 
28,000 
26,000 

80,000 
22,500 

19,000  to 
23,000 
15,500 
18,200 

16,000 
19,600 
19,000  to 

20,000 

I5,OOO 
12,800 

13,100 
II.SOO 

40,000 

16,000  to 
20,000 

60,000 

40,000  III 
30,000  III 

25,ooo|||| 

60,000 
58,000 

54,000 
56,000 
SS.ooo 
56,000 

60,000 
55,ooo 
50,000 

92,000 
SS.ooo 

22,000 

30,000  to 
35,ooo 
31,400 

35,200 

30,000 
26,800 
30,000  to 
35,000 
3  1,  ooo  to 
37,000 

30,400 
27,200 

40,700 
39,700 

65,000 
31,000  to 
35,000 

80,000 

60,000 
SS.ooo 

90,000 
50,000 

35-o 
40.0 

40.0 
30.0 
32.0 
35-o 

28.0 
32.0 
35-0 

"•5 
25.0 

20.0  tO 
15-0 
13-5 

4-5 
6.0 

II  0 

iS.oto 
15-0 

20.0  tO 

16.0 

4.0 
25.0 

32.0 

31.0 

30.0 
6.0  to 

10.0 
I2.O 
20.O 

25.0 
25.0 

To  ber 
cold 
radii 
todi 

29.0 

26.0  to 
18.0 

12.0 

3-5 

3-5 
"•5 
24.0  to 

22.0 

3-3 

28.0 
31-0 

Requir 
bend 
throi 
abou 
us  ec 
thick 

d  i2< 
aboi 
s  equ 
amete 

65  to 
70 

II 

65 

50  to 
55 
57  to 
59 

72  to 

77 

ed 
col 
igh  is 
t  rad 
lual  ( 
ness. 

3° 
It 

al 
r. 

12 

8.0 
ii 
37 

.0 

i 

0° 

- 
o 

Vanadium  : 
Victor  bronze, 
V  0.03,  Cu   58.6,  Zn  38.5, 
Al  1.5,  Fe  i.o   
U.  S.  Navy  f  49  Bib.... 
Bronze,  Aluminum  

Lead: 

Cu  89,  Sn  10,  Pb  i  

Cu  88,  Sn  10,  Pb  2  

Cu  80,  Sn  10,  Pb  10  

Lead,  Phosphor: 
Cu  80,  Sn  10,  Pb  10,  P  trace 
Lead  Zinc,  Red  brass: 
Cu8i,  Sn7,Pbg,  Zn3  

Cu  88,  Sn  8,  Pb  2,  Zn  2  

Lead,  Zinc  Phosphor: 
Cu  73.2,  Sn  11.3,  Pb  12.0, 
Zn  2.5.P  i  

Cast**.... 
Cast  

Casttt 
Casttt 

Rolled  
Cast  
Cast  ».  .  .  . 

Manganese  : 

Cu88,  Snio,  Mn  2  
Nickel,  Zinc: 
Cu88,  Sns,Nis,Zn2(i)... 
Cu8g,  Sn4,Ni4,Zn3(2)... 
Phosphor  : 
Cu  95  Sn  4  9  P  o  i 

CuSg,  Sn  10.5,  P  0.5.  ...... 
Cu  80,  Sn  20,  P  max.  i  
Rods  and  bars§§  up  to  12.7 
mm  (i  in.)  
(minimum)  over  12.7  mm 
to  25.4  mm  (i  in.)  
over  25.4  mm  (i  in.)  
Sheets  and  plates  §§  spring 
temper  
Medium  temper  

tfronze,  Phosphor:  spring  wiri,  hard-drawn  or  hard-rolled  (U.  S.  Navy  Spec.  22  Ws,  Dec.  i,  1915)-     Cug^, 
Sn  min.  4.5,  Zn  max  0.3,  Fe  max.  o.i,  Pb  max.  0.2,  P  0.05  to  0.50;  max.  along,  in  203  mm  (8  in.)  =  4  per  cent. 

Min.  tensile 
Diameter  (group  limits). 

Diameter 
(group  limits). 

Min.  tensile 
strength. 

kg/mm2 

Ib/in2 

mm 

in. 

kg/mm"         Ib/in' 

.0 
.0 

135,000 
125,000 

to  6.  35 
109.52 

100.250 
to  0.375 

77.5           iio,oco 
74.0          105,000 

Over  1.59  mm  to  3.17  mm  (0.125  in.).  .       88 

*  Specification  Values,  Rolled  Brass,  Cu  62,  Zn  37,  Sn  i,  min.  properties  after  U.  S.  Navy  Spec.,  1918. 

t  Specification  Values:   Jan.  3,  1916,  Vanadium  Bronze  Castings,  Cu  61,  Zn  38,  Sn  max.  i  (inch  V).    Mimima. 

I  Compressive  P-limit  15.5  kg/mm2  or  22,000  Ib/in2 

5  Compressive  P-limit  10.5  kg/mm2  or  15,000  Ib/in2  and  28  per  cent  set  for  70  kg/mm2  or  100,000  Ib/in2 

[I  Ultimate  compressive  strength,  54.2  kg/mm2  or  77,100  Ib/in2  (Cu  76,  Sn  7,  Pb  13,  Zn  4). 

If  Compressive  P-limit  8.8  to  9.1  kg/mm2  or  12,500  to  13,000  Ib/in2,  and  34  to  35  per  cent  set  for  70  kg/mm2 

**  Compression:    ultimate  strength  49.5  kg/mm2  or  70,500  Ib/in2 

tt  Modulus  of  Elasticity:    (i)  12,200  kg/mm2  or  17,300,000  Ib/in2;    (2)  10,500  kg/mm2  or  14,000,000  Ib/in2 

it  Compressive  P-limit  17.6  to  28.1  kg/mm2  or  25,000  to  40,000  Ib/in2  and  6  to  10  per  cent  set  for  70  kg/mm* 
or  100,000  Ib/in2  load. 

Specification  Values:  U.  S.  Navy  46  B  sc,  Mar.  i,  1917,  Cu  85  to  oo,  Sn  6  to  n,  Zn  max.  4:  Cast,  Grade  i.  —  Im- 
purities max.  0.8;  min.  tensile  strength  31.6  kg/mm2  or  45,000  Ib/in2  with  20  per  cent  elong.  in  50.8  mm  (2  in.). 

t  Grade  2.  —  Impurities  max.  1.6;  min.  tensile  strength  21.1  kg/mm2  or  30,000  Ib/in2  with  15  per  cent  elong.  in 
50.8  mm  (2  in.). 

§§  Specification  Values:    U.  S.  Navy  468  i^b,  Mar.  i,  1916,  Cu  min.  94.  Sn  min.  3.5,  P  0.50,  rolled  or  drawn. 

Fill  Minimum  yield  points  specified:  for  P-limits  assur""  ^6  per  cent  o(  V!Uu«»«  =hown. 

SMITHSONIAN  TABLES. 


TABLE  65  (continued). 

MECHANICAL   PROPERTIES. 

TABLE  65.  —  Copper  Alloys  —  Three  (or  morel  Components. 


."£   tO 

'g 

g  |? 

'c 

fi 

ijjjj 

3s 

Hardness. 

Alloy  and  approx. 
composition. 

Condition. 

1! 

PH 

m 

| 
fe 

If 

h* 

•fijj 

(3) 

per  cent. 

. 

3J? 

i   V 

gm 
per 
cm3 

ID. 
per 
in3 

Tension, 
kg/mm2 

Tension, 

Ib/in2 

Per  cent. 

It 

Bronze  : 

Silicon  

Cast 







46.0 



65,000 









Cu  70,  Zn  29.5,  Si  0.5  .  . 
Zinc*Comp.  "G"  

Drawn,  hard.  . 
Cast  

8.6 

535 

8.6 

74.0 
27.4 

12,200 

IDS,  000 
38,900 

25.0 

21.0 

64 

13 

Admiralty  gun  metal  .  . 
Comm'c'l  range  

Castt  

— 

5.6  to 
8.4 

22.5  to 

26.7 

8,  ooo  to 
12,000 

32,000  to 

38,000 

25.0  to 

IO.O 

25.0  to 

12.0 

65  to 
75 

10  to 
20 

Spec,  values  

Cast  (mins.).  .  . 

— 

— 

21.  1 

— 

30,000 

14.0 



— 

Cu88,  Sn8,Zn4  

Castt  

8.5 

530 

7-7 

27-5 

1  1,  OOO 

39,200 

30.5 

24.0 

58 

II 

Cu8s,Sni3,Zn2  

Cast  

26.7 

— 

38,000 

2.5 

2-5 

25 

Zinc,  Lead  

Cu90,Sn6.5,Zn2,Pbi.s 

Cast§  .. 



8.4  to 

23*0  to 

12,000  to 

34,000  to 

3  S  •  o  to 

34.0  to 

50  to 

Rods  and  bars  ||  up  to 

II.  2 

28.1 

16,000 

40,000 

25.0 

26.0 

60 

12.7  mm  (£  in.)  

— 

— 

28.1 

56.2 

40,000 

80,000 

30.0 

Required  to  bend 

over  12.7  mm  to  25.4 

cold         through 

mm  (i  in.)  

— 

— 

26.4 

52.7 

37,500 

75,000 

30.0 

1  20°    about    ra- 

over 25.  4  mm  (i  in.).  . 
Shapes,!  |  all  thicknesses 

~ 

— 

24.6 
26.4 

50.7 
52.7 

35,000 
37,500 

72,000 
75,000 

30.0 
30.0 

dius      equal     to 
thickness. 

Sheets  and  plates,!  |o  to 

12.7  mm  (5  in.)  

— 

— 

27-4 

54-8 

39,000^ 

78,000 

30.0 

" 

over  12.7  mm  (£in.).. 

— 

— 

26.4 

52.7 

37,500 

75,000 

30.0 

" 

AluminumTin  : 

Cu88.5,  Alio.4,  Sni.2 
Aluminum  Titanium: 

Cast,  chill.... 

— 

— 

26.0 

48.0 

36,700 

68,000 

4-5 

5-5 

!89 

32 

(Cast**  

— 

— 

13-9 

52.0 

19,800 

74,ooo 

19-5 

23-7 

IOO 

25 

Cugo,  Al  10  

\  Quench, 

1      800°  C.... 

— 



29.0 

74.0 

40,500 

105,200 

I.O 

0.8 

262 



Cu  89,  Al  10,  Fe  i  

Cast  ft  

7-58 

473 

14.1  to 

45-7  to 

20,000  tO 

65,000  to 

30.0  to 

30.0  to 

93  to 

25  to 

I7.6 

56.2 

25,OOO 

80,000 

20.0 

20.0 

IOO 

26 

Lead: 

Cu  71.9,  Pb  27.5,  Sn  0.5 

Cast  

— 

— 

— 

4.2  to 



6,000  to 

3.0  to 

4.  2  tO 

— 

— 

4.6 

6,600 

3-2 

6.7 

Nickel,  Aluminum: 

Cu82.i,Nii4.6,  Al  2.5, 

Zno.7«  
Cu85,Sns,Zn5,Pbs. 

Forged  .  .  . 

— 

- 

44-5 
10.5  to 

90.0 
19-0  to 

63,300 

1  5,000  to 

128,000 
27,000  to 

IO.O 

20.0  tO 

12.0 
2O.O  tO 

50  to 

- 

Cast§§  

•3     A 

23.2 

19,000 

33,000 

16.0 

15.0 

62 

Cu  83,Sn  14,  Zn  2,  Pb  i 

Cast  

— 

— 

10.5  to 

16.2  to 

15,000  to 

23,  ooo  to 

4.0  to 

4.0  to 

20 

13-4 

19.0 

19,000 

27,000 

0.5 

0-5 

— 

24 

Zinc,  Phosphor 

("  Non  Gran") 

Cu86,  Sn  n,Zn3,  Ptr. 

Cast  

— 

— 

13-0 

25.0 

19,000 

•35,000 

9.0 



— 

— 

Vanadium,    See    Brass, 

Vanadium. 

Copper,  Aluminum  or 

Aluminum  Bronze: 

Cuoo,  Al  10  

Cast,  sand  ||||. 

7-5- 

468- 

3-9  to 

51.1  to 

19,800  to 

7  2,  700  to 

28.8  to 

30.0  to 

102  tO 

25  to 

7-45 

465 

23-3 

60.0 

33,200 

85,500 

21.7 

22.4 

106 

26 

CU92.5,  Al  7.2  

Rolled,       and 

7.0 

37.5 

9,600 

53,500 

91.0 

72.9 

81 

19 

ann. 

Aluminum,  Iron  or  Sill- 

Wrought  

— 

— 

9.8 

59-3 

14,000 

84,400 

"•5 

— 

— 



man  bronze 

Cast 





8.1 

55-5 

11,500 

78,850 

14.5 

- 

__ 

__t 

Cu  86.4,  Al  9.7,  Fe  3.9.. 

Cast,  sand.. 





14.0 

54-0 

20,000 

77,000 

24.5 

25-0 

IOO 

_ 

f  Quenched 

850°  C. 

Cu  88.5,  Al  10.5,  Fe  i.o. 

drawn 

i      700°  C.... 

28.0 

65.0 

40,000 

92,000 

14.0 

18.5 

140 

: 

*  Gov't.  Bronze:  Cu  88,  Sn  10,  Zn  2  (values  shown  are  averages  for  30  specimens  from  five  foundries  tested  at  the 
Bureau  of  Standards). 

t  Compressive  P-limit  10.5  kg/mm2  or  15,000  lb/in2  with  29  per  cent  set  for  70  kg/mm2  or  100,000  lb/in2  load. 

t  Values  from  same  series  of  tests  as  first  values  for  "  88-10-2,  averages  for  26  specimens  from  five  foundries  tested 
at  Bureau.,  of,  Standards. 

§  Compressive  P-limit  9.1  kg/mm2  or  13,000  lb/in2  with  34  per  cent  set  for  70  kg/mm2  or  100,000  lb/in2  load. 

||  Specification  mimmums:  U.  S.  Navy  46817,  Dec.  2,  1918,  for  hot-rolled  aluminum  bronze,  Cu  85  to  87,  Al  7 
to  9,  Fe  2.5  to  4.5.  Specification  values  under  P-limit  are  for  yield  point. 

f  Two  and  six  tenths  per  cent  increase  in  strength  up  to  762  mm  (30  hi.)  width. 

**  Compressive  P-limit:  cast,  14.1  kg/mm2  or  20,000  lb/in2  with  11.4  per  cent  set  at  70  kg/mm2  or  100,000  lb/in* 

ft  Compressive  P-limit:  cast,  12.7  to  14.1  kg/mm2  or  18,000  to  20,000  lb/in2  with  13  to  15  percent  set  at  700  kg/mm* 
or  100,000  lb/in2  load. 

tt  Modulus  of  elasticity  14,800  kg/mm2  or  21,150,000  lb/in2 

§§  Compressive  P-limit  8.4  kg/mm2  or  12,000  lb/in2  with  36  per  cent  set  for  70.3  kg/mm2,  or  100,000  lb/in2  load. 

II  II  High  values  are  after  Jean  Escard  "  L 'Aluminum  dans  L'Industrie,"  Paris,  1918.  Compressive  P-limit  13.5 
kg/mm2  or  19,200  lb/in2  with  13.5  per  cent  set  for  70.3  kg/mm2  or  100,000  lb/in2  load. 

SMITHSONIAN  TABLES. 


88 


TABLE  66. 

MECHANICAL   PROPERTIES- 
TABLE  66.  —  Miscellaneous  Metals  and  Alloys. 


Metal  or  alloy. 
Approx.  composition, 
per  cent. 

Condition. 

Density  [ 
or  weight.  1 

*j 
h 

Ultimate  1 
strength.  1 

P-limit. 

Ultimate  1 
strength.  1 

.5  g_ 

f'  £.B 
«?  ~, 

wST 

|l 

aS'o 

Hard- 
ness. 

Brinell  @ 

"too  ktr. 

l| 

£^ 

gm 
per 
cm» 

8.8 
8.9 
iQ-3 

17.2 

11.38 
11.40 

10.5 
1-7 

i? 

8.7 
8.9 

12.  1 
21.5 

10.5 

10.57 

16.6 
7-3 

lb. 

S 

Tension, 
kg/mm2 

Tension, 
lb/in2 

Per  cent. 

*  Cobalt,  Co  99.7  .  . 

Cast  

S5o 
556 
1203 

i°73 

710 
711 

6s"s 
1  06 

I0( 

5i8 
543 

555 

755 
1342 

655 
660 

1035 
456 

2.8 

i67** 

12.6 
21.2 

SS-i 

28.3 

22.8** 
28.1** 

21.  1 
I.I 

23.1 
26.0 
18.0 
26.0 
45-8 

102.0 
1.3 

2.; 
i. 

2. 

4-5 

21.0 

23. 
26.7 

29.9 
46.0 

64.7 

53-4 
109.0 

49-3 
73-8 
64.8 

112.5 

45-7 

56.2 

45-7 
27.0 
37-3 
24.6 
28.1 
36-0 
77.0 
91.0 

2.8 

3-7 
7.0 

IO.2 
9.1 

8.6 

IO.I 

4,000 

23,800  ** 
17,000 

30,100 
78,400 
40,300 

32,500** 
40,000  ** 

30,000 
i,  600 

33,ooo 
37,000 
25,000 
37,ooo 
65,100 

145,000 
i,78o 
3,300 
2,420 
3,130 
6,400 
30,000 
33,ooo 
38,000 
42,500 
65,000 
92,000 
76,000 

155,000 

70,000 
104,000 
92,200 

160,000 
65,000 

80,000 

65,000 
39,ooo 
53,ooo 
35,ooo 
40,000 
51,200 
109,500 
130,000 
4,000 
5,300 

10,000 

14,500 
13,000 
12,200 

14,300 

25.0 

5-7 

II.O 
II.O 

35-0 

18.0 
31-3 
46.3 

25.0 
32.0 

15-0 

18.0 
50.0 

35-0 

1.9 
1.6 

41.0 

8.0 

6.1 

20.0 
61.7 
7O.2 

1-5 
1-3 

81.0 

41.0 

121 
48 

8 

76 
83 

59 
14 

20 

2 

35 

21 

27 

24 

13 

32 

8 

Gold,  Au  100   

/Cast  
\  Drawn  hard  
Drawn  hard  

Drawn  hard  
Cast  
{  Rolled  hard.... 
j  Drawn  soft  .... 
[  Drawn  hard  .... 
Cast 

Copper,  Au  go,  Cu  10  
Copper,  Silver,  Au  58,  Cu 
30  Ag  12 

,ead,  Pbf  

(Comm'c'l.)  

Antimony  iPbgs.5,Sb4.5 
Magnesium,  Mg. 

<  Drawn  hard  

Cast  
Wrought,  aim.  .  . 
Wrought,      com 
Rolled  hard,    " 
Rolled  ann.     ' 
Drawn  hard,  D  = 
1.65      mm     or 
0.065  in  

/Cast.  . 

Nickel,  Ni  98.5  
Ni  99.95.  . 

Nig8  <; 

Ni     . 

ft. 

Ni  

Copper,  iron,  manganese 
or  Monel  metal: 

Ni  67,  Cu  28,  Fe  3,  Mn  2  . 
Ni  66,  Cu  28,  Fe  3-S,  Mn 

2-5 

Ni7i,Cu27,  Fe2§  
46  Mia  ||  

\Rolled 

Wrought  

Drawn  hard  
Cast,  minimums. 
Rolled,  min.,  rods 
\      and  bars  11..  .. 
I  Rolled,         mini- 
<      mum,       sheets 
[      and  plates.  .  .    . 
Drawn  hard.  .  .   . 
Drawn  hard  ...    . 
Drawn  ann  
Cast  

46  Mybll 

II 

Palladium,  Pd 

Platinum,  Pt  

Silver,  Ag  100  

Copper,  Ag  75,  Cu  25.... 
Tantalum,  Ta  

Tin,  Sn  99.8ft  

Antimony,  Copper,  Zinc 
(Britannia  Metal): 
Sn8i,Sbi6,  Cua.Zni. 
Zinc,  Aluminum,  etc. 
(aluminum  solder): 
Sn63,Zni8,  Al  13,  Cu 
3,  Sb  2,  Pb  i  
Sn62,  Znis,Alu,Pb 
8,  Cu3,Sbi  
Zinc,  aluminum: 
Sn  86,  Zn  9,  Al  5  
Aluminum,     zinc,     cad- 
mium: 
Sn  78,  Al  9,  Zn  8,  Cd  5  . 

Drawn  hard.  .  .   . 
Drawn  hard.  .  .    . 
Drawn  hard.  .  .    . 
f  Cast 

Rolled  
[  Drawn  hard  

Cast 

Cast  
Cast,  chill  

Cast,  chill  

Antimony:  Modulus  of  Elasticity  7960  kg/mm2  or  11,320,000  lb/in2  (Bridgman). 

*Compressive  strength:   cast  and  annealed,  86.0  kg/mm2  or  122,000  lb/in2. 

Comm'c'l.  comp.,  C  0.06,  cast,  tensile,  ultimate,  42.8  kg/mm2  or  61,000  lb/in2,  with  20  per  cent  elongation  in  50.8 
or  2  in.    Compression,  ultimate  123.0  kg/mm2  or  175,000  lb/in2 

Stellite,  Co  59.5,  Mo  22.5,  Cr  10.8,  Fe  3.1,  Mn  2.0,  Co.g,  Si  0.8.     Brinell  hardness  512  at  3000  kg. 

t  Modulus  of  elasticity,  cast  or  rolled,  492  kg/mm2  or  700,000  lb/in2;  drawn  hard  703  kg/mm2  or  1,000,000  lb/in2 

I  For  compressive  test  data  on  lead-base  babbitt  metal,  see  table  following  zinc. 

§  Modulus  of  elasticity  15,800  kg/mm2  or  22,500,000  lb/in2. 

||  Specification  values,  U.  S.  Navy,  Monel  metal,  Ni  min.  60,  Cu  min.  23,  Fe  max.  3.5,  Mn  max.  3.5,  C  +  Si  max. 
0.8,  Al  max.  0.5. 

1  Values  shown  are  subject  to  slight  modifications  dependent  on  shapes  and  thicknesses. 

**  Values  are  for  yield  point. 

tt  Compressive  strength:   cast,  4.5  kg/mm2  or  6,400  lb/in2 

Modulus  of  elasticity:  cast  av.  2,810  kg/mm2  or  4,000,000  lb/in2;  rolled  av.  401.0  kg/mm2  or  5,700,000  lb/in2 
SMITHSONIAN  TABLES. 


TABLE  67. 

MECHANICAL   PROPERTIES. 

TABLE  67.  —  Miscellaneous  Metals  and  Alloys. 

(a)    TUNGSTEN  AND  ZINC. 


Metal  or 
alloy 

Density 
or  weight. 

1 

+J-C 

! 

If 

-ji 

Sg 

|s 

Hardness. 

approx. 

Condition. 

fc 

p« 

&s 

W  ° 

«  0 

<§) 

comp. 
per  cent. 

gm 
per 
cm3 

Ib. 
per 
ft3 

Tension, 

kg/mm- 

Tension, 
lb/in2 

Per  cent 

P 

II 

(J  u 

(/)  * 

Ingot  sintered, 
D  =  5.7  mm  or  0.22  in. 

18.0 

1124 

12.7 

_ 

18,000 

0.0 

0.0 

_ 

Swaged  rod, 

D  =  0.7  mm  or  0.03  in. 

— 

— 

— 

151.0 

— 

215,000 

4.0 

28.0 

— 

— 

Drawn  hard, 

Tungsten, 

W99-2* 

I  D  =  0.029     mrn     or 

- 

- 

- 

415.0 

164.0 

— 

500,000 
233,5oo 

3-2 

65.0 

14.0 

— 

- 

Swaged  and  drawn  hot 
97.5%reductionf..  . 

Same   as    above    and 

equiaxed  at  2ooo°C 
in  Hzt 

118.0 

168,000 

0.0 

o.o 

_ 

Cast  

7-o 

437 

(I 

mpurities 

Pb,  Fe 

ind  Cd) 

Coarse  crystalline.  .  .  . 

— 

2.8  to 

— 

4,000  to 

— 

— 

42  to 

8  to 

Fine  crystalline  

— 

— 

— 

8.4 

— 

12,000 

— 

— 

48 

10 

Zinc,  §Zn: 

Rolled  (with  grain  or 
direction  of  rolling)  . 

_ 

_ 

2.0 

19.0 

2,900 

2  7  ,000 







_ 

Rolled  (across  grain  or 

direction  of  rolling)  . 

— 

— 

4-1 

25-3 

5,8oo 

36,000 

— 

— 

— 

— 

Drawn  hard  

M 

443 

7-o 

10,000 

*  Commercial  composition  for  incandescent  electric  lamp  filaments  containing  thoria  (ThCh)  approx.  0.75  per  cent 
after  Z  Jeffries  Am.  Inst.  Min.  Eng.  Bulletin  138,  June,  1918. 

f  After  Z  Jeffries  Am.  Inst.  Min.  Eng.  Bulletin  149,  May,  1919. 

t  Ordinary  annealing  treatment  makes  W  brittle,  and  severe  working,  below  recrystallization  or  equiaxing  tempera- 
ture, produces  ductility  W  rods  which  have  been  worked  and  recrystallized  are  stronger  than  sintered  rods.  The 
equiaxing  temperature  of  worked  tungsten,  with  a  s-min.  exposure,  varies  from  2200°  C  for  a  work  rod  with  24  per  cent 
reduction,  to  1350°  C  ior  a  fine  wire  with  100  per  cent  reduction.  Tungsten  wire,  D  =  0.635  rnm  or  0.025  in. 

§  Compression  on  cylinder  25.4  mm  (i  in.)  by  65.1  mm  (2.6  in.),  at  20  per  cent  deformation: 

For  spelter  (cast  zinc)  free  from  Cd,  av.  17.2  kg/mm2  or  24,500  lb/in2. 

For  spelter  with  Cd  0.26,  av.  27.4  kg/mm2  or  39,000  lb/in2.     (See  Proc.  A.  S.  T.  M.,  Vol.  13,  pi.  19.) 

Modulus  of  rupture  averages  twice  the  corresponding  tensile  strength. 

Shearing  strength:    rolled,  averages  13.6  kg/mm2  or  194,000  lb/in2. 

Modulus  of  elasticity:   cast,  7,750  kg/mm2  or  11,025,000  lb/in2 

Modulus  of  elasticity,  rolled,  8450  kg/mm2  or  12,000  ooo  lb/in2.    (Moore,  Bulletin  52,  Eng.  Exp.  Sta.  Univ.  of  111.) 

(6)   WHITE  METAL  BEARING  ALLOYS  (BABBITT  METAL). 

A.  S.  T.  M.  vol.  xviii,  I,  p.  491. 

Experimental  permanent  deformation  values  from  compression  tests  on  cylinders  31.8  mm  (ij  in.)  diam.  by  63.5  mm 
(2$  in.)  long,  tested  at  21°  C  (70°  F.)     (Set  readings  after  removing  loads.) 


Permanent  deformation  @  21°  C 

Hardness. 

Al- 
loy 
No 

per  cent. 

temp. 

Weight. 

@  454  kg 
=  i  ooo  Ib. 

@  2268  kg 
=  5000  Ib. 

@  4536  kg 
=  10,000  Ib. 

_-CJ 

.S  M 

JJO 

88 

Sn 

Sb 

Cu 

Pb 

C 

F. 

g/cm3 

lb./ft3 

mm 

in. 

mm 

in. 

mm 

in. 

«@ 

@@ 

Tin       Base. 

i 

91  o 

4.5 

4-5 

— 

440 

824 

7-34 

4S8 

0.000 

o.oooo 

0.025 

O.OOIO 

0.380 

0.0150 

28.6 

12.8 

2* 

89.0 

7-5 

3  •» 

— 

432 

808 

7-39 

46! 

.000 

.0000 

.038 

.0015 

•305 

.0120 

28.^ 

12.7 

3 

8.S.3 

8.3 

8.3 

— 

491 

916 

7.46 

465 

.025 

.0010 

.114 

.0045 

.180 

.0070 

34-4 

15.7 

4 

75-0 

12.0 

3-o 

IO.O 

360 

680 

7-52 

469 

.013 

.0005 

.064 

.0025 

.230 

.0090 

29.6 

12.8 

5 

65.0 

15-0 

2.0 

18.0 

350 

66  1 

7-75 

484 

.025 

.0010 

.076 

.0030 

.230 

.0000 

29.6 

n.8 

Lead  Base. 

6 

2O.O 

15.0 

i-5 

63.S 

337 

638 

9-33 

582 

.038 

.0015 

.127 

.0050 

•457 

.Ol8o 

24-3 

ii.  i 

7 

IO.O 

15-0 

75-0 

329 

625 

9-73 

607 

.025 

.0010 

.127 

.0050 

.583 

.0230 

24.1 

11.7 

8 

5-0 

15-0 

— 

80.0 

329 

625 

10.04 

627 

.051 

.0020 

.229 

.0090 

1-575 

.0620 

20.9 

10.3 

9 

5-o 

IO.O 

— 

85.0 

319 

616 

10.24 

640 

.102 

.0040 

•305 

.0120 

2.130 

.0840 

19-5 

8.6 

10 

2.O 

15.0 

— 

83.0 

325 

625 

10.07 

629 

.025 

.0010 

•254 

.0100 

3.910 

•1540 

17.0 

8.9 

ii 

— 

15.0 

— 

85.0 

325 

625 

10.28 

642 

.025 

.0010 

•  254 

.0100 

3.020 

.1190 

17.0 

9.9 

12 

IO.O 

90.0 

334 

634 

10.67 

666 

0.064 

0.0025 

0.432 

0.0170 

7.240 

0.2850 

14-3 

6.4 

*  U  S.  Navy  Spec.  46M2b  (Cu  3  to  4.5,  Sn  88  to  89.5,  Sb  7.0  to  8.0)  covers  manufacture  of  anti-friction-metal  castings. 
> Composition  W.) 

NOTE.  —  See  also  Brass,  Lead  (yellow  brass),  Brass,  Lead-Tin  (Red  Brass);  Bronze,  Phosphor,  etc.,  under  Copper 
alloys 

SMITHSONIAN  TABLES. 


TABLE  68. 

MECHANICAL   PROPERTIES. 
TABLE  68.  —  Cement  and  Concrete. 


(a)   CEMENT. 

CEMENT:    Specification  Values  (A.  S.  T.  M.  Cg  to  17,  Cio  to  09,  and  Cg  to  i6T). 
Minimum  strengths  based  on  tests  of  645  mm2  (i  in2)  cross  section  briquettes  for  tension, 

and  cylinders  50.8  mm  (2  in.)  diameter  by  ioi.6mm  (4  in.)  length  for  compression.    Mortar, 
composed  of  i  part  cement  to  3  parts  Ottawa  sand  by  volume;   specimens  kept  in  damp 
closet  for  first  24  hours  and  in  water  from  then  on  until  tested. 

Cement 

Specific 

Tension. 
Age, 

Compression. 

(1:3  mortar  tested). 

gravity. 

days.            .     . 
kg/mm2 

Ib/in* 

kg/mm2 

lb/in2 

Std.  Portland. 

3.10 

7              o.  16 

2OO 

0.85 

1,200 

White  Portland  

3-07 

28                .24 

300 

1.60 

2,000 

Natural  Av.  .  . 

2.85 

7                •  °3 

5° 



Natural  

28              0.09 

125 

— 



(b)    CEMENT  AND  CEMENT  MORTARS. 

CEMENT  AND 

CEMENT  MORTARS.  —  Bureau  of  Standards  Experimental  Values.     Corn- 

pressive  Strengths  of  Portland  cement  mortars  of  uniform  plastic  consistency.    Data  from 
tests  on  50.8  mm  (2  in.)  cubes  stored  in  water.    Sand:  Potomac  River,  representative  con- 

crete sand. 

Cement. 

Sand. 

Water, 

Age, 
days. 

Compressive  strength. 

Proportions  by  volume. 

per  cent. 

kg/mm2 

Ib/itf 

I 

0 

30.0 

7 

4.  2O 

5,970 

28 

6.40 

9,120 

I 

i 

16.0 

7 

3.10 

4,440 

28 

4-75 

6,750 

I 

2 

13-6 

7 

2 

•05 

2,900 

28 

3.10 

4,440 

I 

3 

13-9 

7 

I 

•25 

1,780 

28 

2 

•05 

2,890 

I 

9 

15  .  i 

7 

O.  10 

1  20 

28 

c 

•15 

200 

NOTE.  —  (From  Bureau  of  Standards  Tech.  Paper  58.)  Neat  cement  briquettes  mixed  at 
plastic  consistency  (water  21  per  cent)  show  0.52  kg/mm2  or  740  lb/in2  tensile  strength  at  28 
days'  age; 

i  Cement:  3  Ottawa  sand-mortar  briquettes,  mixed  at  plastic  consistency  (water  9  per 
cent)  show  0.28  kg/mm2  or  400  lb/in2  tensile  strength  at  28  days'  age. 

SMITHSONIAN  TABLES. 


TABLE  68  (continued). 

MECHANICAL   PROPERTIES. 

(c)   CONCRETE  . 


CONCRETE:  Compressive  strengths.  Experimental  values  for  various  mixtures.  Results  compiled  by  Joint 
Committee  on  Concrete  and  Reinforced  Concrete.  Final  Report  adopted  by  the  Committee  July  i,  1916. 
Data  are  based  on  tests  of  cylinders  203.2  mm  (8  in.)  diameter  and  406.4  mm  (16  in.)  long  at  28  days  age. 
American  Standard  Concrete  Compressive  Strengths. 


Aggregate. 


Units. 


Mix. 


1:4* 


1:6 


Granite,  trap  rock 


Gravel,  hard  limestone  and 
hard  sandstone . . 


Soft     limestone     and    soft 
sandstone.  . 


Cinders. 


kg/mm2 
lb/in2 

kg/mm2 
lb/in2 

kg/mm2 
lb/in2 
kg/mm2 
lb/in2 


2-3 


2.1 

3000 


2  2OO 

0.6 
800 


2.O 
2800 

1.8 
2500 


1800 


700 


2  2OO 

1-4 
200O 

I.I 

1500 

0.4 

600 


1800 

i.i 
1600 

0.8 

1 200 

0.4 

500 


i  .o 
1400 

0.9 
1300 

0.7 

1000 

o-3 
400 


NOTE.  —  Mix  shows  ratio  of  cement  (Portland)  to  combined  volume  of  fine  and  coarse  aggregate  (latter  as 
shown). 

Committee  recommends  certain  fractions  of  tabular  values  as  safe  working  stresses  in  reinforced  concrete 
design,  which  may  be  summarized  as  follows: 
Bearing,  35  per  cent  of  Compressive  strength; 

Compression,  extreme  fiber,  32.5  per  cent  of  Compressive  strength; 

Vertical  shearing  stress  2  to  6  per  cent  of  Compressive  strength,  depending  on  reinforcing; 
Bond  stress,  4  and  5  per  cent  of  Compressive  strength,  for  plain  and  deformed  bars,  respectively. 
Modulus  of  Elasticity  to  be  assumed  as  follows: 


For  concrete  with  strength. 


Assume  modulus  of  elasticity. 


kg/mm2 


lb/in2 


kg/mm2 


lb/in8 


up  to  0.6 
0.6  to  1.5 

1-5  tO  2  . 0 

over  2 .  o 


up  to    800 

8OO  tO  2200 
2200  tO  2900 

over  2900 


530 
1400 


2IOO 


750,000 
2,OOO,OOO 
2,500,000 

3,000,000 


(See  Joint  Committee  Report,  Proc.  A.  S.  T.  M.  v.  XVII,  1917,  p.  201.) 

EDITOR'S  NOTE.  —  The  values  shown  in  the  table  above  are  probably  fair  values  for  the  Compressive  strengths 
of  concretes  made  with  average  commercial  material,  although  higher  results  are  usually  obtained  in  laboratory 
tests  of  specimens  with  high  grade  aggregates.  Observed  values  on  1:2:4  gravel  concrete  show  moduli  of 
elasticity  up  to  3160  kg/mm2  or  4,500,000  lb/in2  and  Compressive  strengths  to  4.2  kg/mm2  or  6000  lb/in2 

Tensile  strengths  average  10  per  cent  of  values  shown  from  Compressive  strengths. 

Shearing  strengths  average  from  75  to  125  per  cent  of  the  Compressive  strengths;  the  larger  percentage 
representing  the  shear  of  the  leaner  mixtures  (for  direct  shear,  Hatt  gives  60  to  80  per  cent  of  crushing  strength) . 

Compressive  strengths  of  natural  cement  concrete  average  from  30  to  40  per  cent  of  that  of  Portland 
cement  concrete  of  the  same  proportioned  mix. 

Transverse  strength:  modulus  of  rupture  of  i :  2\  :  5  concrete  at  i  and  2  months, equal  to  one  sixth  crushing 
strength  at  same  age  (Hatt). 

Weight  of  granite,  gravel  and  limestone,  1:2:4  concretes  averages  about  2.33  g/cm3  or  145  lb/ft3;  that  of 
cinder  concrete  of  same  mix  is  about  1.85  g/cm3  or  115  lb/ft3 

Concrete,  1:2:4  Mix,  Compressive  Strengths  at  Various  Ages. 

Experimental  Values:  one  part  cement,  two  parts  Ohio  River  sand  and  four  parts  of  coarse  aggregate  as 
shown.  Compressive  tests  made  on  203.2  mm  (8  in.)  diameter  cylinders,  406.4  mm  (16  in.)  long.  (After  Pitts- 
burgh Testing  Laboratory  Results.  See  Rwy  Age,  vol.  64,  Jan.  18,  1918,  pp.  165-166.) 


Coarse  aggregate. 


Unit. 


Age. 


14  days. 


30  days. 


60  days. 


180  days. 


Gravel 

Limestone 

Trap  rock 

Granite 

Slag  No.  i 

SlasNo.  2.. 


kg/mm2 

lb/in2 

kg/mm2 

lb/in2 

kg/mm2 

lb/in2 

kg/mm2 

lb/in2 

kg/mm2 

lb/in2 

kg/mm2 

lb/in2 


i-3S 
1921 
1.24 
1758 
1-45 
2063 
1.49 

2122 

*-75 

2484 

i-37 
1941 


1.61 
2294 

i-53 
2174 
1.67 
2386 
1.61 
2292 
2.16 

3075 
1.78 

2525 


2.06 
2925 
2-35 
3343 
2.36 


2.14 
3043 
2-37 
3365 
2.06 
2930 


2.67 
3798 
3-n 
4426 

3-39 
4819 
2.92 


3-38 
4803 
2.64 
3753 


NOTE.  —  Maximum  and  minimum  test  results  varied  about  5  percent  above  or  below  average  values  shown  above. 
SMITHSONIAN  TABLES. 


92 


TABLE  69. 

MECHANICAL   PROPERTIES. 
TABLE  69.  —  Stone  and  Clay  Products. 


(a)    STRENGTH  AND  STIFFNESS  OF  AMERICAN  BUILDING  STONES.* 

Stone. 

Weight, 

average. 

Compression. 
Ultimate  strength. 

Flexure. 
Modulus  of 
rupture. 

Shear. 
Ultimate 
strength. 

Flexure, 
modulus  of  elasticity. 

Average. 

si 

Average. 

to  § 

II 

30 
50 
IOO 

55 

Average. 

Range 
per  cent. 

Average. 

Range 
per  cent. 

! 

* 

1 

1 

<& 
1 

H 

«& 

cg 
1 

I 

^ 

M 

I.  60 
O.QO 
I.OO 
I.  2O 

{ 

.c 

1 
I 

SO 
M 

lb/in» 

Granite.  .  . 
Marble.  .  . 
Limestone 
Sandstone. 

2.6 

2-7 
2.6 

2.2 

165 
170 
1  60 
135 

14.20 
8.85 
6.30 
8.80 

20,2OO 
12,600 
9,000 
12,500 

25 
25 

95 
5° 

!-i5 
1.05 
0.85 
1.05 

1600 
ISOO 
I20O 
1500 

2300 
I3OO 
1400 
I7OO 

20 
25 
45 
45 

5300 
5750 
5900 
2300 

7,500,000 
8,200,000 
8,400,000 
3,300,000 

25 
50 
65 
IOO 

*  Values  based  on  tests  of  American  building  stones  from  upwards  of  twenty-five  localities, 
made  at  Watertown  (Mass.)  Arsenal  (Moore,  p.  184).    Each  value  shown  under  "Range" 
is  one  half  the  difference  between  maximum  and  minimum  locality  averages  expressed  as 
a  percentage  of  the  average  for  the  stone. 

(b)   STRENGTH  AND  STIFFNESS  OF  BAVARIAN  BUILDING  STONE.* 

Stone. 

Weight, 
average. 

Compression. 
Ultimate  strength. 

Flexure. 
Modulus  of 
rupture. 

Shear. 
Ultimate 
Strength.! 

Flexure. 
Modulus  of 
elasticity. 

Average. 

Range 
per  cent. 

Average. 

8>g 

u  o 
*l 

5 

45 

55 

Average. 

|| 
g" 

P4    0 

a 

Average. 

-|! 

r/  S 
& 

§ 

M 

1 

1 

fco 
J4 

"h 

> 

5 

*h 

I 

"is 

ja 

1C 

M 

I.OO 

0-45 
0.6O 
0.50 

.Is 

jQ 

kg/mm2 

Ib/irf 

Granite.  . 
Marble  t 
Limestone 
Sandstone 

2.66 
2.16 
2.48 
2.30 

165 
135 
155 

145 

13.70 
5.60 

8.10 
8.10 

19,500 

8,000 
11,500 
11,500 

5 
15 

5 
75 

0.90 
0.30 
I.  10 

o-45 

1300 
450 

1550 
650 

1420 
62O 
870 
680 

o 

50 

20 

35 

1600 
3450 
2350 
2500 

2,300,000 
4,900,000 
3,350,000 
3,550,000 

30 
90 

35 

*  Values  based  on  careful  tests  by  Bauschinger,  "  Communications,"  Vol.  10. 
t  Shearing  strength  determined  perpendicular  to  bed  of  stone, 
j  Values  are  for  Jurassic  limestone. 

GENERAL  NOTES. —  i.  Later  transverse  strength  (flexure)  tests  on  Wisconsin  building  stones 
(Johnson's  "Materials  of  Construction,"  1918  ed.,  p.  255)  show  moduli  of  rupture  as  follows: 
Granite,  1.90  to  2.75  kg/mm2  or  2710  to  3910  lb/in2;  limestone,  0.80  to  3.30  kg/mm2  or  1160  to 
4660  lb/in2;  sandstone,  0.25  to  0.95  kg/mm2  or  360  to  1320  lb/in2. 

2.  Good  slate  has  a  modulus  of  rupture  of  4.90  kg/mm2  or  7000  lb/in2  (loc.  cit.,  p.  257). 


SMITHSONIAN  TABLES. 


TABLE  69  (continued). 

MECHANICAL   PROPERTIES- 

TABLE  69.  —  Stone  and  Clay  Products. 


93 


(c)   STRENGTHS  OF  AMERICAN  BUILDING  BRICKS.* 

Brick  —  description. 

Absorption 
average 
per  cent. 

Compression. 
Min.  ult.  strength. 

Flexure. 
Min.  modulus  rupture. 

kg/mm2 

Vb/vf 

kg/mm2 

Ib/in* 

Class  A  (Vitrified)   

5 
12 

18 

3-50 
2-45 
1  .40 
1.05 

5000 
3Soo 

2OOO 
I5OO 

0.65 
0.40 
0.30 
O.  2O 

QOO 
600 
400 
300 

Class  B  (Hard  burned)  
Class  C  (Common  firsts)  
Class  D  (Common)  

*•  After  A.  S.  T.  M.  Committee  C~3,  Report  1913,  and  University  laboratories'  tests 
for  Committee  C~3  (Johnson,  p.  281). 


(d)   STRENGTH  IN  COMPRESSION  OF  BRICK  PIERS  AND  OF  TERRA-COTTA  BLOCK  PIERS. 
Tabular  values  are  based  on  test  data  from  Watertown  Arsenal,  Cornell  University, 
U.  S.  Bureau  of  Standards,  and  University  of  111.  (Moore,  p.  185). 


Brick  or  block  used. 

Mortar. 

Compression.* 
Av.  ult.  strength. 

kg/mm2 

lb/in2 

Vitrified  brick  
Pressed  (face)  brick  
Pressed  (face)  brick. 

i  part  P.f  cement  :  3  parts  sand  .... 
i  part  P.  cement  :  3  parts  sand  
i  part  lime  :  3  parts  sand  
i  part  P.  cement  :  3  parts  sand  
i  part  lime  :  3  parts  sand  

i-95 
1.40 

I.  00 

0.70 
0.50 

2.  IO 

2800 
200O 
1400 
1000 
700 
3000 

Common  brick 

Common  brick  

Terra-cotta  brick.  .  . 

i  part  P.  cement  :  3  parts  sand  

*  Building  ordinances  of  American  cities  specify  allowable  working  stresses  in  com- 
pression over  bearing  area  of  12.5  per  cent  (vitrified  brick)  to  17.5  percent  (common 
brick)  of  corresponding  ultimate  compressive  strength  shown  in  table. 

t  P.  denotes  Portland. 


(e)   STRENGTH  OF  COMPRESSION  OF  VARIOUS  BRICKS. 

Reasonable  minimum  average  compressive  strengths  for  other  types  of  brick  than 
building  brick  are  noted  by  Johnson,  "Materials  of  Construction,"  pp.  289  ff.,  as  follows: 


Brick. 

kg/mm2 

lb/in2 

sand-lime  .-    . 

2    IO 

3OOO 

sand-lime  (German)  .     .    . 

I     ^"? 

2180  (av   255  tests) 

paving  

5  60 

8000 

acid-refractor  v  

o  70 

IOOO 

silica-refractory  .  .    . 

I    AO 

2OOO 

The  specific  gravity  of  brick  ranges  from  1.9  to  2.6  (corresponding  to  120  to  160  lb/ft3). 

Building  tile:  hollow  clay  blocks  of  good  quality,  —  minimum  compressive  strength: 
0.70  kg/mm2  or  1000  lb/in2.  Tests  made  for  A.  S.  T.  M.  Committee  C-io  (A.  S.  T.  M. 
Proc.  XVII,  I,  p.  334)  show  compressive  strengths  ranging  from  0.45  to  8.70  kg/mm2 
or  640  to  12,360  lb/in2  of  net  section,  corresponding  to  0.05  to  4.20  kg/mm2  or  95  to  6000 
lb/in2  of  gross  section.  Recommended  safe  loads  (Marks,  "Mechanical  Engineers' 
Handbook,"  p.  625)  for  effective  bearing  parts  of  hollow  tile:  hard  fire-clay  tiles 
0.06  kg/mm2  or  80  lb./in2;  ordinary  clay  tiles  0.04  kg/mm2  or  60  lb/in2;  porous  terra- 
cotta tiles  0.03  kg/mm2  or  40  lb/in.2  The  specific  gravity  of  tile  ranges  from  1.9  to  2.5 
corresponding  to  a  weight  of  120  to  155  lb/ft3. 


SMITHSONIAN  TABLES. 


94 


TABLE  70. 

MECHANICAL  PROPERTIES. 
TABLE  70.  —  Rubber  and  Leather. 

(a)    RTJBBER,  —  SHEET.* 


Ultimate  strength. 

Ult.  elongation. 

Set| 

Grade. 

Longitudinal.f 

Transverse. 

Longit. 

Transv. 

Longit. 

Transv. 

kg/mm2 

lb/in* 

kg/mm2 

lb/in* 

per  cent. 

per  cent. 

I 

I.Q2 

2730 

l.8l 

2575 

630 

640 

II  .  2 

7-3 

2 

i-45 

2070 

1-43 

2030 

640 

670 

6.0 

5-0 

3 

0.84 

1200 

0.89 

1260 

480 

555 

22.1 

I6.3 

4 

1.30 

1850 

I  .20 

1700 

410 

460 

34-o 

24.0 

5 

0.48 

690 

0.36 

5io 

320 

280 

27-5 

25.0 

6 

0.62 

880 

0.48 

690 

315 

3i5 

34-3 

25-9 

*  Data  from  Bureau  of  Standards  Circular  38. 

f  Longitudinal  indicates  direction  of  rolling  through  the  calendar. 

t  Set  measured  after  300  per  cent  elongation  for  i  minute  with  i  minute  rest. 

The  specific  gravity  of  rubber  averages  from  0.95  to  1.25,  corresponding  to  an  average  weight 
of  60  to  80  lb/ft3. 

Four-ply  rubber  belts  show  an  average  ultimate  tensile  strength  of  0.63  to  0.65  kg/mm2  or 
890  to  930  lb./in2  (Benjamin),  and  a  working  tensile  stress  of  0.07  to  o.n  kg/mm2  or  100  to  150 
lb./in2  is  recommended  (Bach). 


(6)   LEATHER,  —  BELTING. 
Oak  tanned  leather  from  the  center  or  back  of  the  hide: 

Minimum  tensile  strengths  of  belts  f  single  2.8  kg/mm2  or  4000  lb./in2 
(Marks,  p.  622)  \  double  2.5  kg/mm2  or  3600  lb./in2 

Maximum  elongation  for  one  hour  application  of  J  single  13.5  per  cent 
1.6  kg/mm2  or  2250  lb./in2  stress  \  double  12.5  percent. 

Modulus  of  elasticity  of  leather  varies  from  an  average  value  of  12.5  kg/mm2  or  17,800  lb/in2 
(new)  to  22.5  kg/mm2  or  32,000  lb./in2  (old). 

Chrome  leather  has  a  tensile  strength  of  6.0  to  9.1  kg/mm2  or  8500  to  12,900  lb/in2. 

The  specific  gravity  of  leather  varies  from  0.86  to  1.02,  corresponding  to  a  weight  of  53.6 
to  63.6  lb./ft3. 


SMITHSONIAN  TABLES. 


TABLE  71. 
MECHANICAL    PROPERTIES. 


95 


TABLE  71.  —  Manila  Rope. 

Manila  Rope,  Weight  and  Strength  —  Specification  Values.  From  U.  S.  Government  Stand- 
ard Specifications  adopted  April  4,  1918. 

Rope  to  be  made  of  manila  or  Abaca  fiber  with  no  fiber  of  grade  lower  than  U.  S.  Govern- 
ment Grade  I,  to  be  three-strand,*  medium-laid,  with  maximum  weights  and  minimum  strengths 
shown  in  the  table  below,  lubricant  content  to  be  not  less  than  8  nor  more  than  12  per  cent  of 
the  weight  of  the  rope  as  sold. 


Approximate 
diameter. 

Circumference. 

Maximum  net  weight. 

Minimum  breaking 
strength. 

mm 

in. 

mm 

in. 

kg/m 

Ib/ft. 

kg 

Ib. 

6-3 

i 

4 

19.1 

1 

0.029 

0.0196 

320 

700 

7-9 

A 

25-4 

I 

0.044 

0.0286 

540 

1,2.00 

9-5 

t 

28.6 

li 

0.061 

o  .  0408 

660 

i,45o 

ii.  i 

A 

3i-8 

li- 

0.080 

0.0539 

790 

i,750 

ii.  9 

If 

34-9 

it 

0.095 

0.0637 

950 

2,100 

12.7 

i 

38-1 

i* 

o.  109 

0-0735 

I,  IIO 

2,450 

14-3 

A 

44-5 

T3 

*  4 

0.153 

o.  1029 

1,430 

3,15° 

15-9 

f 

50.8 

2 

0-195 

0.1307 

1,810 

4,000 

19.  i 

.3 

4 

57-2 

2| 

0.241 

0.1617 

2,220 

4,900 

20.  6 

H 

63-5 

2* 

0.284 

o.  1911 

2,680 

5,900 

22.2 

7 
8 

69.9 

af 

0.328 

0.2205 

3,i7o 

7,000 

2S-4 

I 

76.2 

3 

0-394 

o  .  2645 

3,720 

8,200 

27.0 

*A 

82.6 

3* 

0-459 

o  .  3087 

4,3io 

9,5oo 

28.6 

ii 

88.9 

3* 

0-525 

0.3528 

4,990 

11,000 

31-8 

ii 

95-2 

3f 

0.612 

0.4115 

5,670 

12,500 

33-3 

IT5« 

101  .6 

4 

0.700 

0.4703 

6,440 

14,200 

34-9 

it 

108.0 

4t 

0.787 

0.5290 

7,260 

16,000 

38-1 

ii 

H4-3 

4l 

0-875 

0.5879 

7,940 

17,500 

39-4 

iA 

120.7 

44 

0.984 

0.6615 

8,840 

19,500 

41.2 

if 

127.0 

5 

1.094 

0.7348 

9,750 

21,500 

44-5 

if 

140.0 

5* 

1.312 

0.8818 

n,55o 

25,500 

50.8 

2 

152-4 

6 

I-576 

1.059 

13,610 

30,000 

52.4 

2& 

165.1 

6* 

1.823 

1.225 

15,420 

34,000 

57-2 

a* 

177-8 

7 

2.144 

1.441 

17,460 

38,500 

63.5 

2* 

190  5 

?i 

2.450 

1.646 

19,730 

43,5oo 

66.7 

2f 

203.2 

6 

2-799 

1.881 

22,220 

49,000 

73-o 

2f 

215-9 

8* 

3-I36 

2.107 

24,940 

55,ooo 

76.2 

3 

228.6 

9 

3-543 

2.381 

27,670 

61,000 

79-4 

si 

241-3 

9i 

3-936 

2.645 

30,390 

67,000 

82.5 

si 

254.0 

10 

4-375 

2.940 

33,no 

73,ooo 

*  Four-strand,  medium-laid  rope  when  ordered  may  run  up  to  7  %  heavier  than  three-strand 
rope  of  the  same  size,  and  must  show  95  %  of  the  strength  required  for  three-strand  rope  of  the 
same  size. 

SMITHSONIAN  TABLES 


MECHANICAL  PROPERTIES.    TABLE  72.  —  Hardwoods  Grown  in  U.  S.  (Metric  Units). 


Common  and  botanical 
name. 

Specific 
gravity, 
oven-dry, 
based  on 

Static  bending. 

Impact  bend- 
ing. 

Compression. 

Shear 

Ten- 
sion. 

Hardness. 

1 

1? 

Modulus  of 
elasticity,  kg/mm2 

5 

04 

II 

rt  3 

•si 
fi 

S| 

Parallel 
to  grain. 

Perpendicular  to 
grain  P-limit, 
kg/mm2 

8 

"3  ^ 

0 

12-s 

Load  to 
i  imbed 
11.3  mm 
d.  ball 

vol. 
when 
green. 

vol. 
oven- 
dry. 

*! 
J 

<i« 

II 

2 

P- 

limit 

Ulti- 
mate. 

111 

g  M 
PH 

end 
kg 

side 
kg 

kg/  mm2 

1 

10 

11 

12 

13 

14 

15 

16 

17 

I  Alder,  red 

0-37 
0.46 
0.52 
0.58 
0.36 
0.33 
0-54 
0.47 
0.54 
0.36 
0.47 
0.40 
0-37 
0.44 
0.64 
0.58 
0.44 
o.  62 
0.46 
0.44 
0.60 
o.  64 
0.50 
0.62 
0.66 
0.60 
0.46 
0.44 
0.56 
0.70 
0.56 
0.60 
0.64 
0-37 
0.46 
o.Si 
0-34 

0.43 
0-53 
0.60 
0.71 
0.42 
0.40 
0.66 
0.60 
0.66 
0.40 
0-53 
0.46 
0-43 
0.52 
0.80 
0.66 
0-54 
0.80 
0.52 
0.53 
0.69 

0.61 
0.74 
0.71 
0.67 
0-53 
0.51 
0.66 
0.84 
0.65 
0.71 
0.78 
0.42 
0-54 
0.56 
0.41 

2.65 

1.85 
3-45 
4-30 
2.05 

I.  00 

3-iS 
2.05 
3-25 
2.05 
2-95 

2.20 
2.05 
2-95 
3-4° 
3-25 
2-55 

5-35 
2-95 
2.60 
3.6S 
4-15 
2.40 
4.10 
6.  20 
3-95 
2.  55 

2.20 
3-50 

4-45 
2.60 
3-30 
3-95 
2.25 
2.30 
3-80 
1-25 

4-55 
4.20 
6.40 
7.60 
3-75 
3-50 
5.8o 
4.10 
6.05 
3-8o 
5.65 
3-95 
3-75 

5-20 
6.20 

6.70 

4.85 
7.85 

5-15 

4.80 

6.90 

7.75 

4-55 
5-90 
9.70 
7.20 
4-80 
4.10 
6.40 
7-45 
5-40 
5.85 
7-os 
3-95 
4.60 
6.70 
2-75 

830 
720 
950 
1150 
590 
725 
875 
710 
1080 
680 
920 
655 
710 

IIOO 

830 

840 
725 
1430 

740 

810 
960 
1105 
630 
650 
1300 
910 
780 
660 
1040 
945 
910 
880 
965 
850 
745 

1000 

395 

5.60 

5-io 
8.25 
9.70 
4-85 
4-35 
7-30 
5-50 
8.25 
5-iS 
7.20 
5-55 
5-05 
6.55 
5.00 
7-75 
5-70 

10.00 

6.30 

7.05' 
8.65 

10.10 

6.25 
7.20 
12.90 
8.30 

6.20 

4.80 

8.50 
7.90 
7-30 

7-55 
8.50 
5-65 

6.20 

8.40 
3.60 

0.56 
0.81 
0.91 
1.19 
0.71 
0.43 

1.02 
I.  14 
1.02 

0.61 

0.84 

0.61 
0-53 
0.76 
1.47 
1.27 
0.86 

1.02 
O.76 
0.84 

1-35 
1.88 
1.30 
0.81 

I.  12 
1.20 

1-37 
0.74 
0.91 

1.20 
1.04 
1.07 
1.04 
0-43 
0.84 
0.94 
0.91 

1.85 
i.i5 
2.30 
2.70 

I.  10 
1.20 
I.  80 
1.20 
I.  QO 
1.40 
2.10 

i-45 
1.25 
1-95 

2.0O 
I.  60 

3-4° 
1-95 
1.70 
2.15 
2.40 
1.40 

4.40 
2-35 
1-55 
1-35 

2.20 
2.85 
1.65 
2.10 
2.15 
1.40 
1.70 
2-55 
0.70 

2.  10 
I.  60 
2.70 
2.90 
1-50 

1-55 
2.30 
i-SS 
2.40 
1.70 
2.50 
i-75 
i.  60 

2.20 
2-55 
2.70 
2.OO 
3-7° 
2.40 

1-95 

2.80 
3.20 
1.85 
3-oo 
4.80 
3.10 
1.90 
1-75 
2.80 
3-30 
2.25 
2.50 
2-95 
i.  80 

2.OO 
3-05 
1.05 

0.22 
0.31 

0-57 
0.56 
0.14 
0.15 
0.43 

O.2I 

0.32 

0.19 

0.31 
0.27 
0.17 

0.29 

0.73 
0.53 
0.28 
0.72 
0.42 
0.32 

o.63 
0.70 
0-43 
0.78 

I.  01 
I.  00 

0.40 
0.32 
0.53 
1.04 
0.51 
0.59 
0.78 

0.22 
0.32 
0.42 
0.15 

0.54 
0.61 
0.89 
i.i3 
0.44 
0-43 
0.85 
0.56 
0.78 
0-53 
0.80 
0.56 
0.48 
0.70 
1.07 
0.89 
0.65 
1.09 
0.84 
0-75 
1.04 
0-93 
0.80 
1.18 
1.24 
1.17 
0-73 
0.74 
o  97 

1.20 
0.79 

0.88 
1.03 
0.56 
0.71 
0.86 
0.44 

0.27 
0.35 
0.44 
0.56 
0.13 

0.  20 
0.56 
0.27 

0.34 
0.30 
0.40 
0.30 
0.29 
0.31 

0.47 
0.39 
0.45 
0.42 
0.36 
0.48 

0-43 

0-54 
0.66 
0-43 
0.39 
0-54 
0.63 
0.52 
0-54 
0.54 
0.32 
0.44 
0-43 
0.30 

250 
270 
455 
515 
1  20 
125 
430 
1  80 
370 
185 
340 
240 
175 
270 
640 
445 
275 
595 
365 
285 
575 

390 
635 
740 
655 
355 
305 
455 
720 
465 
5io 
565 
190 
320 
435 
160 

200 
250 
401 
490 
145 
US 
370 
220 
340 
175 
300 
190 
155 
235 
640 
450 
250 
610 
320 
235 
595 

360 
590 
7i5 
630 
335 
270 
4IS 
715 
430 
480 
580 
155 
275 
410 
165 

(Alnus  oregona) 
Ash,  black  
(Fraxinus  nigra) 
Ash,  white  (forest  grown).  . 
(Fraxinus  americana) 
Ash,  white  (second  growth) 
(Fraxinus  americana) 
Aspen  .  . 

(Populus  tremuloidcs) 
Basswood  
(Tilia  americana) 
Beech  

(Fagus  atropunicea) 
Birch,  paper 

(Betula  papyri/era) 
Birch,  yellow 

(Betula  lutea) 
Butternut  

(Juglans  cinerea) 
Cherry,  black  
(Prunus  serotina) 
Chestnut 

(Castanea  dentata) 
Cottonwood 

(Populus  delioides) 
Cucumber  tree  
(Magnolia  acuminata) 
Dogwood  (flowering)  
(Cornus  florida) 
Elm,  cork. 

(Ulmus  racemosa) 
Elm,  white. 

(Ulmus  americana) 
Gum,  blue  
(Eucalyptus  globulus) 
Gum,  cotton  

(Nyssa  aquatica) 
Gam,  red 

(Liquidambar  styraciflua) 
Hickory  pecan  . 

(Uicoria  pecan) 
Hickory,  shagbark  
(Uicoria  mala) 
Holly,  American  

(Ilex  opaca) 
Laurel,  mountain  
(Kalmia  latijolia) 
Locust,  black.   . 

(Robinia  pseudacacia) 
Locust,  honey  

(Gledilsia  triacanlhos) 
Magnolia  (evergreen)  
(Magnolia  foeiida) 
l  Maple,  silver. 

1     (Acer  saccliarinum) 
Maple,  sugar  

(Acer  saccharum) 
Oak,  canyon  live  

(Quercus  chrysolepsi;) 
Oak,  red 

(Quercus  rubra) 
Oak,  white  

(Quercus  alba) 
Persimmon  

(Diospyros  virginiana) 
Poplar,  yellow  

(Liriodendron  tulipifera) 
Sycamore 

(Platanus  occidentalis) 
Walnut,  black  

I     (Juglans  nigra) 
Willow,  black  
1     (Salix  nigra) 

NOTE.  —  Results  of  tests  on  sixty-eight  species;  test  specimens,  small  clear  pieces,  50.8  by  50.8  mm  in  section,  762  mm  long 
for  bending;  others,  shorter.    Data  taken  from  Hulletin  556,  Forest  Service,  U.  S.  Dept.  of  Agriculture,  containing  data  on  130,000 

tests.      See  pages  87  and  99  for  explanation  of  columns 
SMITHSONIAN  TABLES 


MECHANICAL  PROPERTIES.    TABLE  73.  —  Conifers  Grown  in  U.  S.  (Metric  Units). 


97 


Common  and  botanical 
name. 

Specific 
gravity, 
oven-dry, 
based  on 

Static  bending. 

Impact  bend- 
ing. 

Compression, 

Shear 

Ten- 
sion. 

Hardness. 

1 

•M 

I 

A 

Modulus  of 
rupture,  kg/mm2 

Modulus  of 
elasticity,  kg/mm* 

| 

1 
1 

22.7  kg  hammer 
fall  for  failure  —  m. 

Parallel 
to  grain. 

Perpendicular  to 
grain  P-limit, 
kg/mm2 

11 

1* 

M 

Perpendicular  to 
grain  ult.  st. 
kg/mm2 

Load  to 
i  imbed 
11.3  mm 
d.  ball 

vol. 
when 
green. 

vol. 
oven- 
dry. 

P- 
limit. 

Ulti- 
mate. 

end 
kg 

side 
kg 

kg/mm2 

1 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

Cedar,  incense  

0.35 
0.41 
0.31 
o.  29 
0.41 
0.3? 
0.34 
Q-45 
o.  40 
0-37 
0-35 
o.3S 
0.38 
0.38 
o.43 
0.58 
0.50 
0.38 

0-55 
0.44 
0.47 
0.50 
0.36 
0.39 
0.38 

0.36 
0.48 
0-34 
0.49 
0.60 

0.36 
0.47 
0.34 
0.32 
0.47 
0.42 
0.41 
0.52 
0.44 
0.42 
0.41 
0.44 
0-44 
0-43 
0-59 
0.68 
0-59 
0.44 

0.64 
0.51 
0-54 
0.58 
0-39 
o.4S 
0.42 

0-39 
0.41 
o.37 
0.56 
0.67 

2-75 
2-75 
2.30 
1.85 
2.80 
2.74 

2.  10 
3-50 

2-55 
2.55 
2.40 
2-75 
2-95 
2.40 
3-25 
3-95 
3-io 

2.10 

J.80 

2.60 
2.60 
3-iS 
2.30 
2-45 

3-20 

2.40 
2.40 

2.10 
2-95 

4-55 

4-35 
4.80 
3-65 
2-95 
4.80 
4-45 
3-45 
5-50 
4-So 
4-30 
4.00 
4.20 
4.70 
4-30 
5-25 

"6.20 

5.30 

3.85 

6.  10 
4-So 
4.70 
S-6s 
3-75 
4.00 
3.65 

3-75 
4.00 
3.85 
5-os 
7.  10 

590 
1055 
670 
450 
835 
9i5 
675 

IIIO 

830 
915 
900 
795 
790 
835 
950 
1150 
970 
760 

1150 
970 

790 

1020 
685 

935 
710 

750 
830 
830 
875 
695 

5-15 
6.55 
S-05 
3-75 
5.6o 
5-50 
4-85 
6.60 
6.40 
5-70 
5-55 
5-05 
5-55 
5-50 
6.60 
7-95 
6.70 
5-05 

7.60 
5-35 
6.40 
7.90 
4.70 
5-35 
4-70 

4-55 
5-05 
5-05 
5-50 

9.  20 

0.43 
0.64 
0.43 
0.38 
0.61 
0.53 
0.41 
0.63 
0.51 
0.56 
0.51 
0.46 
0.51 
0.51 
0.61 
0.94 
0.81 
0.51 

0.86 
0.71 
0.74 
0.99 
0-43 
0.58 
0.48 

0.46 
0.46 
o.74 
0.71 

0.97 

2.00 
2.IO 

1-75 

1.  00 
2.20 
1.70 

i-55 
2.40 
i.  80 
1.90 
1.70 
1.85 
1.90 
i.  60 
2.30 
2.80 

2.OO 
1-50 

2.70 

1-75 
1.50 
2.50 
1.65 
1-95 
1-45 

1.65 
1.65 
i.  60 

2.20 
2.40 

2.  20 
2.30 
2.0O 
1.40 
2-45 
2.00 
1.70 
2.80 
2.10 
2.10 
1.90 

1-95 

2.30 
2.05 
2.70 
3-15 
2.50 

1.85 

3.10 

2.20 
2-IS 
2.70 
1.85 
2.15 

i-75 

1.90 
1-95 
1.85 
2-45 
3-25 

0.32 
0.27 

0.22 
O.20 
0-33 
0.22 
0.15 
0-37 
0-32 
O.24 
0.22 
0-31 
0.35 
0.25 
0-39 
0.41 
0-39 
0.22 

0.42 
0.25 
0.36 
0.34 
0.25 
0.21 
0.24 

0.22 
0.25 
0.23 
0.34 

0.73 

o.S3 
0.62 
0.51 
0.44 
0.58 
0.47 
0-43 
0.64 
0.62 
0-53 
0.49 
0.51 
0.62 
0-57 
0.65 
0.72 
0.63 
0.49 

0-75 
0-55 
0.67 
0.63 
0.50 
0.50 
0.48 

o.45 
0-54 
0.55 
o.65 
1.14 

0.  20 
0.17 
O.IS 
0.17 
O.20 
0.17 
0.23 
0.14 
0.25 

0.16 
0.13 
o.iS 
0.18 
0.18 
0.16 

0.2O 

o.  20 

0.15 

o.  20 

0.13 
0.25 
0.23 
0.19 
0.18 

0.20 

0.18 
0.15 
0.16 
0.18 
0.32 

260 
25S 
195 
145 
215 
165 
I3S 
230 
205 
190 
135 
175 
230 
245 
215 
260 
185 
145 

250 
165 

210 
220 
ISO 
ISO 
140 

135 
190 
195 

180 
610 

175 
220 
118 
104 
175 
140 
135 
2iS 
180 
165 

us 

ISO 
185 
195 
205 
285 
205 
ISO 

270 
iSS 

220 
25S 
US 

150 

145 

135 

160 
170 
170 

520 

(Libocedrus  decurrens) 
Cedar,  Port  Orford,  
(Chamaecyparis  lawsoniana) 
Cedar,  western  red  
(Thuja  plicata) 
Cedar,  white  

(Thuja  occidentalis) 

(Taxodium  distichum) 
Fir  amabilis             .... 

(Abies  amabilis') 
Fir,  balsam  

(Abies  balsamea) 
Fir,  Douglas  (i)  

(Pseudotsuga  taxifolia) 
Fir,  Douglas  (2)  
(Pseudotsuga  taxifolia) 

(Abies  grandis) 
Fir,  noble                  

(Abies  nobilis) 
Fir,  white  
(Abies  concolor) 
Hemlock,  eastern  

(Tsuga  canadensis) 
Hemlock  western 

(Tsuga  heterophylla) 
Larch,  western  
(Larix  occidentalis) 
Pine  Cuban  

(Pinus  heterophylla) 
Pine,  loblolly  

(Pinus  taeda) 

(Pinus  cantor  ta) 
Pine,  longleaf  

(Pinus  palustris) 

(Pinus  resinosa) 
Pine  pitch               

(Pinus  rigida) 
Pine,  shortleaf  
(Pinus  echinata) 
Pine,  sugar  

(Pinus  lambertiana) 
Pine  western  white 

(Pinus  nwnticola) 
Pine,  western  yellow  
(Pinus  ponderosa) 

(Pinus  strobus) 
Spruce  red       

(Picea  rubens) 
Spruce,  Sitka  

(Picea  sitchensis) 
Tamarack 

(Larix  laricina) 
Yew,  western  

(Taxus  bre-jjfolia) 

NOTE.  —  The  data  above  are  extracted  from  tests  on  one  hundred  and  twenty-six  species  of  wood  made  at  the  Forest  Products 
Laboratory,  Madison,  Wisconsin.  Bulletin  556  records  results  of  tests  on  air-dry  timber  also,  bat  only  data  on  green  timber  are  shown, 
as  the  latter  are  based  on  a  larger  number  of  tests  and  on  tests  which  are  not  influenced  by  variations  in  moisture  content.  The 
strength  of  dry  material  usually  exceeds  that  of  green  material,  but  allowable  working  stresses  in  design  should  be  bas.d  on  strengths 
of  green  timber,  inasmuch  as  the  increase  of  strength  due  to  drying  is  a  variable,  uncertain  factor  and  likely  to  be  offset  by  defects. 
All  test  specimens  were  two  inches  square,  by  lengths  as  shown. 

COLUMN  NOTES.  — 2,  Locality  where  grown,  —  see  Tables  7 4 and  75;  3,  Moisture  includes  all  matter  volatile  at  100°  C  expressed 
as  per  cent  of  ordinary  weight;  6,  Weight,  air  dry  is  for  wood  with  12  per  cent  moisture;  for  density,  see  metric  unit  tables  72  and 
73;  6-10,  762  mm  (30  in.)  long  specimen  on  711.2  mm  (28  in.)  span,  with  load  at  center. 

SMITHSONIAN  TABLES. 


MECHANICAL  PROPERTIES.    TABLE  74.  —  Hardwoods  Grown  in  U.  S.  (English  Units). 


Common  and  botanical 
name. 

Locality 
where  grown. 

Moisture  content,  i 
green,  per  cent.  i 

Weight. 

Static  bending. 

Impact 
bending. 

Compression. 

Shear. 

Ten- 
sion. 

i 

> 

.*}" 

I 

s 

PH 

Modulus  of 
rupture,  Ib/in2 

Modulus  of  elas- 
ticity i  ooo  X  Ib/in2 

% 

pi 

Parallel 
to  grain. 

1  Perpendicular  to 
grain,  P-limit 
Ib/in"- 

1 

•oti 

Perpendicular  to 
grain,  ult.  st.  Ib/in2 

Green. 

Air- 
dry. 

P- 

limit. 

lb/ft» 

!* 

Ib/irf 

1 

2 

11 

13 

14 

15 

Alder,  red  
(Alnus  oregona) 
Ash,  black  
(Fraxinus  nigra) 
Ash,  white  (forest  grown). 
(Fraxinus  americana) 
Ash,  white  (2d  growth)  .  . 
(Fraxinus  americana) 
Aspen  
(Populus  tremuloides) 
Basswood  
(Tilia  americana) 
Beech  

Wash. 

Mich,  and 
Wis. 
Ark.   and   W. 
Va. 

N.  Y. 

Wis. 
Wis.  and  Pa. 
Ind.  and  Pa. 
Wis.  and  Pa. 
Wis. 

Tenn.  and 
Wis. 
Pa. 

Md.  and  Tenn. 
Mo. 
Tenn. 
Tenn. 
Wis. 
Wis.  and  Pa. 
Cal. 
La. 
Mo. 
Mo. 

O.,  Miss.,  Pa. 
and  W.  Va. 
Tenn. 

Tenn. 
Tenn. 
Mo.  and  Ind. 
La. 
Wis. 

Ind.,  Pa.  and 
Wis. 
Cal. 

Ark.,  La.,  Ind. 
and  Tenn. 
Ark.,  La.  and 
Ind 
Mo. 

Tenn. 
Ind.  and  Tenn. 
Ky. 

98 
83 
43 
40 
107 
103 
62 
72 
68 
104 
55 

122 
III 
80 
62 
50 

88 
79 
97 
81 
63 
60 
82 
62 
40 
63 
117 
66 
60 
62 
84 
68 
58 
64 
83 
81 

46 
53 
46 
51 
47 
41 
55 
51 
58 
46 
46 
55 
49 
So 
65 
54 
52 
70 
56 
50 
61 
64 
57 
62 
58 
Oi 
62 
46 
56 
71 
64 
62 
63 
38 
52 
58 

28 
34 
40 
46 

27 

26 

44 
38 
45 
27 
36 
30 
29 
33 
54 
45 
35 
54 
34 
36 
46 
51 
40 
49 
49 
47 
35 
34 
44 
56 
45 
47 
53 
28 
35 
39 

3800 
2600 
4900 
6lOO 
29OO 
27OO 
4500 
2900 
4600 
2900 
4200 
3100 
29OO 
4200 
4800 
4600 
3600 
7600 
4200 
3700 
5200 
5900 
3400 
5800 
8800 
56OO 
360O 
3100 
5OOO 
6300 
3700 
4700 
5600 
320O 

3300 
5400 

6500 
6000 
9100 
10800 
5300 
5000 

8,oo' 

5800 
8600 
5400 
8000 
5600 
5300 
7400 
8800 
9500 
6900 

1  1  200 

7300 
6800 
9800 

1  1  000 

6500 

8400 

13800 

10200 
6800 
5800 
9IOO 
10600 
7700 
8300 
10000 

5600 
6500 
9500 

1170 

IO2O 

1350 
1640 
840 
1030 
1240 

IOIO 

1540 

970 
1310 
930 

IOIO 

1560 
1180 
1190 
1030 

20IO 
IO50 
1150 
1370 
1570 
900 
920 
1850 
1290 
IIIO 

940 
1480 
1340 
1290 
1250 
1370 

I2IO 
1060 
I42O 

8000 
7200 
11700 
13800 
6900 
6200 
10400 
7800 
11700 
7300 

IO20O 
7900 
7200 
9300 
7IOO 
IIOOO 

8  loo 
14200 
oooo 

1  0000 

12300 

14400 
8900 

IO200 

18300 
11800 
8800 
6800 

1  2  100 
II200 
IO4OO 
10700 
I2IOO 
8000 
8800 
II900 

2650 
1620 
3230 
3820 
1620 
1710 
2550 
1650 
2760 
1960 
2940 
2040 
1770 
2760 

2870 
2290 
4870 
2760 
2360 
3040 
3430 
1970 

6280 
3320 

2200 
1950 

3120 

4050 
2330 
2990 
3030 
2  OOO 
2390 
360O 

310 
430 
800 
790 

200 
210 

610 
300 
450 
270 
440 
380 
240 
410 

1030 

750 
390 

I02O 
590 
460 
960 
1000 

610 

IIIO 

1430 
1420 
570 
460 
75o 
1480 
730 
830 

IIIO 

310 
450 
600 

770 
870 
1260 
1600 
620 
610 

I2IO 

790 

IIIO 

760 

1130 

800 
680 
990 
1520 

1270 

920 
1550 

1190 
1070 
1480 
1320 
1130 
1670 
1760 
1660 

1040 
1050 
1380 
1700 

1  1  20 

I25O 
1470 
790 
1000 
1220 

390 
490 
620 
790 
180 
280 
760 
380 
480 
430 
570 
430 
410 
440 

660 
560 
640 
600 
Sio 
680 

610 

770 
930 

610 
560 
770 
970 
740 
770 
770 
460 
630 
570 

(Fagus  atropunicea) 
Birch  paper 

(Betula  papyri/era) 
Birch,  3'ellow 

(Betula  lutea) 
Butternut  
(Juglans  cinerea) 
Cherry,  black  
(Prunus  serotina) 
Chestnut  

(Castanea  dentata) 
Cottonwood  
(Populus  deltoides) 
Cucumber  tree  
(Magnolia  acuminata) 
Dogwood  (flowering)  .... 
(Cornus  florida) 
Elm,  cork  

(Ulmus  racemosa) 
Elm  white 

(Ulmus  americana) 
Gum,  blue  

(Eucalyptus  globulus) 
Gum,  cotton  
(Nyssa  aquatica) 
Gum,  red  
(Liquidambar  styracifiua) 
Hickory  pecan 

(Hicoria  pecan) 
Hickory,  shagbark  
(Hicoria  ovata) 
Holly,  American  
(Ilex  opaca) 
Laurel,  mountain  
(Kalmia  latifolia) 
Locust  black 

(Robinia  pseudacacia) 
Locust,  honey  
(Gledilsia  triacanlhos) 
Magnolia  (evergreen)  
(Magnolia  joetida) 
Maple  silver 

(Acer  saccharinum) 
Maple,  sugar  
(Acer  saccharum) 

(Quercus  chrysolepsis) 
Oak  red 

(Quercus  rubra) 
Oak,  white  
(Quercus  alba) 
Persimmon  
(Diospyros  virginiana) 
Poplar,  yellow  
(Liriodendron  tulipifera] 

(Platanus  occiJentalis) 
Walnut,  black  
(Juglans  nigra) 

NOTE.  —  Results  of  tests  on  sixty-eight  species;  test  specimens,  small  clear  pieces,  2  by  2  inches  in  section,  30 
bending;  others,  shorter.  Tested  in  a  green  condition.  Data  taken  from  Bulletin  556,  Forest  Service,  U.  S.  Dept. 
containing  data  on  130,000  tests.  See  pages  97  and  99  for  explanation  of  columns. 

SMITHSONIAN  TABLES. 


inches  long  tor 
of  Agriculture, 


MECHANICAL   PROPERTIES.    TABLE  75. — Conifers  Grown  in  U.  S.  (English  Units). 


99 


Common  and  botanical 
name. 

Locality 
where  grown. 

Moisture  content,  j 
green,  per  cent. 

Weight. 

Static  bending. 

Impact 
lending. 

Compression. 

Shear. 

Ten- 
sion. 

1 

J2" 

I 

Modulus  of 
rupture,  Ib/in2 

Modulus  of  elas- 
ticity looo  X  Ib/in2 

1 
f& 

Parallel 
to  grain 

Perpendicular  to 
grain,  P-limit 
Ib/in2 

fe 

2! 

Green. 

Air- 
dry. 

Perpendicula 
grain,  ult.  st.  1 

P- 
limit. 

3* 

-53  1* 

!~ 

Ib/ftP 

Ib/in2 

r 

1 

2 

3 

4 

5 

6 

7 

8 

9 

11 

13 

14 

15 

Cedar,  incense  
(Libocedrus  decurrens) 
Cedar  Port  Orford 

Cal.  and  Ore. 
Ore. 

Wash,  and 
Mont. 
Wis. 

^a.  and  Mo. 

Ore.  and 
Wash. 
Wis. 

Wash,  and 
Ore. 
VIont.  and 
Wyo. 
VIont.  and 
Ore. 
Ore. 

Cal. 

Tenn.  and 
Wis. 
Wash. 

VIont.  and 
Wash. 
Fla. 

1  08 
52 

39 

55 
87 

102 
117 
36 
38 

94 
41 
156 
105 
71 
58 
47 
70 
65 
47 
54 
85 
64 
123 
58 
95 

74 
43 
53 
52 
44 

45 
39 

27 
28 
48 
47 
45 
38 
34 
44 
31 
56 
48 
41 
48 
53 
54 
39 
5° 
42 
54 
50 
50 
39 
46 

39 
34 
33 
47 

54 

24 
3i 

23 

21 
30 
27 
25 

34 
32 
27 
26 
26 
29 
29 
37 
45 
39 
28 
43 
34 
35 
37 
26 
30 
28 

27 
28 
26 
38 

45 

3900 
3900 

3300 
2600 
4000 
3900 
3000 
5000 
3600 
3600 
34oo 
3000 
4200 
3400 
4600 
5600 
4400 
3000 
5400 
3700 
37oo 
45oo 
3300 
3Soo 
3100 

3400 
3400 
3000 
4200 
6500 

6200 
6800 

5200 
4200 
6800 
6300 
4900 
7800 
6400 
6100 
5700 
6000 
6700 
6100 
75oo 
8800 
7500 
55oo 
8700 
6400 
6700 
8000 
5300 
5700 
5200 

5300 
5700 
SSoo 
7200 

IOIOO 

840 
1500 

950 
640 
1190 
1300 
960 
1580 
1180 
1300 
1280 
1130 

1120 
1190 
1350 
1630 
1380 

1080 
1630 
1380 

1  1  20 
1450 
970 
1330 
1010 

IO7O 
1  1  80 

1180 
1240 
990 

7300 
9300 

7100 
5300 
8000 
7800 
6900 
9400 
9100 
8100 
7900 
7200 
7900 
7800 
9400 
11300 
9500 
7200 
10800 
7500 
9100 
1  1  200 
6700 
7600 
6700 

6500 
7200 
7000 
7800 
13100 

2870 
3970 

2500 
1420 
3100 
2380 

222O 
3400 
2520 
2680 
2370 
26lO 
2710 
2290 
3250 
3950 
2870 
2100 
3840 
2470 
2100 
3650 
2340 
2770 
2080 

2370 
2360 
2280 
3010 
34^3 

460 
380 

3io 
290 
470 
320 

210 
530 
450 
340 
310 
440 
500 
350 
560 
590 
550 
310 
600 
360 
510 
480 
350 
300 
340 

310 
350 

330 
480 
1040 

830 
880 

720 
620 
820 
670 
610 
910 
880 
700 
700 
730 
880 
810 
920 
1030 
900 
690 
1070 
780 
950 
800 
710 
710 
680 

640 
770 
780 
860 
1620 

280 
240 

2IO 
240 
280 
240 

i  So 
200 
350 

230  | 

I 

180 
260 
263 
260 

2.  S3 
2QD 
280 
220 
2QO 

igo 
3SO 
330 
270 
250 
280 

rfg 

220 

2.SO 
260 

450 

(Chamaecyparis  law- 
soniana) 
Cedar  western  red  

(Thuja  plicata) 
Cedar,  white  
(Thuja  occidentalis) 

(Taxodium  distichum) 
Fir,  amabilis  
(Abies  amabilis) 
Fir  balsam              

(Abies  balsamea) 
Fir,  Douglas  (i)  

(Pseudntsuga  taxifolia) 
Fir  Douglas  (2) 

(Pseudotsuga  taxifolia') 

(Abies  grandis) 

(Abies  nobilis) 
Fir,  white            

(Abies  concolor) 
Hemlock  (eastern)  
(Tsuga  canadensia) 
Hemlock  (western)  
(Tsuga  heterophylla) 

(Larix  occidentalis) 
Pine  Cuban          

(Pinus  heterophylla) 
Pine,  loblolly  
(Pinus  taeda) 
Pine,  lodgepole  

?la.,    N.    anc 
S.  Car. 
Col.,  Mont, 
and  Wyo. 
Fla.,  La.  anc 
Miss. 
Wis. 

Tenn. 
Ark.  and  La. 
Cal. 
Mont. 

Col.,    Mont., 
Ariz.,  Wash 
and  Cal. 
Wis. 

N   H   and 

(Pinus  contorta) 

(Pinus  palustris) 
Pine,  Norway  
(Pinus  resinosa) 
Pine  pitch       

(Pinus  rigida) 

(Pinus  cchinata) 

(Pinus  lambcrtiana) 

(Pinus  monticola) 
Pine,  western  yellow  .... 
(Pinus  pondcrosa) 

Pine  white    

(Pinus  slrobus) 

(Picea  rubcns) 
Spruce,  Sitka  
(Picca  sitchensis) 

Tenn. 
Wash. 

Wis. 
Wash. 

(Larix  laricina) 
Yew  western      

(Taws  brevifolia) 

COLUMN  NOTES  (continued).  —  (7)  recommended  allowable  working  stress  (interior  construction):  I  tabular  value;  experi- 
mental results  on  tests  of  air-dry  timber  in  small  clear  pieces  average  50  per  cent  higher;  kiln-dry,  double  tab  alar  values;  (1 
repeated  falls  of  so-lb.  hammer  from  increasing  heights;  11-12,  2O3.2-mm  (8  in.)  long  specimen* loader!  on  ends  with  deformations 
measured  in  a  i52.4-mm  (6  in.)  gage  length;  (12)  allowable  working  stress  \  tabular  crushing  strength;  (13)  iS2.4-mm  (0  in.)  long 
block  loaded  on  its  side  with  a  central  bearing  area  of  2s8o.6-mm2  (4  in2)  allowable  working  stress,  j  tabular  value.  (14)  so.8-mm 
by  50  8-mm  (2  in.)  projecting  lip  sheared  from  block;  allowable  working  stress,  J  tabular  value;  (15)  63.5-mm  (2^  in.)  specimen  with 
25.4-mm  (i  in.)  free  loaded  length;  allowable  working  stress,  J  tabular  value.  (16-17)  for  values  in  Ibs.  multiply  values  of  metric 
tables  by  2.2. 

SMITHSONIAN  TABLES. 


100 


TABLES   76-77. 
ELASTIC   MODULI- 


TABLE   76.— Rigidity   Modulus 

If  to  the  four  consecutive  faces  of  a  cube  a  tangential  stress  is  applied,  opposite  in  direction  on 
adjacent  sides,  the  modulus  of  rigidity  is  obtained  by  dividing  the  numerical  value  of  the  tangential 
stress  per  unit  per  sq.  mm.)  by  the  number  representing  the  change  of  angles  on  the 

non-stressed  faces,  measured  in  radians. 


Substance. 

Rigidity      Refer- 

Substance. 

Rigidity 
Modulus. 

Refer- 
ence. 

. 

335° 
2580 

355° 
37'5 
37oo 
1240 
4060 
2450 
4780 
4-i3 
445° 
4664 
2850 

3950 
5210 
6706 

7975 
6940 
8108 

75°5 
1710 
7820 
4359 

'4    ! 

5     ; 
10 

II 

5  * 
•5 

j 

10 

19 

5 
14 
5 
'5 

10 

,76 

H 

5 
5 
ii 

Quartz  fibre    

2888 
2380 
2960 
2650 
2566 
2816 
8290 

7458 
8070 
7872 
173° 

'543 
3880 
3820 
6630 
6220 

235° 
2730 
1770 
1280 
1190 
2290 

2O 
21 

5 

10 

16 
ii 
16 
15 

5 
ii 

5 
i9 
5 
J9 
16 

23 
23 
23 
23 

ii         it 

"i   UM 

Silver     

cast,  6oCu+  12  Sn     . 
ith,  slowly  cooled    .    . 
Bronze,  cast,  88Cu+  12  Sn. 

ti 

"      hard-drawn    .... 
:  Steel                     

"     cast    

'*     cast,  coarse  gr.    .     .     . 
"     silver-     

i  Tin,  cast     

M 



Zinc  

u 

Glass                    .         ... 

M 

.esium,  cast      .... 

1'hosphor  bronze     .... 

Granite                 

Marble                  .     . 

Slate 

References  1-16,  see  Table  48.                               21   Boys,  Philos.  Mag.  (5)  30,  1890. 
Ann.  28,  1886.                               22  Thomson,  Lord  Kelvin, 
i.  1  6,  1829.                              23  Gray  and  Milne. 
19  K                            .ttingen,  1886.                       24  Adams-Coker,  Carnegie  Publ.  No.  46, 
20  Threlfall,  Philos.  Mag.  (5)  30,  1890.                          1906. 

TABLE  77.  -Variation  of  the  Rigidity  Modulus  with  the  Temperature. 
»*  =  n<>  ( i  —  a/  —  ft/'2  —  yt'4},  where  /  =  temperature  Centigrade. 


Substance. 

Me 

aio« 

/3io* 

•yio" 

Authority. 

^ 

. 

21  S8 

48 

32 

Pisati,  Nuovo  Cimento,  t 

„  34,  1879. 

Copper 

3200 
3972 

455 
2716 

36 

—  23 

47 

Kohlrausch-Loomis,  Pogg.  Ann.  141. 
Pisati,  loc.  cit. 

1   ff 

572 

28 

K  and  L,  loc.  cit. 

1 

8108 

206 

19 

—  1  1 

Pisati,  loc. 

cit. 

*' 

6940 

48} 

12 

_ 

K  and  L,  loc.  cit. 

.     . 
Silver    . 

1  1  1 
387 

£ 

-8 
ii 

I'i^ati,  loc 

«(                   41 

cit. 

H 

8290 

i»7 

59 

-9 

«                   « 

« 

««*  =  »is  ('—«(/—!  5)1;  Horton,  Philos.  Trans.  204  A,  1905. 

- 
•per  (com- 
mercial) 
Iron 

4-37* 

£26 
8.45 

a  =.00039 

.00038 
.00029 
.00026 

Platinum 
Gold 

Silver 
i    Aluminum 

6.46* 

2-45 
2.67 

2-55 

a  =  .0001  2 
.00031 
.00048  i 
.00148 

Tin               i. 
Lead             o. 
Cadmium     2. 
Quartz          3. 

50*  a  =.00416 
So            .00  1  64 
31            .0058 

DO               .00012 

SMITHSONIAN  TABLC*. 


*  Modulus  of  rigidity  in  io»  dynes  per  sq.  cm. 


TABLES  78-81 . 

TABLE  78. — Interior  Friction  at  Low  Temperatures. 


IOI 


C   is  the  damping  coefficient   for  infinitely   small   oscillations;    T,   the  period   of   oscillation   in   sec- 
onds; N,  the  second  modulus  of  elasticity.     Guye  and  Schapper,  C.  R.   150,  p.  963,    1910. 


Substance    ...       ... 

Cu 

Ni 

\u 

Pd 

Pt 

Ona  T\7 

Length  of  wire  in  cm  . 

22.5 

22.2 

22.3 

22.2 

23.0 

17.2 

17-3 

Diameter  in  mm  

•643 

.411 

.609 

•553 

.812 

.601 

.612 

100°  C      C 

24.1 

I  -34 

27-5 

1.67 

2.98 

55-8 

_ 

T 

2.38lS 

3  .  83  i  s 

3.0IOS 

2.579 

i  .  1435 

i.8o8s 



Nxio-11.... 

3-32 

7-54 

2-55 

5-08 

5-77 

2.71 

— 

o°C     C 

5-88 

.417 

4.82 

1.25 

4.60 

7.19 

4.69 

T 

2.336s 

3-754S 

2.9695 

2.5715 

i  •  133s 

I-759S 

I  .  4085 

Nxio-11.... 
-195°  C     C         .... 

3-45 
3-64 

7-85 

.556 

2.62 
6.36 

5.12 

•744 

3-02 

2.87 
1.64 

2.26 

1.02 

T 

2.2748 

3-577S 

2.9025 

2.5525 

I.  HIS 

1.6945 

1.4255 

Nxio-11.... 

3.64 

8.65 

2.74 

5-19 

6.10 

3.18 

2.20 

TABLE  79. — Hardness. 


Agate                7. 

Brass               3-4. 

Iridosmium                7. 

Sulphur             r-5-2-5 

Alabaster         1.7 

Caiamine  .           5. 

Iron                         4-5. 

Stibnite                    2. 

Alum            2-2.5 

Calcite                 3. 

Kaolin                         i. 

Serpentine          3-4. 

Aluminum        2. 
Amber          2-2.5 

Copper          2.5-3. 
Corundum           9. 

Loess  (o°)                  0.3 
Magnetite                  6. 

Silver                2-5-3- 
Steel                    5-8.5 

Andalusite       7.5 

Diamond           10. 

Marble                     3-4. 

Talc                         i. 

Anthracite        2.2 

Dolomite      3.5-4- 

Meerschaum          2-3. 

Tin                          1.5 

Antimony         3.3 

Feldspar             6. 

Mica                           2.8 

Topaz                      8. 

Apatite              5. 

Flint                     7. 

Opal                       4-6. 

Tourmaline             7.3 

Aragonite         3.5 

Fluorite               4. 

Orthoclase                 6. 

Wax  (o°)                 0.2 

Arsenic             3.5 

Galena                2.5 

Palladium                   4.8 

Wood's  metal         3. 

Asbestos           5. 

Garnet                j. 

Phosphorbronze        4. 

Asphalt         1-2. 
Augite              6. 

Glass            4.5-6.5 
Gold             2.5-3. 

Platinum                     4.3 
Platin-iridium            6.5 

Barite                3.3 

Graphite       0.5-1. 

Pyrite                          6.3 

Beryl                 7.8 

Gypsum         1.6-2. 

Quartz                         7. 

Bell-metal         4. 

Hematite             6. 

Rock-salt                    2. 

Bismuth            2.5 

Hornblende         5.5 

Ross'  metal          2.5-3.0 

Boric  acid         3. 

Iridium                6. 

Silver  chloride           1.3 

From  Landolt-Bbrnstein-Meyerhoffer  Tables  :  Auerbachs,  Winkleraann,  Handb.  der  Phys.  1891. 
TABLE  80. — Relative  Hardness  of  the  Elements. 


C 

IO.O 

Ru 

6-5 

Cu 

3-° 

Au 

2-5 

Sn 

1.8 

Li 

0.6 

B 

95 

Mn 

Sb 

Te 

2-3 

Sr 

1.8 

P 

0.5 

Cr 

9.0 

Pd 

4.8 

Al 

2.9 

Cd 

2.O 

Ca 

'•5 

K 

°-5 

Os 

7.0 

Fe 

4-5 

Ag 

2-7 

S 

2.0 

Ga 

i-S 

Na 

0.4 

Si 

7.0 

Pt 

4-3 

Bi 

2.5 

Se 

2.0 

Pb 

'•5 

Rb 

Ir 

6.5 

As 

3-5 

Zn 

2-5 

Mg 

2.0 

In 

1.2 

Cs 

0.2 

Rydberg,  Zeitschr.   Phys   Chem   33,  1900 

TABLE  81. — Ratio,  p,  of  Transverse  Contraction  to  Longitudinal  Extension  under  Tensile  Stress. 

(Poisson's  Ratio.> 


Metal 

Pb 

Au 

Pd 

Pt 

Ag 

Cu 

Al 

Bi 

Sn 

Ni 

Cd 

Fe 

P 

o-45 

0.42 

o-39 

o-39 

0.38 

o-35 

0-34 

o-33 

0-33 

0.31 

0.30 

0.28 

From  data  from  Physikalisch-Technischen  Reichsanstalt,  1907. 

p  for:  marbles,  0.27;  granites,  0.24;  basic-intrusives,  0.26;  glass,  0.23.     Adams-Coker,  1906. 
SMITHSONIAN  TABLES. 


102 


TABLE  82. 
ELASTICITY    OF    CRYSTALS. 


The  formulae  were  deduced  from  experiments  made  on  rectangular  prismatic  bars  cut  from  the  crystal.  These  bars 
were  subjected  to  cross  bending  and  twisting  and  the  corresponding  Elastic  Moduli  deduced.  The  symbols 
a  /3  y,  o,  /J,  y,  and  cu  /3«  -y.,  represent  the  direction  cosines  of  the  length,  the  greater  and  the  less  transverse 
dimensions  of  the  prism  witn  reference  to  the  principal  axis  of  the  crystal.  E  is  the  modulus  for  extension  or 
compression,  and  1  is  the  modulus  for  torsional  rigidity.  The  moduli  are  in  grams  per  square  centimeter. 


;te. 
10* 
-g-  =  i6.i3««  +  i8.5i0'  +  10.427*  4-  ;(38.7<;0  V  4  i  5-2i7-«' 

I0io 

-^-  =  69.52a*  4-  1 1 7.66)8'  -f- 1 16.467'  -f  2(20. 1 60V  -f  85.297-^  +  1 27.350^) 


Beryl  (Emerald). 
io^u 
-g-  =  4.325  sin'9  4  4.619  cos4?  4  13.328  sin20  cos-?) 

io10 

-Y-  =  1 5.00  —  3.675  cos44>2  —  1 7-536  cos-p  cos-9i 

Fluorite. 
loio 
-JT  =  ^'OS  —  6-26  (a<  4  0!  4  7*) 

~Y  =  58-04  —  50-08  (/B  V'  +  7'«-  -f  «'-'£-) 

Pyrite. 

Ig°=  5.08  -  2.24  (a1  4  0'  4-  71) 

io10 

-^-  =  18.60  —  1 7.95  (0V  4  7'a-  4  0-0^) 

Rock  salt. 

^-  =  33-48  —  9.66  (a4  4  04  4  7l ) 

Ioio 

-^-  =  1 54-58  —  77-28  (0  V  4  7 '«-  4 o-0  •') 

Sylvite. 

^p-  =  7S-1  —  48-2  (o4  +  0*4  74) 

io10 

— -  =  306.0  —  192.8  (0V  4  7- a-  4  a-0') 


where  <j>  0j  <j>.2  are  the  angles  which 
the  length,  breadth,  and  thickness 
of  the  specimen  make  with  the 
principal  axis  of  the  crystal.  ' 


Topaz. 

io10 
-^- 

io10 


=4-34'  a4  4  3-46o04  4  3-77  174  4  2  (3.8790V+  2.8567-^4  2.39^0-) 


4.88a*  4  16.540*  4  I6-4574  +  3O-890V  4  4O.8cy)rV  4  43-5i«-0- 

Quartz. 

^  =  1  2.734  (  I  —  yi)*  4  1  6.693  (  '  —  7-)7J  4  9-70574  —  8.46007  (3B-'  —  0-^) 

15_  :=  ,9.665  +  9-060742  4  22.9847'-7i-  ~  16.920  [(70H-  07i)  (3«a,  -  00i)  -  0,7, 


These  formulx  are  taken  from  Volt's  papers  (Wied.  Ann.  vols.  31,  34,  and  35). 
SMITHSONIAN  TABLES. 


TABLE  83. 
ELASTICITY   OF   CRYSTALS. 


I03 


Some  particular  values  of  the  Elastic  Moduli  are  here  given.  Under  E  are  given  moduli  for  extension  or  compression 
in  the  directions  indicated  by  the  subscripts  and  explained  in  the  notes,  and  under  T  the  moduli  for  torsional 
rigidities  round  the  axes  similarly  indicated.  Moduli  in  grams  per  sq.  cm. 


(a)   ISOMETRIC 

SYSTEM.* 

Substance. 

Ea 

E, 

E,. 

T0                     Authority. 

Fluorite 

1473  X 

10° 

1008  X  io6 

910  X  io6 

345  X  io6 

Voigt.t 

Pvrite 

3530  X 
4I9X 

1C6 

2530  X  io6 
349  X  io6 

2310  X  io6 
303  X  io6 

1075  X  io'J 
I29X  io6 

M 

Rock  salt 

.     .     . 

" 

. 

403  x 

IO6 

339  X  io6 

— 

Koch.J 

Sylvite 

401  X 

IO6 

209  X  10° 

— 

— 

«' 

Sodium  chlorate 

372  X 

405  x 

1$ 

196  X  io6 
319  X  io6 

— 

655  X  lo-5 

Voigt. 
Koch. 

Potassium 

alum  .     . 

181  X 

1  06 

i99Xio« 

— 

Beckenkamp.§ 

Chromium 

alum 

161  X 

I0« 

177  X  io6 

— 

— 

" 

Iron  alum 

.     .     .     . 

I86X 

IO6 

— 

— 

((>)   ORTHORHOMBIC  SYSTEM.|| 

Substance. 

E, 

E, 

i 

E, 

E,          |          ES 

E, 

Authority. 

1'arite 
Topaz 

620  X  ioe 
2304  X  iofi 

540  X 
2890  X 

IO6 
IO6 

959  X  io6 
2652  X  io6 

I 

376  X  io6  1    702  X  io6 
2670  X  io6   2893  X  10° 

740  X  io« 
3180  X  io6 

Voigt. 

M 

Substance. 

Tlf-t,, 

T13  =  T31 

T..-T,, 

Authority. 

Barite 
Topaz 

283  X  io6 
1336X106 

293  Xio6 
I353X  io6 

121  X  IO6 

II04X  io6 

Voigt. 

In  the  MONOCLINIC  SYSTEM,  Coromilas  (Zeit.  fiir  Kryst.  vol.  i)  gives 

Gypsum  \     mi 

1  =  887X106  at 
n  =  313  x  io6  at 

21.9°  to  the  principal  axis. 
75.4° 

Mica       [  Em 

u  =  2213  X  io6  in  the  principal  axis. 

IE. 

n  =  1554  x  io6  at  45°  to  the  principal  axis. 

In  the  HEXAGONAL  SYSTEM,  Voigt  gives 

measurements  on  a  beryl  crystal  (emerald). 

The  subscripts  indicate  inclination  in  degrees 

of 

the  axis  of  stress  to  the  principal  axis  of 

the  crystal 

. 

E0=  2165  X  io6, 

E46=  I796X  io6,    E90=23i2  X  io6, 

TO  =  667  X  io6, 

T90  =  883X  io6. 

The  smallest  cross 

dimension 

of  the 

prism  exp< 

mmented  on  (see  T 

able  82),  was  in 

the  principal  axis  for  this  last  case. 

In  the  RHOMBOHEDRAL  SYSTEM,  Voigt  has  measured  quartz.    The  subscripts  have  the 
same  meaning  as  in  the  hexagonal  system. 

E0=  1030X10°,     E_  45  =1305X106,     E+45  =  850X10°,     E90=  785X10°, 

To  =  508  X  io6,      T90  =  348  X  io6. 
Baumgarten^T  gives  forcalcite 

E0  ==  501  X  io'\     E_ 45  =  441  X  io'1,     E  +  45  =  772  X  io6,     E9o  =  79°  X  ior>. 


*  In  this  system  the  subscript  a  indicates  that  compression  or  extension  takes  place  along  the  crystalline  axis,  and 
distortion  round  the  axis.  The  subscripts  b  and  c  correspond  to  directions  equally  inclined  to  two  and  normal  to  the 
third  and  equally  inclined  to  all  three  axes  respectively. 

f  Voigt,  "  Wied.  Ann."  31,  p.  474,  p.  701,  1887;  34,  p.  981,  1888;  36,  p.  642,  1888. 

J   Koch,  "  Wied.  Ann."  18,  p.  325,  1882. 

§   Uecketikamp,  "Zeit.  fiir  Kryst."  vol.  io. 

li  The  subscripts  i,  2,  3  indicate  that  the  three  principal  axes  are  the  axes  of  stress;  4,  5.  6  that  the  axe; 
are  in  the  three  principal  planes  at  angles  of  45°  to  the  corresponding  axes. 

IT  Baumgarten,  "  Poj-g.  Ann."  152,  p.  369,  1879. 
SMITHSONIAN   TABLES. 


TABLES  84-86. 
COMPRESSIBILITY  OF  GASES. 

TABLE  84.— Relative  Volumes  at  Various  Pressures  and  Temperatures,  the  volumes  at  O8  C  and 
at  1  atmosphere  being  taken  as  1  000  000. 


Oxygen. 

Air. 

Nitrogen. 

Hydrogen. 

Aim. 

0° 

99°-5 

i99°-5 

0° 

99°-4 

200°.  4 

0° 

99°.S 

i99°.6 

0° 

99°.3 

200°.  5 

100 
200 

300 
400 

5°° 
600 

700 
800 
900 

9265 

4570 
3208 
2629 
23I2 

2115 
1979 

1879 
1800 

7000 
4343 
3830 
3244 
2867 
26lO 
2417 
2268 

6283 
4900 
4100 
3570 
3202 
2929 
2718 

973° 
5050 
3658 
3036 

2450 
2288 
2168 
2070 

7360 

S^o 
4170 

3565 
3180 
2904 
2699 

2544 

9430 

6622 
5240 
4422 

3883 

3502 
3219 
3000 

9910 

5'95 
3786 
3142 
2780 

2543 
2374 
2240 
2149 

7445 
5301 
4265 

3655 

2775 
2616 

9532 
6715 
533' 
4515 

3973 
3589 
330° 
3085 

5690 
4030 
3207 
2713 
2387 
2149 
1972 
I832 

7567 
5286 

4M7 

3462 

3006 

2680 
2444 
2244 

9420 

6520 

5°75 
4210 
3627 
3212 
2900 
2657 

IOOO 

1735 

2151 

1992 

2415 

2828 

2068 

1720 

2093 

Amagat:  C.  R.  m,  P-  871,  1890;  Ann.  chim.  phys.  (6)  29,  pp.  68  and  505, 

TABLE  85,— Ethylene. 
pv  at  o°  C  and  i  atm.  =  I. 


Atm. 

0° 

10° 

20° 

30° 

40° 

60° 

80° 

100° 

i37°-5 

i98°.5 

46 

. 

0.562 

0.684 

. 

. 

. 

_ 

_ 

_ 

_ 

48 

— 

0.508 

— 

— 

— 

— 

— 

— 

— 

— 

50 

0.176 

O.42O 

O.629 

0.731 

0.814 

0-954 

1.077 

1.192 

1-374 

1.652 

52 

— 

0.240 

O.598 

— 

— 

— 

™ 

— 

— 

- 

0.229 

0.56l 

- 

- 

- 

— 

— 

•• 

~ 

c6 

— 

O.22/ 

0.524 

— 

— 

— 

— 

— 

— 

— 

100 

O.3IO 

o-33  i 

0.360 

0.403 

0.471 

0.668 

0.847 

1.005 

1.247 

1.580 

150 

2OO 
300 

0.441 
0.365 
0.8o6 

o-459 
0.385 
0.827 

0.485 

0.610 
0.852 

o-S^ 
0.638 
0.878 

0.551 
0.669 

0.649 

0-744 
0.972 

0.776 
0.838 
1.048 

0.924 
0.946 
1.133 

1.178 
1.174 
1.310 

1.540 

1-537 
1.628 

500 
IOOO 

1.2,6 

2.289 

1.280 
2.321 

1.308 
2-354 

2'.387 

1.367 

2.422 

I-43I 
2-493 

1.500 
2.566 

1.578 

2.643 

1.721 
2-798 

1.985 

Amagat,  C.  R.  m,  p.  871,  1890;  116,  p.  946,  1893. 


TABLE  86.— Relative  Gas  Volumes  at  Various  Pressures. 

The  following  table,  deduced  by  Mr.  C.  Cochrane,  from  the  PV  curves  of  Amagat  and  other 
observers,  gives  the  relative  volumes  occupied  by  various  gases  when  the  pressure  is  reduced  from 
the  value  given  at  the  head  of  the  column  to  i  atmosphere: 


Gas. 
(Tcmp.=  x6°C.). 

Relative  volume  which  the  gas  will  occupy  when  the  pressure 
is  reduced  to  atmospheric  from 

"  Perfect  "  gas  

I  atm. 

I 
I 

50  atm. 
50 
48.5 
50-5 
50.9 

52.3 
69.0 

100  atm. 
100 
93.6 

100.6 
101.8 
105.2 
107.9 
477* 

120  atm. 
1  2O 
III.  3 
120.0 
I2I-9 

128.6 

485* 

150  atm. 
ISO 
136.3 
147.6 
150.3 

161.9 
498* 

200  atm. 
2OO 
176.4 
190.8 
194.8 
212.6 

218.8 

515* 

Hydrogen  

\ir       

Oxygen  

Oxygen  (ato°  C.)  

*  Carbon  dioxide  is  liquid  at  pressures  greater  than  90  atmospheres. 
SMITHSONIAN  TABLES. 


TABLES  87-89. 
COMPRESSIBILITY  OF  GASES. 

TABLE  87.— Carton  Dioxide. 


10 


Pressure  in 

Relative  values  of  pv  at  — 

mercury. 

l8°.2 

35°-' 

40°,2 

50°.o 

60°.  o            70°.  o 

8o°.o 

90°  .0 

I00°.0 

30 

liquid 

2360 

2460 

259°   ;    2730       2870 

2995 

3120 

3225 

— 

1725 

I 

900 

2145    i    2330        2525 

2685 

2845 

2980 

80 

62  S 

750 

825 

1200 

1650       1975 

2225 

2440 

2635 

no 

825 

93° 

980 

1090 

1275  i   1550 

1845     ! 

2105 

2325 

140 

1  020 

1  1  20 

1175 

1250 

1360       1525 

1715        ! 

J95° 

2160 

170 

I2IO 

1310 

1360 

1430 

1520         1645 

1780       i 

J975 

2135 

200 

1405 

1500 

1550 

1615 

1705     ;     1810 

1930 

2075 

2215 

230 

T59° 

1690 

1730 

1800 

1890 

1990 

2090 

2210 

2340 

260 

1770 

1870 

1920 

1985 

2O7O 

2166 

2265 

2375 

2490 

290 

1950 

2060 

2IOO 

2I7O 

226O 

2340' 

2440 

2550 

2655 

320 

2i35 

2240            2 

280 

2360 

2440 

2525 

2620 

2725 

2830 

Relative  values  of  pv  ;  pv  at  o°  C.  and  i  atm.  =  i. 

0° 

10° 

20° 

1 

30°        40°    i    60° 

80° 

100° 

137° 

198°            258° 

5° 

0.105 

0.114 

0.680 

0-775     0-75° 

0.984 

1.096 

1.  206 

.380 

100 

0.202 

0.213 

0.229 

0.255     0.309 

0.661 

0.873 

1.030 

•259 

1.582        1.847 

150 

0.295 

0.309 

0.326 

0.346     0.377 

0-485 

0.681 

0.878 

-I.S9 

1.530      1.818 

300 

0-559 

0.578 

0-599 

0.623     0.649 

0.710 

0.790 

0.890 

.108 

1.493      1-820 

500 

0.891 

0.913 

0.938 

0.963     0.990 

1.054 

I.I24 

I.2OI 

•362 

1.678 

IOOO 

1.656 

1.685 

I.7I6 

1.748     1.780 

1.848 

I.92I 

1.999 

" 

Araagat,  C.  R.  in,  p.  871,  1890;  Ann.  chim.  phys.  (5)  22,  p.  353,  1881;  (6)  29,  pp.  68  and  405,  1893. 


TABLE  88.  —  Compressibility  of  Gases. 


p.v.  (\  atm.) 

i     </(/.».) 

Density. 

Density. 

Gas. 

pnVo  (i  atm.). 

p.v.       dp 

~  a. 

t 

t_0 

O       32,  o°C          very  small 
P  =  76cm                 pressure. 

02 

1.00038 

—  .00076 

11.2° 

—  .00094 

32- 

32- 

H2 

N2 
CO 

0-99974 
I.OOOI5 
1.00026 

-j-  .OOO52 
—  .OOO3O 
—  .00052 

10.7 
14.9 
13.8 

+  -00053 

—  .00056 

2.015  (T60) 
28.005 
28.000 

2.0173 
28016 
28.003 

CO2 

1.00279 

—   00558 

15.0 

—  .00668 

44.268 

44.014 

N2O 

1.00327 

—  .00654  '    u.o     !  —.00747 

44.285 

43.996 

Air 

I.OOO26 

—  .00046  i    11.4 

NH3 

1.00632 

-    1  -  II    - 

" 

Rayleigh,  Zeitschr.  Phys.  Chem.  52,  p.  705,  1905. 
TABLE  89.  -  Compressibility  of  Air  and  Oxygen  between  18°  and  22°  C. 

Pressures  in  meters  of  mercury,  pv,  relative- 


Air 

P 
pv 

24.07 
26968 

34-90 

26908 

45-24 
26791 

55-30 
26789 

64.00 
26778 

72.16 
26792 

84.22 
26840 

101.47 
27041 

2I4-54 

:  29585 

304.04 
32488 

02 

P 

pv 

24.07 

26843 

34.89 

26614 

- 

55-5° 
26185 

64.07 
26050 

72-15 
25858 

84.19 
25745 

101.06 
25639 

214.52 
26536 

303-03 
28756 

Amagat,  C.  R.  1879. 


SMITHSONIAN  TABLES. 


100 


TABLES  9O-91. 

RELATION    BETWEEN    PRESSURE,    TEMPERATURE    AND 
VOLUME  OF  SULPHUR   DIOXIDE   AND   AMMONIA.* 


TABLE    90.-  Sulphur  Dioxide. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experi- 
ments as  indicated  at  the  top  of  the  different  columns. 


Pressure  in  I 
Atmos. 

Correspond!  nt;  Volume  for  Ex- 
periments aT  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for 
Experiments  at  Temperature  — 

58c.o 

99°.6 

.83°.  2 

S8°.o 

99°.6 

l83°.2 

10 

8560 

9440 

_ 

12 

6360 

7800 

- 

10000 

- 

9.60 

-         '• 

14 

16 

4040 

6420 

~ 

9000 

9.60 

10-35 

- 

18 

- 

4405 

- 

8000 

10.40 

ii  85 

- 

20 

— 

4030 

- 

-030 

ii  55 

13.05 

- 

24 
28 

~ 

3345 
2780 

3180 

6000 

12.30 

14.70 

- 

32 

- 

2305 

2640 

5000 

13-15 

16.70 

- 

36 

- 

2260 

4OOO 

14.00 

20.15 

- 

40 

— 

145° 

2O4O 

3500 

14.40 

23.00 

- 

g 

- 

- 

1375 

3000 

- 

26.40 

29.10 

70 

— 

- 

1130 

2500 

— 

30-15 

33-25 

80 
90 

— 

: 

93° 

790 

2000 

- 

35-20 

40.95 

100 

- 

- 

680 

I5OO 

- 

39.60 

55-20 

120 

- 

- 

545 

1000 

- 

- 

76.00 

I4O 
100 

- 

- 

43° 
325 

500 

— 

- 

117.20 

TABLE  91.  -Ammonia. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experiments 
indicated  at  the  top  of  the  different  columns. 


B 

li 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Pressure  in  Atmospheres  for  Experiments 
at  Temperature  — 

I1 

46^.6 

W-6 

,83°.6 

300.2 

46°.  6             99°.  6 

i83°.o 

10 

9500 

_ 

_ 

IOOOO 

8.85 

9-5° 

12.5 
i5 

20 

7245 
5880 

7635 
4645 

4875 

9000 
8000 

9.60 
10.40 

10.45 
11.50 

12.00 

- 

25 

- 

3560 

7000 

II.O5 

13.00         13.60 

- 

30 

35 
40 

45 

- 

2875 
2440 
2080 
1795 

268^ 
2345 
2035 

6000 
5000 
4000 

II.80 

I2.OO 

14-75 
1  6.60 

18-35 

15-55 
1  8.60 
22.70 

19.50 
24.00 

50 

- 

1490 

1775 

3500 

- 

18.30 

25.40 

27.20 

55 

— 

1250 

1590 

3000 

- 

- 

29.20 

3I-50 

70 

975 

1450 

1  2J.C 

2500 

- 

- 

34.25 

37-35 

80 

- 

_ 

•**3 

1125 

2000 

- 

- 

41-45 

45-50 

90 

- 

- 

'035 

1500 

- 

- 

4970 

58.00 

100 

95° 

1000 

" 

*" 

59^5 

93.60 

*  From  the  experiments  of  Roth, 
SMITHSONIAN  TABLE*. 


Wied.  Ann.' 


1880. 


TABLE  92. 
COMPRESSIBILITY  OF   LIQUIDS- 


107 


At  the  constant  temperature  /,  the  compressibility  /3  =  (i/Vo)(dV/dP).  In  general  as  P  in- 
creases, /3  decreases  rapidly  at  first  and  then  slowly;  the  change  of  /3  with  /  is  large  at  low  pressures 
but  very  small  at  pressures  above  1000  to  2000  megabars.  i  megabar  =  0.987  atmosphere  =  io« 
dyne/cm2. 


Substance. 

u 
d 

1 

Pressure,  ' 
megabars.  L 

Pl°' 
a>vfi  M 
E^gjX 

sis* 

Reference.  1 

Substance. 

o 

0 

d 
1 

Pressure, 
megabars. 

*N-o 

I^X 

li  rs 

Reference.  1 

Acetone  

14 
20 
20 

23 
500 

I  OOC 

III 
61 

C.2 

9 

I 
j 

Ethyl  ether,  ct'd.. 

tt        tt        ti 

Ethyl  iodide... 

20 
20 
2O 

I,  OOO 
I2,OOO 
2OO 

61 

10 

81 

I 
I 
16 

M 

4.O 

I  ^  OOO 

9 

I 

M                 « 

2O 

4.OO 

60 

16 

;Yrnyl  alcohol  

Id. 

27 

88 

IO 

a             « 

2O 

*;oo 

64 

i 

iso... 

2O 

2OO 

84 

1  6 

a             « 

2O 

1,000 

co 

i 

"       iso... 
«          « 

20 
2O 

400 

70 
61 

16 
i 

(c             « 

Gallium 

20 
IO 

12,000 
•200 

8 

7     C  7 

i 
6 

i.         n 
ti         « 

20 
2O 

1,000 
I  ^  OOC 

46 
8 

i 
i 

Glycerine  
Hexane 

15 

°o 

5 
200 

22 
117 

12 

16 

«          « 

4.O 

I  ">  OOO 

8 

i 

20 

4.00 

01 

16 

Benzene 

17 

80 

2    3 

Kerosene  

20 

C.OO 

c; 

i 

2O 

?OO 

77 

16 

u 

20 

I,  OOO 

AC 

i 

u 

2O 

4OO 

6? 

16 

tt 

20 

I2,OOC 

8 

i 

Bromine 

^6* 

16 

ll 

12  OOO 

8 

I  3 

14 

2O 

4.OO 

CJ 

16 

Mercury  

20 

3OO 

VQ"> 

7 

Butyl  alcohol,  iso.. 
"        iso.. 

"        iso.. 
"        iso.. 
iso.. 

."       Is0'  ' 
Carbon  bisulphide.  . 

«              it 
n              ti 

Carb.  tetrachloride. 

a              n 

lo 
2O 
20 
20 
20 
2O 

16 

20 
2O 
2O 
20 
2O 

8 

200 
400 
500 
I,  OOO 

12,000 

21 
50C 
1,000 

12,000 

200 

AOO 

97 
81 
64 
56 
46 
8 
86 

57 
48 
6 
86 
7* 

2 

16 
16 
i 

i 
i 

10 

i 
i 
i 
16 
16 

M 
(4 

Methyl  alcohol.  .  .  . 

u                « 
(«                 « 
a                u 
it                it 
it                tt 

Nitric  acid  
Oils:  Almond  
Castor 

22 
22 
22 

15 
2O 
20 
2O 
2O 
2O 
O 

15 
I  r 

500 
I,  OOO 
12,000 

23 
200 
400 
500 
I,OOO 
I2,OOO 
17 

5 

r 

3-97 
3-9i 
2-37 
103 

95 
80 

65 
54 
8 
32 
53 
46 

8 

0      | 

8 

10 

16 
16 

i 
j 

i 

U 

T    -> 

~     : 
12 

Chloroform  
tt 

2O 
2O 

200 
4OO 

83 
70 

16 
16 

Linseed  
Olive  

15 

I  ^ 

5 

5i 

12 

12 

Dichlorethylsulfidc  . 
Ethyl  acetate 

32 
3^ 
I  3 

I,  OOO 
2,000 

2? 

34 

24 

jO"? 

5 
5 

IO 

Rape-seed  
Phosph.  trichloride  . 

2O 
IO 
2O 

250 

^oc 

59 

71 

0} 

15 
II 

I 

M                 tt 

it                 tt 

Ethyl  alcohol  

a          n 

2O 

20 

14 

23 
2D 

2OO 
400 

23 
500 
I,  OOO 

90 

75 

100 

63 

CA 

16 
16 

10 

i 

i 

it              tt 

Propyl  alcohol,  n.  .  . 
"       n... 
"       (n?) 

2D 

20 
20 
2O 
2O 

1,000 
12,000 
2OO 
400 
sOO 

47 
S 

77 
67 
65 

I 
I 

16 

16 

i 

tt          n 
Ethyl  bromide.   . 

«                 it 
it                tt 

20 
2O 
20 
2O 

12,000 
200 
40O 
COQ 

8 

IOO 

82 
70 

i 
16 
16 

"       (n?). 
"       (n?). 
Toluene  

20 
20 
20 
2O 

1,000 

12,000 

2OO 
4OO 

47 
7 

74 
64 

i 
i 
16 

it. 

it                tt 
it                it 

2O 
2O 

1,000 

12,000 

54 
8 

Turpentine  
Water  

20 
2O 

13 

74 
4-) 

15 
ii 

Ethyl  chloride. 

ICT 

2  3 

i  ^i 

IO 

« 

2O 

2OC 

43 

it) 

2O 

rOO 

IO2 

a 

2O 

4OO 

41 

if. 

«           it 

2O 

I  OOO 

66 

a 

2O 

50C 

59 

4 

it           it 

2O 

I2,OOO 

8 

u 

4O 

50C 

P 

4 

Ethyl  ether.  . 

2< 

2T. 

1  88 

IO 

tt 

4O 

IOOO 

33 

4 

a        it 

2O 

?OC 

84. 

i 

tt 

4O 

12,000 

9 

4 

Xylene,  meta  

it         tt 

20 

2O 

200 
4OO 

69 
60 

16  i 
16 

For  references,  see  page  108. 
IITHSONIAN  TABLES. 


loS 


I  ABLE  93. 

COMPRESSIBILITY  OF  SOLIDS. 


If  I"  is  the  volume  of  the  material  under  a  pressure  P  megabars  and  Vo  is  the  volume  at  atmospheric  pressure,  then 
the  compressibility  0  =  —  (i/l'o)  (dV/dP).  Its  unit  is  cmVmegadynes  (reciprocal  megabars).  io6//3  is  the  bulk  modu- 
lus in  absolute  units  (dynes/cm1).  The  following  values  of  /8,  arranged  in  order  of  increasing  compressibility,  are  for 
P  =  o  and  room  temperature,  i  megabar  =  io»  dynes  =  1.013  kg/cm2  =  0.987  atmosphere. 


Substance. 

Compres- 
sion per 
unit  vol. 
per  mega- 
bar  X  io« 

Bulk 
modulus. 
dynes/cm1 
X  10* 

Reference. 

Substance. 

Compres- 
sion per 
unit  vol. 
per  mega- 
bar  X  io« 

Bulk 
modulus. 

dynes/cm2 
Xio'2 

Reference. 

Tungsten  
Boron  
Silicon  
Platinum 

0.27 
0-3 
•  32 
.38 

•  53 

:8 

.60 

•  7 
•75 
.84 
.89 

99 
03 
33 
39 
74 
89 
09 
17 

3-7 
3-0 
3-1 

-3 

.2 

•  9 

I 

.67 
•4 
•33 
.19 

.12 
.12 

.OI 
0.97 
0.75 
0.72 
0-57 

0.53 
0.48 
0.46 

I     2 
I     2 

i  3 
5 

I,  2 

Plate  glass  
Lead  

•  23 
.27 
•3 
•  4 
•  7 
•9 
3-0 
3-0 
3-1 
4.12 
4-5 
5-7 
7-4 
9-0 

9-2 
12.  O 
12.9 
13-0 
IS.6 

20.5 

31-7 
40.0 
61.0 

0-45 
0.44 
0.43 
0.42 
0-37 
0-34 
0.33 
0.33 
0.32 
0.24 

0.22 
O.I7S 
0.135 
0.  Ill 
0.109 
0.083 
0.078 
0.077 
0.064 
0.049 
O.032 
0.025 

0.016 

I     2 

Thallium. 
Antimony 
Quartz... 

...;.... 

Nickel 

Molybdenum  .... 
Tantalum  
Palladium  

Magnesiui 
Bismuth  . 
Graphite. 
Silica  glas 
Sodium  ch 
Arsenic  .  . 
Calcium  . 
Potassium 
Lithium  .  . 
Phosphorv 
Selenium  . 
Sulphur.. 
Iodine  .  .  . 
Sodium  .  . 
Phosphoru 
Potassium 
Rubidium 
Calcium  . 

n  
i  

Gold   . 

loride  .  .  . 

chloride 
is  (red)'.'. 

s  (white) 

Pyrite  
Copper  

Brass  

Chromium  
Silver.  .  . 

Mg.  silicate,  crys. 
Aluminum  
Calcite  

Zinc. 

Tin 

Gallium  
Cadmium  

NOTE.  —  Winklemann,  Schott,  and  Straulel  (Wied  Ann.  61,  63,  1897,  68,  1899)  give  the  following  coeffi- 
cients (among  others)  for  various  Jena  glasses  in  terms  of  the  volume  decrease  divided  by  the  increase  of 
pressure  expressed  in  kilograms  per  square  millimeter: 

No.                               Glass. 

Compres- 
sibility. 

1 
Xo. 

Glass. 

Compres- 
sibility. 

665           .. 

7520 
5800 
4530 
3790 

2154 
S  208 
500 
S  196 

Kalible 
Heavies 
Very  H 
Tonerdl 

silicat 

3660 

1209        Barytbo 
16        Nutnmk 
278 

'osilicat 

tBleisilicat. 
eavy  Bleisili( 
sorat  with  s< 

.      3550 
e     3470 

ilkzinksilicat  

:at  
)dium,  baryt 

The  following  values  in  cm2/kg  of  io«  X  Compressibility  are  given  for  the  corresponding  temperatures  by 
Griineisen,  Ann.  der  Phys.  33,  p.  65,  1910. 

Al  —  191°,  1.32;  17°,  1.46;  125°,  1.70.                                        Fe  —  190°,  0.61;  18°,  0.63;  165°,  0.67. 
Cu  —  191°,  0.72;  17°,  0.77;  165°,  0.83.                                         Ag  —  191°,  0.71;  16*,  0.76;  166°,  0.86. 
Pt  —  189°,  0.37;  17°,  0.39;  164°,  0.40.                                        Pb  —  191°,  (2.5);  14°,  (3.2). 

References  to  Table  92,  p.  107: 

(1)  Bridgman,  Pr.  Am.  Acad.  49,  i,  1913; 

(2)  Roentgen,  Ann.  Phys.  44,  i,  1891; 

:;tni-l'al;izzo,  Mem.  Acad.  Lin.  3,  18,  1883; 
:^'man,  Pr.  Am.  Acad.  48,  341,  1912; 
(s)  Adams,  Williamson,  J.  Wash.  Acad.  Sc.  9,  Jan.  19, 
1919; 

(6)  Richards,  Boyer,  Pr.  Nat.  Acad.  Sc.  4,  389,  1918; 

(7)  Richanl-,,  J.  Am.  Ch.  Sex:.  37,  1646,  1915; 

\m.  Acad.  47,  381,  1911; 


(9)  Amagat,  C.  R.  73,  143,  1872; 
do)  Amagat,  C.  R.  68,  1170,  1869; 
(n)  Amagat,  Ann.  chim.  phys.  29,  68,  505,  1893; 

(12)  de  Metz,  Ann.  Phys.  41,  663,  1890; 

(13)  Adams,  Williamson,  Johnston,  J.  Am.  Chem.  Soc. 

41,  27,  1919; 

(14)  Colladon,  Sturm,  Ann.  Phys.  12,  39,  1828; 

(15)  Quincke,  Ann.  Phys.  19,  401,  1883; 

(16)  Richards  el  al.  J.  Am.  Ch.  Soc.  34,  988,  1912. 


References  to  Table  93,  p.  108: 

(1)  Adams,  Williamson,  Johnston,  J.  Am.  Ch.  Soc.  41,  39, 

tpXJK 

(2)  Richards,  ibid.  37,  1646,  1915; 

(3)  Bridgman,  Pr.  Am.  Acrid.  44,  279, 1909;  47,  366, 1911; 


(4)  Adams,  Williamson,  unpublished; 

(5)  Richards,  Boyer,  Pr.  Nat.  Acad.  Sc.  4, 
(6-)  Voigt,  Ann.  Phys.  31,  1887;  36,  1888. 


5,  1918; 


SMITHSONIAN  TABLES. 


TABLE  94. 
SPECIFIC  GRAVITIES  CORRESPONDING  TO  THE   BAUME  SCALE. 

The  specific  gravities  are  for  i5.56°C  (6o°F)  referred  to  water  at  tLe  same  temperature  as  unity 
For  specific  gravities  less  than  unity  the  values  are  calculated  from  the  formula  : 


Degrees  Baume  = 


140 


Specific  Gravity 


—130. 


For  specific  gravities  greater  than  unity  from: 

Degrees  Baume  =  145  — - 


Specific  Gravity 


Specific  Gravities  less  than  i. 

0.00 

0.01 

O.O2 

0.03                 0.04 

0.05         0.06         0.07 

O.o8                  O.OQ 

Specific 

i 

Gravity. 

Degrees  Baume'. 

0.00 

1  03-33 

99-51 

95.81 

92.22 

88.75 

85.38 

82.12 

78.95       75.88       72.90 

.70 

7O.OO 

67.18 

6444 

61.78 

59-19 

56.67 

54-21 

51.82 

49-49 

47-22 

.80 

45.00 

42.84 

40-73 

38.68 

36-67 

34-7  J 

32.79 

30.92 

29.09 

27-30 

.90 

23-85 

22.17 

20.54 

18.94 

17-37 

15-83 

M-33 

12.86 

11.41 

1.  00 

IO.OO 

Specific  Gravities  greater  than  i. 

o.oo 

0.0  1 

0.02 

0.03                  0.04 

0.05     !     0.06 

' 

0.07 

0.08          0.09 

Specific 

i 

Gravity. 

Degrees  Baume. 

.OO 

O.OO 

1.44 

2.84 

4.22 

5.58 

6.91 

8.21 

9.49 

10.74 

11.97 

.IO 

13.18 

14-37 

15-54 

16.68 

17.81 

18.91 

20.00 

21.07 

22.12 

23-r5 

.20 

24.17 

25.16 

26.15 

27.11 

28.06 

29.00 

29.92 

30-83 

31-73 

32.60 

•30 
.40 

£ 

4M3 
48.33 
54.38 
59-71 
6444 

34.31 

42.16 

48.97 

54-94 
60.20 
64.89 

35^5 
42.89 
49.60 

55-49 
60.70 

65.33 

35-98 
43.60 

50.23 
56.O4 

61.18 
65.76 

36.79 
44-31 
50.84 
56.58 
61.67 
66.20 

37-59 
45.00 

51-45 
57-12 
62.14 
66.62 

38.38 

45-68 
52.05 

57.65 
62.61 

39.16 
46.36 
52-64 
58-17 
63.08 

39-93 
47-03 
53-23 
58.69 

63-54 

40.68 
47-68 
53-8o 
59-20 
63-99 

SMITHSONIAN  TABLES. 


I10  TABLE  95, 

DENSITY    IN   GRAMS    PER  CUBIC  CENTIMETER   OF  THE    ELEMENTS, 

LIQUID  OR  SOLID. 

N.  B.     The  density  of  a  specimen  may  depend  considerably  on  its  state  and  previous  treatment. 


Element. 

Physical  State. 

drams  per 
cu.  cm.* 

Tempera- 
ture °c.t 

Authority. 

Aluminum 

commercial  h'd  d'n 

2.70 

20° 

Wolf,  Bellinger,  1910 

M 

Antimony 

wrought 
vacuo-distilled 

2.65-2.80 
6.618 

2O 

Kahlbaum,  1902. 

" 

ditto-compressed 

6.691 

2O 

<« 

» 

amorphous 

6.22 

Herard. 

Argon 

liquid 

1.3345 

-I83 

Baly-Donnan. 

•• 

" 

I-4233 

—  189 

''           " 

Arsenic 

crystallized 

5-73 

M 

•• 

amorph.  br.-black 

3-70 

Geuther. 

.. 

yellow 

3-88 

Linck. 

Barium 

3-78 

Guntz. 

Bismuth 

solid 

9.70-9.90 

«• 

electrolytic 

9-747 

Classen,  1890. 

•  • 

vacuo-distilled 

9.781 

2O 

Kahlbaum,  1902. 

•• 

liquid 

IO.OO 

271 

Vincentini-Omodei. 

•' 

solid 

9.67 

271 

«               .. 

Boron 

crystal 

2-535 

Wigand. 

.1 

amorph.  pure 

2-45 

Moissan. 

Bromine 

liquid 

3.12 

Richards-Stull. 

Cadmium 

cast 

8.54-8.57 

wrought 

8.67 

M 

vacuo-distilled 

8.648 

2O 

Kahlbaum,  1902. 

M 

solid 

8-37 

318 

Vincentini-Omodei. 

" 

liquid 

7-99 

318 

«              « 

Caesium 

1-873 

2O 

Richards-Brink. 

Calcium 

1-54 

Brink. 

Carbon 

diamond 

3-52 

Wigand. 

•' 

graphite 

2.25 

<< 

Cerium 

electrolytic 

6.79 

Muthmann-  Weiss. 

" 

pure 

7.02 

»               « 

Chlorine 

liquid 

'•507 

-33-6 

1  )rugman-Ramsay. 

Chromium 

6.52-6.73 

" 

pure 

6.92 

20 

Moissan. 

Cobalt 

8.71 

21 

Tilden,  Ch.  C.  1898. 

Columbium 

8.4 

15 

M  uthmann-W'eiss. 

Copper 

cast 
annealed 

^r8-95 

2O 

Bellinger,  1911 

wrought 
hard  drawn 

8.85-8.95 

20 

«            « 

vacuo-distilled 

8.9326 

2O 

Kahlbaum,  1902. 

ditto-compressed 

8.9376 

2O 

"               " 

liquid 

8.217 

Roberts-  Wrightson. 

Erbium 

4-77 

St.  Meyer,  Z   Ph.  Ch.  37. 

Fluorine 

.  liquid 

1.14 

—  2OO 

Moissan-Dewar. 

Gallium 

5-93 

23 

de  Boisbaudran. 

Germanium 

546 

20 

Winkler. 

Glucinum 

1.85 

Humpidge. 

Gold 

cast 

'9-3 

" 

wrought 

'9-  33 

" 

vacuo-distilled 

18.88 

20 

Kahlbaum,  1902. 

14 

ditto-compressed 

19.27 

20 

«« 

Helium 
Hydrogen 

liquid 
liquid 

0.15 
0.070 

-269 

—  252 

Onnes,  1908. 
Dewar,  Ch.  News,  1904. 

Indium 

7.28    ' 

Richards. 

•To  reduce  to  pounds  per  cu.  ft.  multiply  by  62.4. 

t  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 

Compiled  from  Clarke's  Constants  of  Nature,  Landolt-Bornstein-MeyerhofTer's  Tables,  and  other  sources.   Where 
no  authority  is  stated,  the  values  are  mostly  means  from  various  sources. 

SMITHSONIAN  TABLES. 


TABLE  P5  (continued). 


Ill 


DENSITY  IN   GRAMS   PER  CUBIC  CENTIMETER  OF   THE   ELEMENTS, 

LIQUID  OR  SOLID. 


Element. 

Physical  State 

Grams  per 
cu.  cm.* 

Tempera- 
ture °c.t 

Authority. 

Iridium 

22.42 

17 

Deville-Debray 

Iodine 

4.940 

2O 

Kichards-Stull 

Iron 

pure 

7-85-7.88 

K 

gray  cast 

7-03-7-I3 

" 

white  cast 

7-58-7-73 

« 

wrought 

7.80-7.90 

«' 

liquid 

688 

Roberts-Austen 

« 

steel 

7.60-7.80 

Krypton 

liquid 

2.16 

—  146 

Ramsay-Travers 

Lanthanum 

6.15 

Muthmann-  Weiss 

Lead 

vacuo-distilled 

11.342 

20 

Kahlbaum,  1902 

M 

ditto-compressed 

u-347 

2O 

it 

II 

solid 

11.005 

3^5 

Vincentini-Omodei 

M 

liquid 

10.645 

3-5 

"               " 

" 

11 

10.597 

400° 

Day,  Sosman,  Hostetter, 

" 

" 

10.078 

850° 

1914 

Lithium 

o-534 

20 

Richards-Brink,  '07 

Magnesium 

1.741 

Voigt 

Manganese 

7.42 

Prelinger 

Mercury 

liquid 

I3-596 

o 

Regnault,  Volkmann 

«» 

M 

I3-546 

20 

•« 

M 

13.690 

—38.8 

Vincentini-Omodei 

" 

solid 

M-I93 

—  38.8 

Mallet 

" 

" 

i4-383 

—  1  88 

Dewar,  1902 

Molybdenum 

9.01 

Moissan 

Neodvmium 

6.96 

Muthmann-  Weiss 

Nickel 

8.60-8.90 

Nitrogen 

liquid 

0.810 

—195 

Baly-Donnan,  1902 

it 

" 

0.854 

—205 

"           "            " 

Osmium 

22.5 

Deville-Debray 

!     Oxygen 

liquid 

1.14 

—184 

Palladium 

12.16 

Richards-Stull 

Phosphorus  \ 

white 

1.83 

" 

red 

2.2O 

" 

metallic 

2-34 

15 

Hittorf 

Platinum 

21.37 

20 

Richards-Stull 

Potassium 

0.870 

20 

Richards-Brink,  '07 

M 

solid 

0.851 

62.1 

Vincentini-Omodei 

a 

liquid 

0.830 

62.1 

«               i< 

Praesodymium 

6-475 

Muthmann-  Weiss 

Rhodium 

12.44 

Holborn  Henning 

Rubidium 
Ruthenium 

'•532 
I  2.  06 

20 
o 

Richards-  Brink,  '07 
Toby 

Samarium 

7-7-7-8 

Muthmann-  Weiss 

Selenium 

4-3-48 

Silicon 

cryst. 

2.42 

20 

Richards-Stull-Brink 

" 

amorph. 

2-35 

15 

Vigoroux 

Silver 

cast 

10.42-10.53 

wrought 

10.6 

vacuo-distilled 

10.492 

20 

Kahlbaum,  1902 

ditto-compressed 

10.503 

20 

».                       u 

liquid 

9-51 

Wrightson 

Sodium 

0.9712 

20 

Richards-Brink,  '07 

solid 

0.9519 

97.6 

Vincentini-Omodei 

liquid 

0.9287 

97.6 

"              " 

1.0066 

—  188 

Dewar 

Strontium 

2.50-2.58 

Matthie<sen 

Sulphur 

2.0-2.1 

liquid 

I.8ll 

JI3 

Vincentini-Omodei 

1 

*To  reduce  to  pounds  per  cubic  ft.  multiply  by  62.4. 

t  Where  the  temperature  is  not  given,  ordinary  atmosphere  temperature  is  understood 
$  Black  phosphorus,  2.69,  Bridgman,  1918. 
SMITHSONIAN  TABLES. 


H2    TABLES  95 


AND  96.    DENSITY  OF   VARIOUS  SUBSTANCES. 


TABLE  95  (co*ti**e.i\  -  Density  In  grams  per  cubic  centimeter  and  pounds  per  cubic  foot  of  the  elements, 

liquid  or  solid. 


Element. 

Physical  State. 

(  Irams  per 
cu.  cm. 

Tempera- 
ture 

Authority. 

Tantalum 

1  6.6 

Tellurium 
Thallium 

crystallized 
amorphous 

6.25 

6.02 

n.86 

20 

Beljankin. 
Richards-Stull. 

Thorium 

12.16 

17           Bolton. 

Tin 

white,  cast 

7.29 

Mutthiessen. 

H 

"      wrought 

7-3° 

" 

"      crystallized 
"      solid 

6.97-7.18 
7.184 

226 

Vincentini-Omodei 

" 

liquid 

6.99                 226 

See  Table  65 

It 

gray 

5-8 

Titanium 

4-5                      18 

Mixter. 

Tungsten 
Uranium 

18.6-19.1 
18.7                        !3           Zimmerman*. 

Vanadium 

5.69 

Ruff-Martin. 

Xenon 

liquid 

109           Ramsay-Travers. 

Yttrium 

3.80 

St.  Meyer. 

Zinc 

cast 

7.04-7.16 

,', 

wrought 
vacuo-distilled 

7.19 
6.92 

20 

Kahlbaum,  1902. 

I 

ditto-compressed 
liquid 

7-13 
6.48 

20 

Roberts-  Wrightson. 

Zirconium 

6.44 

TABLE  96.  —  Density  in  grams  per  cubic  centimeter  and  in  pounds  per  cubic  foot  of  different  kinds  of  wood. 

The  wood  is  supposed  to  be  seasoned  and  of  average  dryness. 


Wood. 

Grams 
per  cubic 
centimeter. 

Pounds 
per  cubic 
foot. 

Wood. 

Grams 
per  cubic 
centimeter. 

Pounds  | 
per  cubic  | 
foot. 

Alder 

0.42-0.68 

26-42 

Hazel 

0.6o-0.8o 

37-49 

Apple 

0.66-0.84 

41-52 

Hickory 

0.60-0.93 

37-58 

Ash 

0.65-0.85 

40-53 

Holly 

0.76 

47 

Bamboo 
Basswood.    See  Linden. 

0.31-0.40 

19-25 

Iron-bark 
Juniper 

1.03 
0.56 

64 
35 

Beech 

0.70-0.90 

43-56 

Laburnum 

0.92 

57 

Blue  gum 

I.OO 

62 

Lancewood 

0.68-1.00 

42-62 

Birch 

0.51-0.77 

32-48 

Lignum  vitae 

I.I7-I-33 

73-83 

Box 

0.95-1.16 

59-72 

Linden  or  Lime-tree 

0.32-0.59 

20-37 

Bullet-tree 
Butternut 

IXK 

0.38 

65 

24 

Locust 
Logwood 

0.67-0.71 
.91 

42-44  > 
57 

Cedar 
Cherry 

0.49-0.57 
0.70-0.90 

30-35 

43~56 

Mahogany,  Honduras 
"      '     Spanish 

0.66 
0.85 

4i 

53 

Cork 

0.22-0.26 

14-16 

Maple 

0.62-0.75 

39-47 

I  )ogwood 

0.76 

47 

Oak 

0.60-0.90 

37-56 

Ebony 

'•11-1.33 

69-83 

Pear-tree 

0.61-0.73 

38-45 

Kim 

0.54-0.60 

34-37 

Plum-tree 

0.66-0.78 

41-49 

Fir  or  Pine,  American 

Poplar 

0-35-0-5 

22-31 

White 

0-35-0.50 

22-31 

!   Satinwood 

0-95 

59 

Larch 
Pitch 

0.50-0.56 
0.83-0.85 

31-35 
52-53 

Sycamore 
Teak,  Indian 

0.40-0.60 
0.66-0.88 

24-37 
4i-55 

Red 

0.48-0.70 

3°-44 

"      African 

0.98 

61 

Scotch 

0-43-0.53 

27-33 

Walnut 

0.64-0.70 

40-43 

Spruce 
Yellow 

0.48-0.70 
0.37-0.60 

30-44 
23-37 

Water  gum 
Willow 

I.OO 

0.40-0.60 

62 

24-37 

Greenheart 

0.93-1.04 

58-65 

*  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 
SMITHSONIAN  TABLES. 


TABLE  97. 


DENSITY  IN  GRAMS  PER  CUBIC  CENTIMETER  AND  POUNDS  PER  CUBIC 
FOOT  OF  VARIOUS  SOLIDS. 

N.  B.     The  density  of  a  specimen  depends  considerably  on  its  state  and  previous  treatment  ;  especially  is  this  the 
case  with  porous  materials. 


Material. 

Grams  per 

Pounds  per 

Material. 

Grams  per 

Pounds  per 

cu.  cm. 

cu.  foot. 

cu.  cm. 

cu.  foot. 

Agate 

2.5-2.7 

156-168 

Gum  arabic 

1.3-1.4 

80-  85 

Alabaster  : 

Gypsum 

2-3I-2.33 

144-145 

Carbonate 

2.69-2.78 

168-173 

Hematite 

4-9-5-3 

»  J 

306-330 

Sulphate 

2.26-2.32 

I4I-I45 

Hornblende 

3-° 

I87 

Albite 
Amber 

2.62-2.65 
I.o6-I.Il 

163-165 

66-  69 

Ice 

Ilmenite 

0.917 
4-5-5- 

57-2 
280-310 

Amphiboles 

2.9-3.2 

180-200 

Ivory 

1.83-1.92 

114-120 

Anorthite 

2.74-2.76 

171-172 

Labradorite 

2.7-2.72 

168-170 

Anthracite 

1.4-1.8 

87-112 

Lava  :  basaltic 

2.8-3.0 

I75~l85 

Asbestos 

2.O-2.8 

125-175 

trachytic 

2.0-2.7 

125-168 

Asphalt 

I.I-I-5 

69-  94 

Leather  :  dry 

0.86 

54 

Basalt 

2.4-3.1 

150-190 

greased 

i.  02 

64 

Beeswax 

0.96-0.97 

60-  6  r 

Lime  :  mortar 

1.65-1.78 

103-111 

Beryl 

2.69-2.7 

168-168 

slaked 

1.3-1.4 

81-  87 

Biotite 

2.7-3.1 

170-190 

Limestone 

2.68-2.76 

167-171 

Bone 

1.7-2.0 

106-125 

Litharge  : 

Brick 

1.4-2.2 

87-137 

Artificial 

9-3-9-4 

580-585 

Butter 

0.86-0.87 

53-  54 

Natural 

7.8-8.0 

490-500 

Calamine 

4-1-4-5 

255-280 

Magnetite 

4-9-5-2 

306-324 

Caoutchouc 

0.92-0.99 

57-62 

Malachite 

3-7-4-  i 

231-256 

Celluloid 

i-4 

»7 

Marble 

2.6-2.84 

160-177 

Cement,  set 

2.7-3.0 

170-190 

Meerschaum 

0.99-1.28 

62-  80 

Chalk 

1.9-2.8 

118-175 

Mica 

2.6-3.2 

165-200 

Charcoal  :    oak 

o.57 

35 

Muscovite 

2.76-3.00 

172-225 

pine 

0.28-0.44 

1  8-  28 

Ochre 

3-5 

218 

Chrome  yellow 

6.00 

374 

Oligoclase 

2.65-2.67 

165-167 

Chromite 

4-32-4-57 

270-285 

Olivine 

3-27-3-37 

204-210 

Cinnabar 

8.12 

5°7 

Opal 

2.2 

137 

Clay 

1.8-2.6 

122-162 

Orthoclase 

2.58-2.61 

161-163 

Coal,  soft 

1.2-1.5 

75-  94 

Paper 

0.7-1.15 

44-  72 

Cocoa  butter 

0.89-0.91 

56-  57      1 

Paraffin 

0.87-0.91 

54-  57 

Coke 

1.0-1.7 

62-105      \ 

Peat 

0.84 

52 

Copal 

1.04-1.14 

65-  71 

Pitch 

1.07 

67 

Corundum 

3.9-4.0 

245-250 

Porcelain 

2-3-2.5 

I43-1  56 

Diamond  : 

Porphyry 

2.6-2.9 

162-181 

Anthracitic 

1.66 

104 

Pyrite 

4-95-5-  * 

309-318 

Carbonado 

3-oi-3-25 

188-203 

Quartz 

2.65 

165 

Diorite 

2.52 

157 

Quartzite 

2-73 

170 

Dolomite 

2.84 

177 

Resin 

1.07 

67 

Ebonite 

1.15 

72 

Rock  salt 

2.18 

136 

Emery 

4.0 

250 

Rutile 

6.00-6.5 

374-406 

Epidote 

3-25-3-5 

203-218 

Sandstone 

2.14-2.36 

I34-H7 

Feldspar 

2-55-2-75 

159-172 

Serpentine 

2.50-2.65 

156-165 

Flint 

2.63 

164 

Slag,  furnace 

2.0-3.9 

125-240 

Fluorite 

3.18 

198 

Slate 

2-6-3.3 

162-205 

Gamboge 

1.2 

75 

Soapstone 

2.6-2.8 

162-175 

Garnet 

3-  1  5-4-  3 

197-268 

Starch 

1.53 

95 

Gas  carbon 

1.88 

117 

Sugar 

1.61 

100 

Gelatine 

1.27 

1  80 

Talc 

2.7-2.8 

168-174 

Glass  :  common 

2.4-2.8 

150-'  7  5 

Tallow 

0.91-0.97 

57-  60 

flint 

2-9-5-9 

180-370 

Topaz 

3-5-3-6 

219-223 

Glue 

1.27 

80 

Tourmaline 

3-0-3-2 

190-200 

Granite 

2.64-2.76 

165-172 

Zircon 

4.68-4-70 

292-293 

Graphite 

2.30-2.72 

144-170 

SMITHSONIAN  TABLES. 


TABLE  98. 


DENSITY  IN  GRAMS  PER  CUBIC  CENTIMETER  AND  POUNDS  PER  CUBIC 
FOOT  OF  VARIOUS  ALLOYS. 


Alloy. 


Brasses:  Yellow,  7oCu  +  3°Zn,  cast 8.44  527 

rolled 8.56  534 

«•                "                  "              drawn 8.70  542 

Red,  9oCu  +  loZn 8.60  536 

White,  5oCu+5oZn 8.20  511 

Bronzes:  goCu-fioSn 8.78  548 

S5Cu+i5Sn 8.89  555 

8oCu-p-2oSn 8.74  545 

75Cu-j-25Sn 8.83  551 

German  Silver:  Chinese,  26-3Cu-|- 36.6Zn-f- 36.8Ni         .         .         .  8^30  518 

Berlin  (i)  52Cu  +  26Zn-f22Ni       ....  8.45  527 

"             «•     (2)  59Cu-f  3oZn  -f  uNi      ....  8.34  520 

"      (3)  63Cu  +  3oZn  -f  6Ni        .        .        .         .  8.30  518 

Nickelin 8.77  547 

Lead  andTin:  87.sPb+ i2.5Sn         .        .        .        .        .        .        .  10.60  661 

i6Sn 10.33  644 

10.05  627 

9-43  588 

J-3Sn 8-73  545 

Bismuth,  Lead,  and  Tin  :   53Bi  +  4oPb  -f  7Cd          ....  10.56  659 

Wood's  Metal:  5oBi+ 25Pb+ i2.5Cd+ i2.5Sn     ....  9.70  605 

Cadmium  and  Tin :  32Cd  +  68Sn 7.70  480 

Gold  and  Copper:  98 Au  +  2Cu 18.84  u?6 

"      "         "          o,6Au  -j-  4Cu J8-36  1145 

94Au-f-6Cu 17.95  ll20 

92Au-f-8Cu 17.52  1093 

ox>Au  4-  loCu 17.16  1071 

88Au-j~I2Cu 16.81  1049 

86  A  u  +  14^11 16.47  I027 

Aluminum  and  Copper:  ioAl-f-9oCu 7.69  480 

"          "           5A1  -j-  95^u 8.37  522 

3Al-f97Cu 8.69  542 

Aluminum  and  Zinc  :  91  Al  -\-gZn 2.80  175 

Platinum  and  Iridium :  9oPt+ioIr.         ...                  .         .  21.62  1348 

8«Pt+  i  Sir 21.62  1348 

66.67  Pt  +  33-33lr 21.87  !3^4 

5Pt  +  95lr 22.38  1396 

Constantmn :  6oCn  4- 4ONi 8.88  554 

Nfagnalium:  7oAl  -j-  3©Mg 2.0  125 

Manganin  :  84Cu  +  i2Mn -|- 4Ni 8.5  530 

Platinoid:  German  silver  -j-  little  Tungsten 9.0  560 


Grams 

per  cubic 

centimeter. 


Pounds 

per  cubic 

toot. 


SMITMSOM 


TABLES. 


TABLES  99-100. 

TABLE  99.-DENSITIES  OF  VARIOUS  NATURAL  AND  ARTIFICIAL 

MINERALS. 

(See  also  Table  97.) 


Name  and  Formula. 

Density 
grams 

Sp.Vol. 
cc.  per 

erence.  1 

Name  and  Formula. 

Density 
grams 

Sp.  Vol. 
cc.  per 

1 
K 

per  cc. 

gram. 

2 

per  cc. 

gram. 

"£ 

K 

Pure    compounds,    all    at 

Feldspars  : 

25°C 

Magnesia,  MgO 

3-603 

•2775 

, 

Albite  glass,  NaAlSi3O8 
art. 

2-375 

4210 

6 

Lime,  CaO 

3-306 

•3025 

2 

Albite  cryst.,  NaAlSi3O8 

Forms  of  SiO2: 

art. 

2.597 

.3851 

« 

Quartz,  natural 

2.646 

•3779 

" 

Anorthite  glass, 

"       artificial 

2.642 

•3785 

" 

CaAl2Si2O8,  art. 

2.692 

•37  *  5 

« 

Cristobalite,  artificial 

2.319 

•43  *  2 

" 

Anorthite  cryst, 

Silica  glass 

2.2O6 

4533 

u 

CaAl2Si2O8,  art. 

2-757 

.3627 

« 

Forms  of  Al2SiO5  : 

Soda  anorthite, 

Sillimanite  glass 

2-53 

•395 

3 

NaAlSiO4,  art. 

2.563 

.3902 

7 

Sillimanite  cryst. 

3.022 

•3309 

Borax,  glass,  Na2B4O7 

2.36 

.423 

6 

Forms  of  MgSiO3  : 

"       cryst.        " 

2.27 

•440 

« 

/8  Monoclinic  pyroxene 

3-  183 

.3142 

5 

Fluorite,  natural,  CaF2 

a  Orthorhombic  pyroxene 

3-i66 

•3T59 

(20°) 

3.180 

•3*45 

8 

/3'  Monoclinic  amphibole 

" 

(NH4)2S04                 (30°) 

^765 

.5666 

9 

7'  Orthorhombic  amphi- 
bole 
Glass 

2.849 
2-735 

•3510 
•3656 

« 
« 

K2S04                        (30°) 
KC1,  fine  powder      (30°) 
Forms  of  ZnS  : 

2.657 
1.984 

•3764 
.5040 

Forms  of  CaSiO3  : 

Sphalerite,  natural* 

4.090 

.2444 

10 

a  (Pseudo-wollastonite) 
£  (Wollastonite) 

2.904 
2.906 

•3444 
•3441 

2 

Wurtzite,  artificialt 
Greenockite,  artificial 

4.087 
4.820 

•2447 
.2075 

« 

Glass 

2.895 

•3454 

" 

Forms  of  HgS  : 

Forms  of  Ca2SiO4  : 

Cinnabar,  artificial 

8.176 

.1223 

" 

o  —  calcium-orthosilicate 

3.26 

•3°7 

ii 

Metacinnabar,  artifi- 

)8 —      « 

3-27 

•306 

M 

cial 

7.58 

.132 

« 

7  —      " 

2.965 

•337 

11 

ff  —      " 

Minerals  : 

Lime-alumina  compounds  : 

Gehlenite,    from    Velar- 

3CaO  •  A12O3 

3.029 

•3301 

3 

den  a 

3-°3 

•33° 

n 

«CaO*3A)A 

2.820 

•3546 

Spurrite,  from  Velardena, 

CaO  •  Al,03 
3CaO  •  5A12O3 

2.972 

•3365 

M 

2Ca2Si04  •  CaCO3 
Hillebrandite,  from  Vel- 

3-005 

.3328 

M 

3CaO  •  5A12O3,  unstable 

ardena, 

form 

3-°4 

•329 

" 

CaSiO3'Ca(OH)2 

2.684 

•3726 

(« 

Forms  of  MgSiO3  •  CaSiO3  : 
Diopside,  natural,  cryst. 

3.258 

.3069 

4 

Pyrite,  natural,  FeS, 
Marcasite,  natural,  FeS2 

5-OI2 
4-873 

•'995 
•2052 

10 

artificial,  " 
glass 

3-265 
2.846 

•3063 
•35*4 

*  Only  0.15%  Fe  total  impurity. 
t  Same  composition  as  Sphaler- 

ite. 

References:  i,  Larsen  1909;  2,  Day  and  Shepherd;  3,  Shepherd  and  Rankin,  1909;  4,  Allen  and 
White,  1909;  5,  Allen,  Wright  and  Clement,  1906;  6,  Day  and  Allen,  1905;  7,  Washington  and 
Wright,  1910;  8,  Merwin,  1911  ;  9,  Johnston  and  Adams,  1911 ;  10,  Allen  and  Crenshaw,  1912; 
II,  Wright,  1908. 

All  the  data  of  this  table  are  from  the  Geophysical  Laboratory,  Washington. 

TABLE  10O.-DENSITIES  OF  MOLTEN  TIN  AND  TIN-LEAD   EUTECTIC. 


Temperature 
Molten  tin 
37  pts.  Pb,  63,  Sn.* 

250°C. 
6.982 

8.01  1 

300° 
6-943 
7-965 

400° 
6.875 
7-879 

500° 
6.814 
7.800 

600° 

6-755 
7-731 

900° 
6.578 

1200° 

6-399 

1400° 
6.280 

1600° 
6.162 

*  Melts  at  181.    Day  and  Sosman,  Geophysical  Laboratory,  unpublished. 

For  further  densities  inorganic  substances  see  table  219. 
organic  220. 

SMITHSONIAN  TABLES. 


TABLES  101-102. 
WEIGHT  OF   SHEET    METAL. 

TABLE  101.— Weight  ol  Sheet  Metal.    (Metric  Measure.) 

This  table  gives  the  weight   in  grams  of  a  plate  one  meter  square  and  of  the  thickness  stated  in  the 

first  column. 


Thickness 

in  thou- 
sandths of 

Iron. 

Copper. 

Brass. 

Aluminum. 

Platinum. 

Gold. 

Silver. 

a  cm. 

1 

78.0 

89.0 

85.6 

26.7 

215.0 

193.0 

105.0 

2 

156.0 

178.0 

I7I.2 

53-4 

430.0 

386.0 

2IO.O 

3 
4 

234.0 
312.0 

267.0 
356.0 

256.8 
342.4 

80.  i 
1  06.8 

6450 
860.0 

579-0 
772.0 

315.0 
42O.O 

5 

390.0 

445-0 

428.0 

133-5 

1075.0 

965.0 

525-0 

6 

468.0 

534-0 

513.6 

160.2 

1290.0 

1  1  58.0 

630.0 

7 

546.0 

623.0 

599.2 

186.9 

1505.0 

I351-0 

735-0 

8 

624.0 

712.0 

684.8 

213.6 

1720.0 

1544.0 

840.0 

9 

7O2.O 

801.0 

770.4 

240.3 

1935-0 

1737.0 

945-0 

10 

780.0 

890.0 

856.0 

267.0 

2150.0 

1930.0 

1050.0 

TABLE  102.  -  Weight  of  Sheet  Metal.    (British  Measure.) 


Iron. 

Copper. 

Brass. 

Aluminum. 

Platinum. 

in  Mils. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Ounces  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Ounces  per 
Sq.  Foot. 

1 

.04058 

.04630 

.04454 

.01389 

.2222 

.1119 

1.790 

2 

3 

.08116 
.12173 

.09260 
.13890 

.08908   ' 
^3363 

.02778 
.04167 

•4445 

.6667 

.2237 
•3356 

3-579 

5-369 

4 

.16231 

.18520 

.17817 

•05556 

.8890 

-4474 

7.158 

5 

.20289 

.23150 

.22271 

.06945 

I.III2 

•5593 

8.948 

6 

•24347 

.27780 

.26725 

-08334 

J-3335 

.6711 

10.738 

7 

.28405 

.32411 

•3II79 

.09723 

1-5557 

.7830 

12.527 

8 

•32463 

•37041 

•35634 

.11112 

1.7780 

.8948 

14.3*7 

9 

.36520 

.41671 

.40088 

.I25OI 

2.0OO2 

1.0067 

1  6.106 

10 

.40578 

.46301 

•44542 

.13890 

2.2224 

1.1185 

17.896 

Gold. 

Silver. 

Thickness 
in  Mils. 

Troy 
Ounces  per 
Sq.  Foot. 

Grains  per 
Sq.  Foot. 

Troy 
Ounces  per 
Sq.  Foot. 

Grains  per 
Sq.  Foot. 

1 

1.4642 

702.8 

0.7967 

382.4 

2 

2.9285 

MOW 

I-5933 

764-8 

3 

4.3927 

2108.5 

2.3900 

II47.2 

4 

5-0570 

2811.3 

3.1867 

1529.6 

5 

7.3212 

35M-2 

3-9833 

1912.0 

6 

8.7854 

4217.0 

4.7800 

2294.4 

7 

10.2497 

4919.8 

5'5767 

2676.8 

8 
9 

II-7I39 
13.1782 

5622.7 
6325-5 

6-3734 
7.1700 

3059-2 
3441.6 

10 

14.6424 

7028.3 

7.9667 

3824.0 

SMITHSONIAN  TABLES. 


TABLE  103. 


117 


DENSITY  OF  LIQUIDS. 

Density  or  mass  in  grams  per  cubic  centimeter  and  in  pounds  per  cubic  foot  of  various  liquids. 


Liquid. 

Grams  per 
cubic  centimeter. 

Pounds  per 
cubic  foot. 

Temp.  C. 

Acetone         .                           .... 
Alcohol,  ethyl                           .... 
methyl                      .... 
Aniline           .                          .... 
Penzene        .                         .... 
Bromine        .                           .... 
Carbolic  acid  (crude)  *         .... 

0.792 
0.807 
0.810 
1-035 

3.187 
0.950-0.965 

T    2O  "? 

49-4 
50-4 
50-5 
64.5 
56.1 
199.0 
59.2-60.2 

80  6 

20° 
0 
0 

o 

0 
0 

15 

I    480 

02  ^ 

18 

O  8C.7 

r-j    c 

IOO 

Ether    

O   7^6 

OoO 
^r   Q 

o 

o  66—0  69 

A  I    O—  A  1   O 

Glycerine      

1.260 
o  87=; 

78.6 
ZA  6 

0 
IOO 

Miik      ..::.:    : 

Naphtha  (wood)   ...... 
Naphtha  (petroleum  ether)  .... 
Oils  :  Amber         
Anise-seed  
Camphor     
Castor         ..... 

1.028-1.035 
0.848-0.810 
0.665 
0.800 
0.096 
0.910 
0060 

64.2-64.6 
52.9-50.5 

41.5 
49.9 
62.1 
56.8 
60  * 

0 

15 
15 

16 

1C 

i  04—1  06 

65  -66 

2C, 

002^ 

C7   7 

je 

o  926 

j/  •  / 

57  8 

16 

Creosote      ...... 
Lard             
Lavender     .         .         .         .         . 
Lemon         ...... 
Linseed  (boiled)  
Neat's  foot  
Olive  

1.040-1.100 
0.920 

0.877 

0.844 

0.942 
0.913-.  917 
o  918 

64.9-68.6 
57-4 
54.7 

11:1 

57.0-57-2 

C7     -3 

15 

II 

16 
15 

1C 

Palm  ...... 

Ooo^ 

^6  ; 

JC 

o  650 

3UO 

40  6 

o 

« 

o  62^ 

?8  o 

2C. 

Peppermint          
Petroleum   
(light)          .... 
Pine   
Poppy           
Rapeseed  (crude)            .... 
(refined)       .... 

0.90-.  92 
0.878 
0.795-0-805 
0.850-0.860 
0.924 
0.915 
0.913 

o  055 

50-57 
54-8 
49.6-50.2 
53.0-54.0 
•57.7 
57-1 
57-0 

CQ    6 

25 
0 

15 
15 

15 
15 

1C 

cc 

25 

O  QIO 

=7.7 

30 

i<          « 

Train  or  Whale           . 
Turpentine.                   .... 
Valerian      .                  .... 
Wintergreen                 .... 
Pyroligneous  acid                  .... 
Water  .                  .                  .... 

0.906 
0.918-0.925 

0.873 
0.965 

1.18 
0.800 

I.OOO 

56.5 
57.3-57.7 
54.2 
60.2 

74. 
49-9 
62.4 

00 

15 

16 
16 

25 

0 

4 

SMITHSONIAN  TABLES. 


Il8  TABLE  104. 

DENSITY  OF  PURE  WATER  FREE  FROM  AIR.    O°  TO  41°  C. 

[Under  standard  pressure  (76  cm),  at  every  tenth  part  of  a  degree  of  the  international  hydrogen  scale  from  o°  to  41° 

C,  in  grams  per  milliliter  J] 


De- 
crees 

Tenths  of  Degrees. 

Mean 
Differ- 

Sentl- 

ences. 

rrade. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

I 

3 

4 

0.9998681 
9267 
9679 
9922 

I.OOOOOOO 

8747 
93^5 
9711 

9937 
*9999 

8812 
9363 
9741 

*"51 

887q 
9408 
9769 
9962 

*9992 

8936 

9452 
9796 

9973 
*9986 

8996 

9494 
9821 
998i 
*9979 

9053 
9534 
9844 
(#88 
*9970 

9I09 

9573 
9866 

9994 
*996o 

9i63 
96io 
9887 
9998 
*9947 

92l6 

9645 
9905 

*0000 

*9934 

4-  59 

4-  24 

±1 

5 

0.999  9919 

9902 

9884 

9864 

9842 

9819 

9795 

9769 

9742 

9713 

-  24 

6 

9682 

9650 

9617 

9582 

9545 

9507 

9468 

9427 

9385 

934i 

—  39 

8 

9296 
8764 

9249 
8703 

9201 
8641 

9151 

8577 

9100 
8512 

9048 

8445 

8994 
8377 

8308 

8237 

8823 
8165 

El 

9 

8091 

8017 

7940 

7863 

7784 

7704 

7622 

7539 

7455 

7369 

—  81 

10 

7282 

7*94 

7105 

7014 

692I 

6826 

6729 

6632 

6533 

6432 

—  9q 

n 

633  r 

6228 

6124 

6020 

59  1  3 

5805 

5696 

5586 

5474 

5362 

—  108 

12 

5248 

5*32 

5016 

4898 

4780 

4660 

4538 

4415 

429I 

4166 

—  121 

13 

4040 

3912 

3784 

3523 

339  r 

3257 

3122 

2986 

2850 

—133 

27I2 

2572 

2431 

2289 

2147 

2003 

1858 

1711 

i564 

1416 

—145 

15 

1266 

1114 

0962 

0809 

0653 

0499 

0343 

0185 

0026 

*9865 

—156 

16 

0.998  9705 

9542 

9378 

9214 

^48 

8881 

8713 

8544 

8373 

8202 

—  168 

1  7 

8029 

7856 

7681 

7505 

7328 

715° 

697i 

6791 

6610 

6427 

—178 

18 

6244 

6058 

5873 

5686 

5498 

5309 

5"9 

4927 

4735 

4541 

—190 

i  19 

4347 

4152 

3955 

3757 

3558 

3358 

3158 

2955 

2752 

2549 

—  200 

20 

2343 

2137 

1930 

1722 

1511 

1301 

IOC)O 

0878 

0663 

0449 

—211 

21 

0233 

0016 

*9799 

*958o 

*9359 

*9i39 

*89i7 

*8694 

*847O 

*8245 

—  221 

22 

0.997  8019 

7792 

7564 

73351  7104 

6873 

6641 

6408 

6173 

5938 

—232 

23 

5702 

5466 

5227 

4^8   4747 

4506 

4264 

4021 

3777 

—242 

24 

3286 

3039 

2790 

2541   2291 

2040 

1788 

1535 

1280 

1026 

—252 

i  *6 

0770 
0.9968158 

7892 

0255 
7624 

*9997  *9736 
7356   7087 

*9476 
6817 

*92I4 

6545 

*895i 
6273 

*8688 
6000 

*8423 

5726 

—26l 
—271 

'  27 
28 
29 

2652 
0.995  976i 

5^6 
2366 
9466 

4898 
2080 
9171 

4620 
8$ 

4342 
1505 
8579 

4062 
1217 
8282 

3782 

0928 

7983 

3500 
0637 
7684 

3218 
0346 
7383 

2935 
0053 
7083 

—280 

30 

6780 

6478 

6174 

5869 

5564 

5258 

495° 

4642 

4334 

4024 

—3°7 

31 

37H 

3401 

*3°89 

2776 

2462 

2147 

1832 

I5I5 

1198 

0880 

—  315 

32 

0561 

0241 

*9599 

+9276 

*8954 

*83o4 

*7979 

*7653 

—324 

33 

0-994  7325 

6997 

6668 

6338   6007 

5676 

5345 

5011 

4678 

4343 

—332 

34 

4007 

3671 

3335 

2997 

2659 

2318 

1978 

1638 

I296 

0953 

—340 

35 

0610 

0267 

*9922 

*9576  *923o 

*8883 

*8534 

*8i86 

*7837 

*7486 

—347 

36 

0.9937136 

6784 

6432 

6078   5725 

5369 

5OI4 

4658 

43oi 

3943 

37 

35»5 

3226 

2866 

2505 

2144 

1782 

1419 

1055 

o69i 

0326 

—  362 

i  38 

0.9929960 

9593 

9227 

8859 

8490 

8120 

7751 

7380 

7008 

6636 

—370 

39 

6263 

5890 

5516 

5140 

4765 

4389 

4011 

3634 

3255 

2876 

—377 

40 

2497 

2116 

1734 

1352 

097! 

0587 

0203 

*98i8 

*9433 

*9°47 

-384 

41 

0.991  8661 

1  According  to  P.  Chappuis,  Bureau  international  des  Poidt  et  Mesures,  Travaux  et  Mdmoires,  13;  1907. 
SMITHSONIAN  TABLES. 


TABLE  105.  1 19 

VOLUME  IN  CUBIC  CENTIMETERS  AT  VARIOUS  TEMPERATURES  OF  A 
CUBIC  CENTIMETER  OF  WATER    FREE  FROM  AIR  AT  THE 
TEMPERATURE    OF    MAXIMUM    DENSITY.      0°  TO  4O°  C. 

Hydrogen  Thermometer  Scale. 


Temp. 

.0 

.1 

.2 

•3 

•4 

•  5 

.6 

•7 

.8 

•9 

0 

1.000132 

125 

118 

112 

1  06 

IOO 

095 

089 

084 

079 

I 

073 

069 

064 

059 

055 

051 

047 

043 

039 

°35 

2 

032 

029 

026 

023 

020 

018 

016 

013 

on 

009 

3 

008 

006 

005 

OO4 

003 

002 

OOI 

OOI 

000 

000 

4 

000 

000 

oo(9 

OOI 

OOI 

002 

003 

OO4 

005 

007 

5 

008 

OIO 

OI2 

014 

016 

018 

02  1 

023 

026 

O2Q 

6 

032 

035 

039 

042 

046 

050 

054 

058 

062 

066 

7 

070 

075 

080 

085 

090 

095 

101 

1  06 

112 

118 

8 

124 

130 

J37 

142 

149 

156 

162 

169 

I76 

184 

9 

191 

198 

206 

214 

222 

230 

238 

246 

254 

263 

10 

ii 

272 
367 

281 

377 

388 

398 

308 
409 

420 

327 

43° 

337 
441 

347 
453 

464 

12 

476 

487 

499 

511 

522 

534 

547 

559 

584 

13 

596 

609 

623 

636 

649 

661 

675 

688 

702 

7i5 

14 

729 

743 

757 

772 

786 

800 

815 

830 

844 

859 

15 

873 

890 

905 

920 

935 

951 

967 

983 

998 

015* 

16 

1.001031 

047 

063 

080 

097 

"3 

130 

147 

164 

182 

17 

198 

216 

233 

252 

269 

287 

3°5 

323 

34i 

358 

18 

378 

396 

41  c 

433 

452 

490 

510 

548 

!9 

568 

588 

606 

626 

646 

667 

687 

707 

728 

748 

20 

769 

790 

811 

832 

853 

874 

895 

916 

938 

96o 

21 

98! 

002* 

024* 

046* 

068* 

091* 

113* 

135* 

158* 

181* 

22 
23 

1.002203 
436 

226 
459 

249 
483 

271 
5°7 

295 

556 

342 
58i 

364 
605 

389 
629 

412 
654 

24 

679 

704 

729 

754 

779 

804 

829 

854 

879 

90S 

25 

932 

958 

983 

OIO* 

036* 

061* 

088* 

115* 

141* 

1  68* 

26 

1.003195 

221 

248 

275 

302 

330 

357 

384 

412 

439 

27 

467 

495 

523 

55° 

579 

607 

635 

663 

692 

720 

28 

749 

776 

806 

836 

865 

922 

981 

Oil* 

29 

1.004041 

069 

IOO 

129 

160 

189 

220 

250 

280 

310 

3° 

34, 

371 

403 

432 

464 

494 

526 

557 

588 

619 

31 

651 

682 

7*3 

744 

777 

808 

840 

872 

9<H 

936 

32 

968 

OOI* 

033* 

066* 

098* 

132* 

163* 

197* 

229* 

263* 

33 

1.005296 

328 

361 

395 

427 

461 

496 

53° 

562 

597 

1  34 

631 

665 

698 

732 

768 

802 

836 

871 

904 

940 

35 

1 

975 

009* 

044* 

078* 

115* 

150* 

I85* 

219* 

255* 

290* 

Reciprocals  of  the  preceding  table. 


SMITHSONIAN  TABLES. 


120 


TABLE  106. 

DENSITY  AND   VOLUME   OF  WATER. 
—10°  TO  +250°  C. 

The  mass  of  one  cubic  centimeter  at  4°  C.  is  taken  as  unity. 


Temp.  C. 

Density. 

Volume. 

Temp.  C. 

Density. 

Volume. 

—10° 

0.99815 

I.OOI86 

+35° 

0.99406 

1.00598 

=3 

.  843 
869 

157 

I3l 

36 

37 

371 
336 

669 

—7 

892 

108 

38 

300 

706 

-6 

912 

088 

39 

263 

743 

—5 

0.99930 

1.00070 

40 

0.99225 

1.00782 

—4 
—3 

945 
958 

°55 
042 

4i 
42 

.  l87 
147 

821 
861 

—  2 

970 

031 

43 

107 

901 

—  I 

979 

02  1 

44 

066 

943 

+0 

0.99987 

1.00013 

45 

0.99025 

1.00985 

I 

993 

007 

46 

0.98982 

1.01028 

2 

997 

003 

47 

94° 

072 

3 

999 

001 

48 

896 

116 

4 

I.OOOOO 

I.OOOOO 

49 

852 

162 

5 

0.99999 

I.OOOOI 

50 

0.98807 

1.01207 

6 

997 

003 

51 

762 

254 

7 

993 

007 

52 

715 

301 

8 

98§ 

OI2 

53 

669 

349 

9 

981 

019 

54 

621 

398 

10 

0-99973 

1.00027 

55 

0.98573 

1.01448 

ii 

12 

963 
9S2 

048 

60 
65 

324 
059 

705 
979 

'3 

940 

060 

70 

0.97781 

1.02270 

H 

927 

073 

75 

489 

576 

15 

0.99913 

1.00087 

80 

0.97183 

1.02899 

16 

897 

103 

85 

0.96865 

1.03237 

17 

880 

120 

90 

534 

590 

18 

862 

138 

95 

192 

959 

J9 

843 

"57 

IOO 

0.95838 

1-04343 

20 

0.99823 

1.00177 

110 

0.9510 

•0515 

21 

802 

198 

120 

•9434 

.0601 

22 
23 

780 
757 

220 
244 

130 
140 

•9352 
.9264 

.0693 
.0794 

24 

733 

268 

150 

•9173 

.0902 

25 

0.99708 

1.00293 

160 

0.9075 

.1019 

26 

682 

320 

170 

.8973 

•1145 

27 

655 

347 

1  80 

.8866 

.1279 

28 

627 

375 

190 

.8750 

.1429 

29 

598 

404 

200 

.8628 

.1590 

30 

0.99568 

1.00434 

210 

0.850 

.177 

3' 

537 

465 

220 

.837 

•'95 

32 
33 

506 

473 

497 
53° 

230 
240 

.823 
.809 

3 

34 

440 

563 

250 

•794 

•259 

From  —  10°  to  o°  the  values  are  due  to  means  from  Pierre,  Weidner,  and 
Rosetti ;  from  o°  to  41°,  to  Chappuis,  42°  to  100°,  to  Thiesen;  110°  to  250°,  to 
means  from  the  works  of  Ramsey,  Young,  Waterston,  and  Him. 

SMITHSONIAN  TABLES. 


TABLE  1O7. 


121 


DENSITY  OF  MERCURY 

Density  or  mass  in  grams  per  cubic  centimeter,  and  the  volume 
in  cubic  centimeters  of  one  gram  of  mercury. 




Mass  in 

Volume  of 

i 

Mass  in 

Volume  of 

Temp.  C. 

grams  per 

i  gram  in 

Temp.C 

grams  per 

i  gram  in 

cu.  cm. 

cu.  cms. 

cu.  cm. 

cu.  cms. 

—10° 

13-6198 

0.0734225 

30° 

13.5213 

0.0739572 

—9 

6173 

4358 

31 

5189 

9705 

-8 

6148 

4492 

32 

5164 

9839 

—7 

6l24 

4626 

33 

5140 

9973 

-6 

6099 

4759 

34 

5Il6 

40107 

—5 

13.6074 

0.0734893 

35 

13.5091 

0.0740241 

—4 

6050 

5026 

36 

5066 

0374 

—3 

6025 

5160 

37 

5042 

0508 

—  2 

6OOO 

5293 

38 

5018 

0642 

—I 

5976 

5427 

39 

4994 

0776 

—0 

13.5951 

0.0735560 

40 

13.4909 

0.0740910 

I 

5926 

5694 

50 

4725 

2250 

2 

5828 

60 

4482 

3592 

3 

5877 

596i 

70 

4240 

4 

5852 

6095 

80 

3998 

6282 

5 

13.5827 

0.0736228 

90 

13.3723 

0.0747631 

6 

5803 

6362 

100 

3515 

8981 

7 

5778 

6496 

no 

3279 

50305 

8 

5754 

6629 

1  20 

3040 

1653 

9 

5729 

6763 

130 

2801 

3002 

1O 

13.5704 

0.0736893 

140 

13.2563 

0.0754  '54 

ii 

5680 

7030 

150 

2326 

5708 

12 

5655 

7164 

1  60 

2090 

7064 

13 

5630 

7298 

170 

i853 

8422 

14 

5606 

7431 

180 

1617 

9784 

15 

13.5581 

0.0737565 

19O 

13-1381 

0.0761149 

16 

5557 

7699 

200 

1145 

2516 

17 

5532 

7832 

210 

0910 

3886 

18 

5507 

7966 

220 

0677 

5260 

19 

5483 

8100 

230 

0440 

6637 

20 

13.5458 

0.0738233 

240 

13.0206 

0.0768017 

21 

5434 

8367 

250 

12.9972 

9402 

22 

5409 

8501 

260 

9738 

7090 

23 

5385 

8635 

270 

9504 

2182 

24 

536o 

8768 

280 

9270 

3579 

25 

13.5336 

0.0738902 

29O 

12.9036 

0.0774979 

26 

9036 

300 

8803 

6385 

27 

5287 

9170 

310 

8569 

7795 

28 

5262 

9304 

320 

8336 

9210 

29 

5238 

9437 

330 

8102 

80630 

3O 

13.5213 

0.0739571 

340 

350 

12.7869 
7635 

0.0782054 
3485 

360 

7402 

4921 

Based  upon  Thiesen  und  Scheel,  Tatigkeitber.  Phys.-Techn.  Reichsanstalt, 
1897-1898;  Chappuis,  Trav.  Bur.  Int.  13,  1903.  Thiesen,  Scheel,  Sell; 
Wiss.  Abh.  Phys.-Techn.  Reichsanstalt  2,  p.  184,  1895,  and  i  liter 
=  1.000027  cu.  dm. 

SMITHSONIAN   TABLES. 


122 


TABLE  1O8. 
DENSITY    OF    AQUEOUS    SOLUTIONS, 


The  following  table  gives  the  density  of  solutions  of   various  salts  in   water.     The  numbers  give  the   weight  in 
grams  per  cubic  centimeter.     For  brevity  the  substance  is  indicated  by  formula  only. 


Substance. 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 
the  solution. 

u 

d 

Authority. 

5 

10 

15 

20 

25 

3° 

40 

5° 

60 

KOH' 

1.047 
1.040 

1.008 

1.082 

1.127 

I.2I4 
I.I76 

1.284 
1.229 

'•354 
1.286 

I'5°3 
1.410 

1.659 
L538 

1.809 
1.666 

15- 

Schiff. 

M 

Na20      .     .     . 

1.073 

1.144 

i.  218 

1.284 

1.354 

1.421 

L557 

1.689 

1.829 

'5- 

11 

NaOH    .     .     . 

1.058 

1.114 

1.169 

1.224 

1.279 

1.331 

1.436 

J-539 

1.642 

J5" 

" 

NH8  .... 

0.9/8 

0.959 

0.940 

0.924 

0.909 

0.896 

- 

16. 

Carius. 

NH4C1   . 
KC1    .     .     .     . 

1.015 
1.031 

1.030 
1.065 

1.044 
1.099 

1.058 
I-I35 

1.072 

- 

- 

- 

- 

15- 

'5- 

Gerlach. 

NaCl       .     .     . 

I  O7  C 

1.072 

I.  IIO 

I.15O 

I  IQI 

_ 

_ 

— 

_ 

Ci 

LiCl  .     . 

I  O^Q 

1.085 

1.116 

l.jyi 

1.181 

^•2  S  5 

i  ?. 

4( 

CaCl2     .     .    . 

I.04I 

\3& 

1.132 

1.181 

1.232 

1.286 

1.402 

- 

- 

j 

(I 

CaCl2  +  6H2O 

I.OI9 

1.040 

1.061 

1.083 

I.IO5 

1.128 

1.176 

1.225 

1.276 

18. 

Schiff. 

AlCla      .     .     . 

1.030 

1.072 

i.  in 

i-i53 

I.I96 

1.241 

1.340 

15- 

Gerlach. 

MgCl2    .     .     . 

I.04I 

1.085 

1.130 

1.177 

1.226 

1.278 

— 

— 

" 

MgCl2-f-6H2O 

I.OI4 

1.032 

1.049 

1.067 

1.085 

1.103 

1.141 

1.183 

1.222 

24. 

Schiff. 

ZnCl2      .     .     . 

1.043 

1.089 

1-13S 

1.184 

1.236 

1.289 

1.417 

1-563 

1-737 

'9-5 

Kremers. 

CdCl2     .     .    . 

1.043 

1.087 

1.138 

1.193 

1.254 

I.3!9 

1.469 

T.653 

1.887 

19-5 

« 

SrCl2  . 

T  O<14 

1.092 

1  .  1  4^ 

i  108 

T    ">  •">  I 

s"*  pi-lQ^Vv 

SrClo  +  6H2O 

1.027 

1.053 

.1.082 

1.  1  ytj 
I.  Ill 

I.O42 

1.174 

1.242 

1-317 

._ 

J5. 

u 

BaClo     .     .     . 
BaCl2+2H20 

1.045 

I-°35 

1.094 
1.075 

1.147 
1.119 

I.2O5 
I.I66 

1.269 
I.2I7 

1-273 

- 

- 

21. 

u 

Schiff. 

CuClo     .     .     . 

1.044 

1.091 

1.155 

1.  221 

I.29I 

1.360 

1-527 

_ 

_ 

I7>5 

Franz. 

NiCl2     .    .    . 

1.048 

1.098 

1-157 

1.223 

1.299 

~L 

_ 

_ 

!7-5 

« 

HgCl2     .     .     . 
Fe2Cl6    .     .    . 
PtCl4.     .     .     . 

1.041 
1.041 
1.046 

1.092 
1.086 
1.097 

1.130 

I-I53 

I.I79 
I.2I4 

1.232 

1.285 

1.290 
1.362 

1.413 
1.546 

T-545 
1-785 

1.668 

20. 

Men  dele  jeff. 
Hager. 
Precht. 

SnCl2+2H2O 
14  -j-  5H2O 

1.032 
1.029 

1.067 
1.058 

1.104 
1.089 

1.  122 

I.I85 

I-I57 

1.229 
I-I93 

1.329 

1.274 

1.444 
1-365 

1.580 
1.467 

15- 

Gerlach. 

LiBr  .... 

I-°33 

1.070 

i.  in 

I-I54 

1.202 

1.252 

1.366 

1.498 

J9-5 

Kremers. 

KBr   .... 

1-035, 

1-073 

1.114 

I-I57 

1.205 

L254 

1.364 

_ 

" 

NaBr      .     .     . 

1.038 

1.078 

1.123 

I.I72 

1.224 

1.279 

1.408 

!-563 

- 

19-5 

u 

MgBr2    .     .     . 

rf      ft 

1.041 

1.085 

1.135 

I.I89 

1-245 

1.308 

1.449 

1.623 

_ 

J9-5 

u 

ZnBr2     .     .     . 
CdBr2     .     , 
CaBr2     .     .    . 
BaBr2     .     .     . 

1.043 
1.041 
1.042 
1.043 

1.088 
1.087 
1.090 

1.144 
I-I39 
I-I37 
1.142 

1.202 
I.I97 
I.I92 
I.I99 

1.263 

1.258 
2.250 
I.26o 

1.328 

I-327 

J-473 
1.479 

*-4S9 
1.483 

1.648 
1.678 
1.639 
1.683 

1.873 

19-S 
19-5 

u 

a 

SrHro 
KI     ".     .     .     . 
I.il      .     . 

1.043 
1.036 

1.089 
1.076 
1.077 
i.  080 
1.089 

1.140 

1.118 

1.  122 
I.I26 
I.I38 

I.IgS 
1.164 
I.I7O 

I.I77 
I.I94 

1.200 

1.216 

1.222 
1.232 
1-253 

'•328 
1.269 
1.278 
1.292 
1.316 

1.489 

T-394 
1.412 
1.430 
1.467 

1.693 

1-544 

T-573 
1.598 
1.648 

1-953 
1.732 

1-775 
i.  808 

1-873 

19-5 
19-5 
19-5 
19.5 

u 

Nal    .     .     .     . 
ZnI2   .     .     . 

1.038 
1.043 

CdI2  .     . 

i.  086 

I.I36 

I.I92 

I.25I 

,.3,7 

1.474 

1.678 

_ 

I95 

u 

Mjil-j.     .     .     . 
CaI2  .... 
-     .     .     . 
BaI2  .... 

1.041 
1.042 
i  .043 
1.043 

i.  086 
1.088 
1.089 
1.089 

I.I38 
I.I40 

I.I92 
I.I96 
I.I98 
I.I99 

1.252 
1.258 
1.260 
1.263 

1.318 

'•319 

1.328 

'•331 

1.472 

1-475 
1.489 

1-493 

1.666 
1.663 
1.693 
1.702 

1.908 

r-953 
1.968 

19-S 
19-5 
19-5 

« 

NaClO8. 

.     . 

'•035 
1.039 

1.068 

i.  08  1 

1.106 
1.127 

I-I45 
I.I76 

I.I88 
1.229 

JJ33 

1.329 

- 

- 

19-5 
19.5 

u 

KXO;;          .          .          . 

1.031 

1.064 

1.099 

1-13S 

_ 

_ 

_ 

_ 

Gerlach. 

NaNO,  .     .     . 
AgNO,  .    .     . 

1.031 
1.044 

1.065 
1.090 

I.IOI 

1.140 

1.140 

1.180 

'•255 

1.222 
I.322 

1.479 

1.416 
1-675 

1.918 

20.2 

Schiff. 
Kohlrausch. 

*  Compiled  from  two  papers  on  the  subject  by  Gerlach  in  the  "  Zeit.  fur  Anal.  Chim.,"  vols.  8  and  27. 
SMITHSONIAN  TABLES. 


TABLE  108  (continued). 
DENSITY    OF    AQUEOUS   SOLUTIONS. 


I23 


1 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 

the  solution. 

U 

Substance. 

d 

Authority. 

i 

5 

10 

15 

20 

25 

30 

4o 

so 

60 

H 

NH4N03     .     .     • 
Zn(N03),    .     .     . 

1.020 
1.048 

I.O4I 
1.095 

.063 

.146 

.085 
.2OI 

.107 
•263 

•'31 

-325 

1.178 
1.456 

1.229 

1.282 

17-5 

Gerlach. 
Franz. 

Zn(N03)2  +  6H2O 
Ca(N03)2    .     .     . 

1-037 

1.054 
1-075 

.118 

•"3 

.162 

.211 

.178 
.260 

1.250 
1.367 

1.329 
1.482 

1.604 

14. 

17-5 

Oudemans. 
Gerlach. 

Cu(NO3)2    .     .     . 

1.044 

1.093 

-143 

•203 

.263 

.328 

1.471 

- 

- 

17-5 

Franz. 

Sr(N03)2     .     .     . 

1.039 

1.083 

.129 

.179 

- 

- 

- 

- 

- 

19-5 

Kremers. 

Pb(N03)2     .     .     . 

1.043 

I.09I 

•143 

.199 

.262 

•332 

— 

— 

- 

17.5 

Gerlach. 

Cd(N03)2    .     .     . 

1.052 

1.097 

.150 

.212 

.283 

•355 

r-536 

1-759 

- 

17.5 

Franz. 

Co(N03)2     .     .     . 

1.045 

1.090 

•137 

.192 

.252 

.318 

1.465 

— 

— 

17-5 

" 

Ni(N03)2     .     .     . 

1.045 

1.090 

•137 

.192 

.252 

.318 

1.465 

- 

- 

17-5 

" 

Fe2(N03)6  .     .     . 

1.039 

1.076 

.117 

.I60 

.210 

.261 

T-373 

1.496 

1-657 

17-5 

n 

Mg(NO3)2+6H2O 
Mn(NO3)2+6H20 

I.OI8 
I.O25 

1.038 
1.052 

.000 

.079 

.082 
.108 

.105 
.138 

.129 
.169 

1.179 
1-235 

1.232 
1-307 

1.386 

21 

8 

Schiff. 
Oudemans. 

K2C03    .... 

1.044 

1.092 

.141 

.192 

-245 

•300 

1.417 

1-543 

- 

15 

Gerlach. 

K2CO3  +  2H2O  . 

1.037 

I.O72 

.no 

.150 

.191 

•233 

1.320 

1.415 

1.511 

15- 

Na2CO3ioH2O     . 

I.OI9 

1.038 

•057 

.077 

.098 

.118 

- 

- 

- 

15- 

" 

(NH4)2S04      .     . 

1.027 

i-°55 

.084 

•IT3 

.142 

.170 

1.226 

1.287 

- 

19. 

Schiff. 

Fe2(S04)3    .     .     . 

1.045 

1.096 

.150 

.207 

.270 

.336 

1.489 

- 

- 

18. 

Hager. 

FeSO4-|-7H2O    . 

1.025 

T-°53 

.081 

.in 

.141 

.173 

1.238 

— 

— 

17.2 

Schiff. 

MgSO4    .... 

1.051 

1.104 

.161 

.221 

.284 

- 

- 

- 

- 

15 

Gerlach. 

MgS04+7H2O. 

I.O25 

1.050 

-075 

.101 

.129 

•'55 

1.215 

1.278 

- 

15- 

" 

Na2S04+ioH2O 

I.OI9 

1.039 

•°59 

.O8l 

.102 

.124 

— 

— 

15. 

" 

CuSO4+  5H2O  . 

I.03I 

1.064 

.098 

•T34 

.173 

.213 

— 

— 

— 

18. 

Schiff. 

MnSO4  -f-  4H-)O  . 

1.031 

1.064 

1.099 

.135 

.174 

.214 

1.303 

1.398 

— 

J5- 

Gerlach. 

ZnS04-f  7H20    . 

1.027 

1-057 

1.089 

.122 

.156 

.191 

1.269 

1-443 

20.5 

Schiff. 

Fe2(S04)3.K2SO4 

+  24H20      .     . 

I.O26 

1.045 

i.  066 

1.088 

1.  112 

1.141 

— 

— 

— 

17.5 

Franz. 

1  Cr2(S04)8-K2SO4 

-|-  24H2O      .     . 

1.016 

1.033 

1.051 

1-073 

1.099 

1.126 

1.188 

1.287 

J-454 

17-5 

M 

MgS04  +  K2SO4 

+  6H2O  .     .     . 

1.032 

i.  066 

I.IOI 

I.I38 

- 

- 

- 

- 

- 

15. 

Schiff. 

(NH4)2S04  + 

FeS04  +  6H2O 

1.028 

1.058 

1.090 

1.  122 

I-I54 

1.191 

- 

- 

- 

19- 

M 

K2Cr04  .... 

1.039 

1.082 

1.127 

I.I74 

1.225 

1.279 

!-397 

- 

- 

x9-5 

II 

K2Cr2O7      .     .     . 

1.035 

1.071 

1.108 

- 

_ 

- 

- 

- 

- 

19-5 

Kremers. 

Fe(Cy)6K4  .     .     . 

1.028 

1.059 

1.092 

I.I26 

- 

- 

- 

- 

- 

Schiff. 

Fe(Cy)6K3  .     .     . 
Pb(C2H302)2  + 

1.025 

T-053 

1.070 

I.II3 

— 

~ 

~ 

— 

-~ 

13 

7H2O 

r  071 

1.064 

I.  IOO 

T   T  "37 

I  177 

i.  220 

1.71  s 

1.426 

_ 

I  C. 

Gerlach. 

2NaOH  +  As2O5 

' 

*•*// 

*•  j  j 

A  'T-  **  ^ 

3 

-f-  24H2O      .     . 

i.  020 

1.042 

1.  066 

1.089 

I.II4 

1.140 

1.194 

- 

- 

14. 

Schiff. 

5 

10 

is 

20 

30 

40 

60 

80 

ICO 

SO* 

O4O 

1.084 

I7-> 

179 

1.^77 

1.789 

1.1:64 

1.840 

_ 

I  C. 

Brineau. 

SO2 

OI7 

1.028 

CM  C 

of  ^ 

/  / 

*.  o^y 

J^T 

_ 

o 

4- 

Schiff. 

O77 

1.069 

4i 

141 

1.217 

1.422 

i  so6 

_ 

1C. 

Kolb. 

C4H606  .... 

.O2I 

1.047 

.070 

•  L  -4  L 
.096 

1.150 

.207 

T" 

'- 

- 

D 

15- 

Gerlach. 

C^    F  T  O 

018 

1.038 

_  -O 

O7Q 

1.  127 

.170 

1.277 

_ 

_ 

15. 

*' 

Cane  sugar  .     .     . 

I.OI9 

1.039 

.060 

•**/  y 

.082 

.1  _  j 
I.I29 

.178 

/  o 

1.289 

_ 

_ 

M 

HC1    

I.O2S 

I.OSO 

.07  S 

.101 

I.I  SI 

.2OO 

_ 

_ 



15. 

Kolb. 

HBr    

^~  j 
I  O7S 

^  wj 

O7  7 

•**/  j 

.is8 

J 

I.2S7 

•376 

_ 

_ 

_ 

14. 

Topsoe. 

HI                ... 

1-wj  j 
I.  O77 

-""Y  j 

O77 

.118 

.165 

**  Jf 

1.271 

Of 

.400 

_ 

_ 

_ 

13. 

" 

H2SO4               .     . 

w*)/ 
T  O72 

.w/  / 
.069 

.106 

.  1  4S 

*•       / 

1.223 

.707 

I.  SOI 

1.772 

1.838 

15. 

Kolb. 

T  O4O 

.082 

I  °7 

1  1j 
174 

1.277 

J     1 

J 

/  3 

17.5 

Stolba. 

P205   *    .... 

l'°35 

1.027 

.077 
•057 

•  l  -/ 
.119 
.086 

'  *  /  *T 
.167 
.119 

*••"/  o 

v'i88 

-3~85 
.264 

1.676 

1.438 

: 

- 

^7-5 
15- 

Hager. 
Schiff. 

HNO8    .         .     '. 

T  028 

1.056 

.088 

.119        I.l84 

.250 

1.373 

1.459 

1.528 

I  c. 

Kolb. 

C2H4Oo 

T  OO7 

I.OI4 

.021 

.028        I.04I 

.052 

i.  068 

.055 

.5. 

Oudemans. 

124  TABLE  1O9. 

DENSITIES  OF  MIXTURES  OF  ETHYL  ALCOHOL  AND  WATER    IN  CRAMS 

PER   MILLILITER. 

The  densities  in  this  table  are  numerically  the  same  as  specific  gravities  at  the  various  temperatures  in  terms  of  water 
at  4°  C.  as  unity.  Based  upon  work  done  at  U.  S.  Bureau  of  Standards.  See  Bulletin  Bur.  Stds.  vol.  9,  no.  3 ;  con- 
tains extensive  bibliography  ;  also  Circular  1-9,  1913. 


Per  cent 
C,H8OH 
by  weight 

Temperatures. 

10°  C. 

15°  C. 

20°  C. 

25°  C. 

30°  C. 

35°  C. 

4o°  C. 

0 

0-99973 

0.99913 

0.99823 

0.99708 

0.99568 

0.99406 

0.99225 

I 

785 

725 

636 

520 

379 

217 

034 

2 

602 

542 

453 

336 

194 

031 

.98846 

3 

426 

365 

275 

J$7 

014 

.98849 

663 

4 

258 

195 

.98984 

.98839 

672 

485 

5 

008 

032 

.98938 

817 

670 

501 

311 

6 

.98946 

.98877 

780 

656 

5°7 

335 

142 

7 

80  1 

729 

627 

500 

347 

172 

8 

660 

584 

478 

346 

189 

009 

808 

9 

524 

442 

33* 

193 

031 

.97846 

641 

10 

393 

304 

187 

043 

•97875 

685 

475 

ii 

267 

171 

047 

•97897 

723 

527 

312 

12 

I4I 

041 

.97910 

753 

573 

'1° 

13 

026 

.97914 

775 

6ti 

424 

216 

.96989 

H 

.97911 

790 

643 

472 

278 

063 

829 

'5 

800 

669 

5'4 

334 

133 

.96911 

670 

16 

692 

552 

387 

199 

.96990 

760 

512 

'7 

583 

433 

259 

062 

844 

607 

352 

18 

473 

129 

.96923 

697 

452 

189 

'9 

363 

191 

.96997 

782 

547 

294 

023 

20 

252 

068 

864 

639 

395 

«34 

•95856 

21 

*39 

.96944 

729 

495 

242 

•95973 

687 

22 

024 

818 

592 

348 

087 

809 

516 

23 

.96907 

689 

453 

199 

.95929 

643 

343 

24 

787 

SS8 

312 

048 

769 

476 

168 

11 

665 

539 

424 

287 

168 
020 

.95895 
738 

607 
442 

306 

•94991 
810 

11 

406 
268 

144 

.95867 
710 

576 
410 

272 
098 

•94955 
774 

3 

29 

125 

844 

548 

241 

.94922 

590 

248 

30 

•95977 

686 

382 

067 

74i 

403 

°55 

31 

823 

524 

212 

.94890 

557 

214 

.93860 

32 

665 

038 

709 

37° 

02  1 

662 

33 

502 

1  86 

.94860 

525 

180 

•93825 

461 

34 

334 

Oil 

679 

337 

.93986 

626 

257 

35 

162 

.94832 

494 

146 

79° 

425 

051 

36 

.94986 

650 

306 

.93952 

59  r 

221 

.92843 

% 

805 
620 

464 
273 

114 
•939  '9 

756 
556 

016 

.92808 

634 
422 

39 

43  i 

079 

720 

353 

.92979 

597 

208 

40 

238 

.93882 

518 

148 

770 

385 

.91992 

4' 

42 

43 

042 
.93842 
639 

682 
478 

271 

3r4 
107 
.92897 

.92940 
729 

558 
344 
128 

170 
.91952 
733 

774 
554 
332 

44 

433 

062 

685 

301 

.91910 

5*3 

108 

45 

226 

.92852 

472 

± 

692 

291 

.90884 

g 

017 
.92806 
593 

640 
426 

21  I 

257 
041 
.91823 

.91868 

649 
429 

472 
250 
028 

069 
.90845 
621 

660 

434 
207 

49 

379 

•9*995 

604 

208 

.90805 

396 

.89979 

50 

162 

776 

384 

.90985 

580 

168 

750 

SMITHSONIAN   TABLES. 


T  ABLE  1O  9  (">«''««"*)•  125 

DENSITY  OF  MIXTURES  OF   ETHYL  ALCOHOL  AND  WATER   IN  CRAMS 

PER    MILLILITER. 


Per  cent 
|C2HBOH 

by  weight 

Temperature. 

10°  C. 

15°  C. 

20°  C. 

25°  C. 

30°  C. 

35°  C. 

40°  C. 

5° 

0.92162 

0.91776 

0.91384 

0.90985 

0.90580 

0.90168 

0.89750 

51 

•9I943 

555 

160 

76o 

353 

.89940 

519 

723 

333 

.90936 

534 

o  02£ 

710 

288 

53 

502 

IIO 

711 

307 

.89896 

479 

056 

54 

279 

.90885 

485 

079 

667 

248 

.88823 

P 

°55 
.90831 

659 

433 

258 
031 

.89850 
621 

437 
206 

016 
.88784 

589 
356 

57 

607 

207 

.89803 

392 

.88975 

552 

122 

58 

.89980 

574 

162 

744 

3^9 

.87888 

59 

»54 

752 

344 

•88931 

512 

085 

653 

60 

.89927 

523 

"3 

699 

278 

.87851 

417 

61 

698 

293 

.88882 

466 

044 

615 

1  80 

62 

468 

062 

650 

233 

.87809 

379 

•86943 

63 

237 

.88830 

417 

.87998 

574 

142 

705 

64 

006 

597 

183 

763 

337 

.86905 

466 

65 
66 

.88774  . 

364 
130 

.87948 

527 
291 

100 

.86863 

667 
429 

227 
.85987 

67 
68 

308 
074 

.87895 
660 

477 
241 

054 
.86817 

625 

387 

190 
.85950 

747 

69 

.87839 

424 

004 

579 

148 

710 

266 

70 

602 

187 

.86766 

340 

.85908 

470 

025 

72 

365 
127 

.86949 

710 

527 
287 

100 

.85859 

667 
426 

228 
.84986 

.84783 
540 

73 

.86888 

470 

047 

618 

184 

743 

297 

74 

648 

229 

.85806 

376 

.84941 

500 

053 

75 

408 

.85988 

564 

134 

698 

257 

.83809 

;6 

77 

1  68 

.85927 

747 
5°5 

322 
079 

.84891 
647 

455 

211 

013 
.83768 

564 

78 

685 

262 

.84835 

.83966 

523 

0  S74 

79 

442 

018 

590 

J58 

720 

.   277 

.82827 

80 

I97 

.84772 

344 

.8391  1 

473 

029 

578 

81 

.84950 

525 

096 

664 

224 

.82780 

329 

82 

702 

277 

.83848 

4i5 

.82974 

53° 

83 

453 

028 

599 

164 

724 

279 

.81828 

84 

203 

.83777 

348 

.82913 

473 

027 

576 

85 

-8395  * 

525 

095 

660 

220 

.81774 

322 

86 

697 

271 

.82840 

405 

.81965 

519 

067 

87 

441 

014 

583 

148 

708 

262 

.80811 

88 

181 

•82754 

323 

.81888 

448 

003 

552 

89 

.82919 

492 

062 

626 

186 

.80742 

291 

90 

654 

227 

.81797 

362 

.80922 

478 

028 

91 

3»6 

.81959 

529 

094 

JJ 

211 

.79761 

92 

114 

688 

257 

.80823 

3»4 

.79941 

49  i 

93 
94 

.81839 
561 

134 

.80983 
705 

549 
272 

in 
.79835 

669 

393 

220 
.78947 

i 

278 
.80991 

.80852 
566 

424 
138 

.79991 
706 

555 
271 

114 
.78831 

670 

99 

698 

399 

094 

274 

•79975 
670 

.79846 
547 
243 

415 

117 

.78814 

.78981 
684 
382 

542 
247 
•77946 

100 

.77806 
507 

100 

.79784 

360 

•78934 

506 

075 

641 

203 

SMITHSONIAN   TABLES. 


TABLE  110. 

DENSITIES  OF  AQUEOUS   MIXTURES  OF   METHYL  ALCOHOL, 
CANE  SUGAR,  OR  SULPHURIC  ACID. 


1'er  cent 
by  weight 
of 
substance. 

Methyl 
Alcohol. 

Cane 
Sugar. 

20° 

Sulphuric 
Acid. 

D^C. 

Per  cent 
by  weight 
of 
substance. 

Methyl 
Alcohol. 

D^  C. 

Cane 
Sugar. 

20° 

Sulphuric 
Acid. 

O 
I 

0.99913 

.99727 

0.998234 
1.  002  1  20 

0.99823 
1.00506 

50 

0.91852 
•91653 

1.229567 
1.235085 

'•39505 
1.40487 

2 

•99543 

1.006015 

1.01178 

52 

•9'45' 

1.240641 

1.41481 

3 

•99370 

1.009934 

1.01839 

53 

.91248 

1.246234 

1.42487 

4 

.99198 

I.OI388I 

1.02500 

54 

.91044 

1.251866 

1.43503 

5 

.99029 

1.017854 

1.03168 

55 

.90839 

'•257535 

1.4453° 

6 

.98864 

I.02I855 

1.03843 

56 

.90631 

1.263243 

1.45568 

7 

.98701 

1.025885 

1.04527 

57 

.90421 

1.268989 

1.46615 

8 

•98547 

1.029942 

1.05216 

58 

.90210 

1.274774 

1.47673 

9 

•98394 

1  .034029 

1.05909 

59 

.89996 

1.280595 

1.48740 

10 

.98241 

1.038143 

I.06609 

60 

.89781 

1.286456 

1.49818 

ii 

.98093 

1.042288 

1.07314 

61 

•89563 

1.292354 

1.50904 

12 

•97945 

1.046462 

1.08026 

62 

.89341 

1.298291 

I.5I999 

13 

X  ** 

.97802 

1.050665 

1.08744 

63 

.89117 

1.304267 

1.53102 

.97660 

1  .054900 

1.09468 

64 

.88890 

1.310282 

I.542I3 

1C 

.97518 

1.059165 

1.10199 

65 

.88662 

I.3I6334 

'•55333  • 

16 

•97377 

1.063460 

1.10936 

66 

•88433 

1.322425 

1.56460 

'7 

•97237 

1.067789 

1.11679 

67 

.88203 

1.328554 

'•57595 

18 

.97096 

1.072147 

1.12428 

68 

.87971 

'•334722 

1.58739 

19 

•96955 

I.076537 

I-I3I83 

69 

•87739 

1.340928 

1.59890 

20 

.96814 

1.080959 

'•'3943 

70 

•87507 

1.347174 

1.61048 

21 

22 

23 
24 

.96673 

•96533 
.96392 
.96251 

1.085414 
1  .089900 
1.094420 
1.098971 

1.14709 
1.15480 
1.16258 
1.17041 

7' 

72 

73 
74 

.87271 

•87033 
.86792 
.86546 

I.353456 
I.359778 
1.366139 
I-372536 

1.62213 
1.63384 
i  .64560 
1.65738 

11 

.96108 
•95963 

I-I03557 
I.I08I75 

1.17830 
1.18624 

76 

.86300 
.86051 

1.378971 
1.385446 

1.66917 
1.68095 

27 

I.II2828 

1.19423 

77 

.85801 

'•391956 

1.69268 

28 

15668 

I.II75I2 

1.20227 

78 

•8555' 

'•398505 

'•70433 

29 

•955'8 

I.I2223I 

1.21036 

79 

.85300 

1.405091 

'.71585 

3° 

.95366 

1.126984 

1.21850 

80 

.85048 

1.411715 

1.72717 

32 

•95213 
.95056 

I.I3I773 
1.136596 

1.22669 
1.23492 

81 

82 

.84794 
.84536 

1.418374 
1.425072 

1.73827 
1.74904 

33 

.94896  • 

I.I4I453 

1.24320 

83 

.84274 

1.431807 

'•75943 

34 

•94734 

1.146345     1-25154 

84 

.84009 

I-438579 

1.76932 

35 

•94570 

1.15127? 

1.25992 

85 

•83742 

1.445388 

1.77860 

36 

.94404 

1.156238 

1.26836 

86 

.83475 

1.452232 

1.78721 

37 

.94237 

1.161236 

1.27685 

87 

.83207 

I.459II4 

1.79509 

38 

.94067 

1.166269 

1.28543 

88 

•82937 

1.466032 

1.80223 

39 

.93894 

1.171340 

1.29407 

89 

.82667 

1.472986 

1.80864 

40 

.93720 

1.176447 

1.30278 

90 

.82396 

1.479976 

1.81438 

4' 

•93543 

1.  181592 

I-3II57 

9' 

.82124 

1.487002 

1.81950 

42 

•93365 

1.186773 

1.32043 

92 

.81849 

1.494063 

1.82401 

43 

•93'85 

I.I9I993 

1.32938 

93 

.81568 

1.501  158 

1.82790 

44 

.93001 

1.197247 

'•33843 

94 

.81285 

1.508289 

'  -83  1  1  5 

45 

•92815 

1.202540 

'•34759 

95 

.80999 

'•5'5455 

1.83368 

46 

.92627 

1.207870 

96 

•80713 

1.522656 

1.83548 

47 

.92436 

1.213238 

1.36625 

97 

.80428 

1.529891 

1.83637 

48 

.92242 

1.218643 

'•37574 

98 

.80143 

1.537161 

1.83605 

49 

.92048 

1.224086 

'•38533 

99 

•79859 

1.544462 

50 

.91852 

1.229567 

L39505 

100 

•79577 

1.551800 

(i)     Calculated  from  the  specific  gravity  determinations  of  Doroschevski  and  Rozhdestvtnski  at 
'5° /'5°  C. ;  J.  Knss.,  1'hys.  Chem.  Soc.,  41,  p.  977,  1909. 

According  to  Dr.  F.  I'lato;  Wiss.  Abh.  der  K.  Normal-Eichungs-Kommission,  2,  p.  153,  1900. 
Dr.  Domke's  table;  Wiss.  Abh.  der  K.   Normal-Eichungs-Kommission, 


Calculated   from 
5,  p.  131,  1900. 

SMITHSONIAN  TABLES. 


All  reprinted  from  Circular  19,  U.S.  Bureau  of  Standards,  1913. 


TABLE  111. 
DENSITY  OF   GASES 


127 


The  following  table  gives  the  density  as  the  weight  in  grams  of  a  liter  (normal  liter)  of  the  gas 
at  o°  C,  76  cm  pressure  and  standard  gravity  (sea-level,  45°  latitude),  the  specific  gravity  referred 
to  dry,  carbon-dioxide-free  air  and  to  pure  oxygen,  and  the  weight  in  pounds  per  cubic  foot.  Dry, 
carbon-dioxide-free  air  is  of  remarkably  uniform  density;  Guye,  Kovacs  and  Wourtzel  found  maxi- 
mum variations  in  the  density  of  only  7  to  8  parts  in  10,000.  For  highest  accuracy  pure  oxygen 
should  be  used  as  the  standard  gas  for  specific  gravities.  Observed  densities  are  closely  propor- 
tional to  the  molecular  weights. 


Gas. 

Formula. 

Weight  of 
normal 
liter  in 
grams. 

Specific  gravity. 

Pounds  per 
cubic  foot. 

Refer. 

Air  =  i 

02=  i 

Air 

C2H2 
NH3 
A 
Br2 
C4Hio 
C02 
CO 
C12 

C2N2 
C2H6 
C2H4 
F2 
He 
HBr 
HCI 
HF 
H2 
H2S 
Kr 
CH4 
CH3C1 
C2H60 
Ne 
N2 
NO 
N2O 
02 
CsH8 
H20 
S02 
X 

I  .  2930 
I.I79I 
0.7708 
1.7809 
7.14 

2-594 
1.9768 
I  .  2504 
3-221 

f  0.41  to 
\o.96 

2.323 
1-3562 
1.2609 
1.70 
0.1785 
3.616 
1.6398 
0.922 
0.08987 
1.538 
3.708 
0.7168 
2.304 

2.  IIO 
0.9002 
1.2507 
1.3402 
1-9777 
1.42905 
2.0196 
0.593 
2.9266 

5.851 

I.OOOO 

0.9119 

0.5961 

1-3773 
5-52 
2.006 
1.5289 
0.9671 
2.491 
/  0.32  to 

10.74 

1.797 
1.0489 
0.9752 

i-3i 
0.1381 

2-797 
1.2682 
0.713 
0.06950 
1.189 
2.868 

Q-5544 
1.782 
1.632 
0.6962 
0.9673 
1.0365 
1.5296 
1.1052 
1.5620 
0.462 
2.2634 
4.525 

o  .  9048 
0.8251 

0-5394 
i  .  2462 
5.00 
1.815 

1-3833 
0.8750 
2.254 
/  o  .  29  to 

10.67 

1.626 
0.9490 

0.8823 
1.19 

0.1249 

2.530 
1-1475 
0.645 

0.06289 
1.076 

2.595 

0.5016 
t.  6x2 

1-477 
0.6299 
0.8752 
0.9378 
1-3839 

I.OOOO 

1.4132 

0.418 

2.0479 
4.094 

0.08072 
0.07361 
0.04812 
O.linS 
0.446 
0.1619 
0.12341 
0.07806 
O.2OII 

/  '0.026  to 

\  o  .  060 

0.1450 
0.08467 
0.07872 

0.106 
0.01115 
0-2257 
0.10237 
0.0576 
0.005610 
0.09602 
0-2315 
0-04475 
0.1438 
0.1317 
0.05620 
0.07808 
0.08367 
0.12347 
0.089214 
0.12608 
0.0373 
0.18270 
0.3653 

I 
2 

3 
3 
4 
4 
3 
3 
3 

4 
5 

2 

6 
14 
4 
3 
8 

9 
3 

7 
5 
10 

10 

7 
3 
3 
3 
n 

12 
13 

3 

7 

Acetylene            

Ammonia  

Argon  

Bromine  

Butane  

Carbon  dioxide  

Carbon  monoxide  
Chlorine 

Coal  gas 

Cyanogen 

Ethane       

Ethylene  

Fluorine  

Helium  
Hydrobromic  acid  
Hydrochloric  acid  
Hydrofluoric  acid  
Hydrogen 

Hydrogen  sulphide  
Krypton        

Methane     .  .  

]Methyl  chloride 

Methyl  ether 

Neon                     • 

Nitrogen             

Nitric  oxide  

Nitrous  oxide  
Oxygen  

Propane  

Steam  at  100°  C  

Sulphur  dioxide 

Xenon  

References:    (i)  Guye,   Kovacs,    Wourtzel,    Jour.    chim.    phys.,    10,    p.    332,    1912; 
(2)  Stahrfoss,  Arch.  Sc.  phys.  et  nat.,  IV,   28,   p.  384,  1909;    (3)  Guye,  Jour.   chim. 
phys.,  5,  p.  203,  1907  (contains  review  of  best  determinations  and  indicates  most  proba- 
ble values);   (4)  Computed;   (5)  Baume  and  Perrot,  Jour.  chim.  phys.,  7,  p.  369,  1909; 
(6)  Moissan,  C.  R.,  138,  1904;   (7)  Watson,  Jour.  Chem.  Soc.,  97,  p.  833,  1910;   (8) 
Thorpe,  Hambley,  Jour.  Chem.  Soc.,  53,  p.  765,   1888;    (9)  Morley,  Smithsonian  Con- 
tributions to  Knowledge,  1895;  (10)  Baume,  Jour.  chim.  phys.,  6,  p.  i,  1908;  (n)  Ger- 
mann,  Jour,  of  Phvs.  Chem.,  19,  p.  437,  1915;    (12)  Timmermans,  C.  R.,  158,  p.  789, 
1914;    (13)  Peabody's  Steam  Tables,  1909;   (14)  Taylor,  Phys.  Rev.,  10,  p.  653,   1917. 

SMITHSONIAN  TABLES. 


128 


TABLE  112. 
VOLUME    OF   CASES, 


Values  ol  1  +  .00367  *. 

The  quantity  i  +  .00367  t  gives  for  a  gas  the  volume  at  <°  when  the  pressure  is  kept 
constant,  or  the  pressure  at  (°  when  the  volume  is  kept  constant,  in  terms  of  the 
volume  or  the  pressure  at  o°. 

(t)  This  part  of  the  table  gives  the  values  of  i  -f  .00367 1  for  values  of  t  between  o° 
and  10°  C.  by  tenths  of  a  degree. 

(1»)  This  part  gives  the  values  of  i  +  .00367  /  for  values  of  /  between  — 90°  and  4-  1990° 
C.  by  10°  steps. 

These  two  parts  serve  to  give  any  intermediate  value  to  one  tenth  of  a  degree  by  a  sim- 
ple computation  as  follows  :  —  In  the  (£)  table  find  the  number  corresponding  to 
the  nearest  lower  temperature,  and  to,  this  number  add  the  decimal  part  of  the 
number  in  the  (a)  table  which  corresponds  to  the  difference  between  the  nearest 
temperature  in  the  (*)  table  and  the  actual  temperature.  For  example,  let  the 
temperature  be  682°. 2  : 

We  have  for  680  in  table  (6)  the  number  ....    3-49560 

And  for  2.2  in  table  (a)  the  decimal .00807 

Hence  the  number  for  682.2  is 3-5°367 

(0)  This  part  gives  the  logarithms  of  i  +  .00367 1  for  values  of  t  between  —  49°  and 
+  399°  C.  by  degrees. 

(d)  This  part  gives  the  logarithms  of  i  -+-.00367  /  for  values  of  t  between  400°  and  1990° 
C.  by  10°  steps. 

(a)  Values  of  1  +  .00367  /  for  Values  of  /  between  0°  and  10°  G.  by  Tenths 
of  a  Degree. 


t 

0.0 

0.1 

0.2 

0.3 

0.4 

0 

1.  00000 

1.00037 

1.00073 

I.OOIIO 

1.00147 

I 

.00367 

.00404 

.00440 

.00477 

.00514 

2 

.00734 

.00771 

.00807 

.00844 

.00881 

3 

.OIIOI 

.01138 

.01174 

.01211 

.01248 

4 

..01468 

•01505 

.01541 

.01578 

.01615 

5 

1.01835 

1.01872 

1.01908 

I.OI945 

1.01982 

6 

7 

.02202 

.02569 

.02239 
.02606 

.02275 
.02642 

.02312 
.02679 

.02349 
.02716 

8 

.02936 

.02973 

.03009 

.03046 

.03083 

9 

•03303 

•03340 

•03376 

•03413 

.03450 

1 

0.5 

0.6 

0.7 

0.8 

0.9 

0 

i 

1.00184 
.00550 

1.00220 
.00587 

1.00257 
.00624 

1.00294 
.00661 

1.00330 
.00697 

2 

.00918 

.00954 

.00991 

.01028 

.01064 

3 
4 

.01284 
.01652 

.OI32I 
.01688 

•01358 
.01725 

•01395 
.01762 

.01431 
.01798 

5 

6 

1.02018 
.02386 

1.02055 
.02422 

1.02092 
.02459 

1.02129 
.02496 

1.02165 

.02532 

7 

.02752 

.02789 

.02826 

.02863 

.02899 

8 
9 

.03120 
.03486 

•03I56 
•03S23 

•03193 
•03560 

.03290 
•03597 

.03266 
•03633 

SMITHSONIAN  TABLES. 


TABLE    112.    {continued). 

VOLUME  OF    GASES. 


I29 


(b)  Values  of  1  t  .00367 1  lor  Values  of  t  between  —90°  and  -f  1990°  0.  by 
10°  Steps. 


t 

00 

10 

20 

30 

40 

—000 

I.OOOOO 

0.96330 

0.92660 

0.88990 

0.85320 

4000 

100 
2OO 
300 
4OO 

1.  00000 

1.36700 

1.73400 

2.IOIOO 

2.46800 

1.03670 
1.40370 
1.77070 
2.13770 
2.50470 

1.07340 
1.44040 
1.80740 
2.17440 
2.54140 

I.IIOIO 

1.47710 

1.84410 

2.2IIIO 

2.57810 

1.14680 
1.51380 
1.88080 
2.24780 
2.61480 

500 

600 
700 
800 
900 

2.83500 

3.20200 

3.56900 
3.93600 
4.30300 

2.87170 

3.23870 
3.60570 
3.97270 
4-33970 

2.90840 

3-2754° 
3.64240 
4.00940 
4.37640 

2.94510 
3.3I2IO 
3.67910 
4.04610 
44I3IO 

2.98180 
3.34880 
3.71580 
4.08280 
4.44980 

1000 

IIOO 
1200 

1300 

1400 

4.67000 

5.03700 
5.40400 
5.77100 

6.  1  3800 

4.70670 
5-07370 
5.44070 
5.80770 
6.17470 

4-7434° 
5.11040 

5-4774° 
5.84440 
6.21140 

4.78010 
5.I47IO 

S-SMio 
5.88110 
6.24810 

4.81680 
5.18380 
5.55080 
5.91780 
6.28480 

1500 

1600 
1700 
1800 
1900 

6.50500 
6.87200 

7.23900 

7.60600 

7.97300 

6.54170 

6.90870 

7.27570 
7.64270 

8.00970 

6.57840 
6.94540 
7.31240 
7.67940 
8.04640 

6.61510 
6.98210 
7.34910 
7.71610 
8.08310 

6.65180 
7.01880 
7.38580 

& 

2000 

8.34000 

8.37670 

8.41340 

8.45010 

8.48680 

* 

50 

60 

70 

80 

90 

—  ooo 

0.81650 

0.77980 

0.74310 

0.70640 

0.66970 

+000 

TOO 
200 

300 
400 

1.18350 

J-SSQS0 
1.91750 
2.28450 
2.65150 

1.22020 
1.58720 
1.95420 
2.32120 
2.68820 

1.25690 
1.62390 
1.99090 
2.35790 
2.72490 

1.29360 
1.66060 
2.02760 
2.39460 
2.76160 

I-33030 
1.69730 
2.06430 
2.43130 
2.79830 

5OO 

600 
700 
800 
900 

3.01850 
3-38550 
3-7525o 
4.11950 
4.48650 

3-0552°    ' 
34222O 
3.78920 
4.15620 
4.52320 

3.09190 

3-4589° 
3.82590 
4.19290 
4-5599° 

3.12860 
3-49560 
3.86260 
4.22960 
4.59660 

3-I6530 
3-53230 
3-89930 
4.26630 

4-63330 

1000 

IIOO 

1  200 
1300 
1400 

4-85350 
5.22050 

5-  587  5° 
5-9545° 
6.32  1  50 

4.89020 
5.25720 
5.62420 
5.99120 
6.35820 

4.92690 

5-2939° 
5.66090 
6.02790 
6.39490 

4.96360 
5-33°6o 
5.69760 
6.06460 
6.43160 

5.00030 
5-36730 
5-7343° 
6.10130 
6.46830 

1500 

1600 
1700 
1800 
1900 

6.68850 

7-°555° 
7.42250 
7.78950 
8.15650 

6.72520 
7.09220 
745920 
7.82620 
8.19320 

6.76190 
7.12890 

7-4959° 
7.86290 
8.22990 

6.79860 
7.16560 
7-5326o 
7.89960 
8.26660 

6.83530 
7.20230 
7-56930 
7.93630 
8.30330 

2000 

8-52350 

8.56020 

8.59690 

8.63360 

8.67030 

SMITHSONIAN  TABLES. 


1 3o 


TABLE  112  (continued). 


VOLUME    OF 

(c)  Logarithms  of  1  +  .00367  t  lor  Values 


t 

0 

1 

2 

3 

4 

Mean  diff. 
per  degree. 

—  40 

1931051 

1.929179 

1.927299 

1.925410 

7-9235I3 

1884 

—  30 

•947546 

•945744 

•943934 

.942117 

1805 

—  20 

.966892 

.965169 

.963438 

.961701 

•959957 

1733 

—  10 

.983762 

.982104 

.980440 

•978769 

.977092 

1667 

—  O 

o.oooooo 

.998403 

.996801 

.995192 

•993577 

1605 

4-0 

0.000000 

0.001591 

0.003176 

0.004755 

0.006329 

1582 

10 

.015653 

.017188 

.018717 

.020241 

.02  1  760 

1526 

20 

.030762 

•032244 

•033721 

•03  5  i  93 

.036661 

1474 

3° 

.045362 

.046796 

.048224 

.049648 

.051068 

1426 

40 

.059488 

.060875 

.062259 

.063637 

.065012 

1381 

50 

0.073168 

0.074513 

0.075853 

0.077190 

0.078522 

1335 

60 

.086431 

•087735 

.089036 

.090332 

.091624 

1299 

70 

.099301 

.100567 

.101829 

.103088 

.104344 

I259 

80 

.11  1800 

.113030 

.114257 

.115481 

.116701 

1226 

90 

.123950 

.125146 

.126339 

.127529 

.128716 

1191 

100 

0.135768 

0.136933 

0.138094 

0.139252 

0.140408 

1158 

110 

.147274 

.248408 

.149539 

.150667 

•I5I793 

1129 

120 

.158483 

.159588 

.160691 

.161790 

.162887 

IIOI 

130 

.169410 

.170488 

•i7I563 

.172635 

•173705 

1074 

140 

.180068 

.181120 

.182169 

.183216 

.184260 

1048 

150 

0.190472 

0.191498 

0.192523 

o.i93545 

0.194564 

1023 

160 

.200632 

.201635 

.202635 

•203634 

.204630 

IOOO 

170 
180 

.210559 

.220265 

.211540 
.221224 

.212518 
.222180 

.   -213494 
.223135 

.214468 
.224087 

976 
956 

190 

•229759 

•230697 

•231633 

.232567 

.233499 

935 

200 

0.239049 

0.239967 

0.240884 

0.241798 

0.242710 

916 

2IO 

.248145 

.249044 

.249942 

.250837 

•25I731 

897 

2  2O 
230 

•257054 
.265784 

•257935 
.266648 

.258814 
.267510 

•259692 
.268370 

.260567 
.269228 

878 
861 

240 

•274343 

.275189 

.276034 

.276877 

.277719 

844 

250 

0.282735 

0.283566 

0.284395 

0.285222 

0.286048 

828 

260 

.290969 

.291784 

•292597 

.293409 

.294219 

8^3 

270 
280 

.299049 
.306982 

.299849 
.307768 

•308552 

.301445 
.309334 

.302240 
•310115 

784 

290 

•314773 

.315544 

•3*63*4 

•3  i  7083 

•3  17850 

769 

300 

0.322426 

0.323184 

0.323941 

0.324696 

0.325450 

756 

310 
320 

•329947 

•337339 

.330692 
.338072 

•33'435 
•338801 

•332178 
•339533 

•3329J9 
.340262 

743 
730 

33° 
340 

•3446o8 
•351758 

•345329 
.352466 

•346048 
•353^74 

.346766 
.353880 

.347482 
•354585 

719 

707 

350 

0.358791 

0.359488 

0.360184 

0.360879 

0-361573 

696 

360 

•365713 

•366399 

.367084 

.367768 

.368451 

684 

370 

•372525 

•373201 

•373875 

•374549 

•375221 

674 

390 

•379233 
•385439 

•379898 
.386494 

.380562 
•387148 

.381225 
.387801 

.381887 
•388453 

664 
654 

SMITHSONIAN  TABLES. 


TABLE     112      (continued). 

CASES. 

of  t  between  —49°  and  +399°  0.  by  Degrees. 


1 

5 

6 

7 

8 

9 

Mean  diff. 
per  degree. 

—  40 

1.921608 

1.919695 

^•917773 

7.915843 

1.913904 

1926 

—  30 

20 

.940292 
.958205 

.938460 
.956447 

.936619 
.954681 

.934771 
.952909 

.932915 
.951129 

1845 
1771 

—  10 

.975409 

•973719 

.972022 

.970319 

.968609 

1699 

—  o 

.991957 

.990330 

.988697 

.987058 

.985413 

1636 

+  0 

0.007897 

0.009459 

0.011016 

0.012567 

0.014113 

1554 

10 

.023273 

.024781 

.026284 

.027782 

.029274 

1500 

20 

.038123 

.039581 

.041034 

.042481 

.043924 

145° 

30 
40 

.052482 
.066382 

•053^93 
.067748 

.055298 
.069109 

.056699 
.070466 

.058096 
.071819 

1402 
1359 

50 

60 

0.079847 
.092914 

0.081174 
.094198 

0.082495 
.095486 

0.083811 
.096765 

0.085123 
.098031 

1315 

I28l 

70 

•105595 

.106843 

.108088 

.109329 

.110566 

1243 

80 

.117917 

.119130 

.120340 

.121547 

.122750 

1210 

90 

.129899 

.131079 

.132256 

•13343° 

.134601 

II75 

100 

0.141559 

0.142708 

0.143854 

0.144997 

0.146137 

1144 

no 

.152915 

.154034 

•155151 

.156264 

-1  5737  5 

i«a 

120 

.163981 

.164072 

.166161 

.167246 

.168330 

1087 

130 

.174772 

.175836 

.176898 

.177958 

.179014 

1060 

140 

.185301 

.186340 

•187377 

.188411 

.189443 

1035 

150 

0.195581 

0.196596 

0.197608 

0.198619 

0.199626 

IOII 

1  60 

.205624 

.206615 

.207605 

.208592 

.209577 

988 

170 

•215439 

.216409 

.217376 

•218341 

.219304 

966 

1  80 

.225986 

.226932 

.227876 

.228819 

946 

190 

.234429 

•235357 

.236283 

.237207 

.238129 

925 

200 

0.243621 

0.244529 

0.245436 

0.246341 

0.247244 

906 

210 

.252623 

•253512 

.254400 

.255287 

.256172 

887 

2  2O 

.261441 

.262313 

.263184 

.264052 

.264919 

870 

230 

.270085 

.270940 

.271793 

.272644 

•273494 

853 

240 

.278559 

.279398 

.280234 

.281070 

.281903 

836 

250 

260 

0.286872 
.295028 

0.287694 
.295835 

0.288515 
.296640 

0.289326 
.297445 

0.290153 
.298248 

820 

805 

270 

.303034 

.303827 

.304618 

•305407 

.306196 

790 

280 
290 

.310895 
.318616 

•3Il673 
•3  T  938  1 

.312450 
.320144 

.313226 
.320906 

.314000 
.321667 

7£6 
763 

300 

0.326203 

0.326954 

0.327704 

0.328453 

0.329201 

750 

310 

•333659 

•334397 

•335J35 

.335871 

.336606 

737 

320 

.340989 

•34I7I5 

.342441 

•343  I  64 

.343887 

724 

330 

.348198 

.348912 

.349624 

.350337 

.351048 

7i3 

340 

•355289 

•355991 

•356693 

•357394 

•358093 

701 

350 

360 
370 
380 

0.362266 
.369132 
.375892 
.382548 

0.362957 
.369813 
.376562 
•383208 

0.363648 

•370493 

•377232 
.383868 

0.364337 
•371171 
.377900 

•384525 

0.365025 
.371849 
•378567 
•385183 

690 

678 
668 
658 

39° 

.389104 

.389754 

•390403 

.391052 

.391699 

648 

SMITHSONIAN  TABLES. 


132  TABLE    112   (continued). 

VOLUME    OF   GASES. 

(d)  Logarithms  of  1  +  .00367  /  for  Values  of  t  between  400°  and  1990°  0.  by  10°  Steps. 


t 

00 

10 

20 

30 

40 

400 

0-392345 

0.398756 

0.405073 

0.411300 

0.417439 

500 

0452553 

0.458139 

0.463654 

0.469100 

0.474479 

600 

.505421 

•510371 

.515264 

.520103 

.524889 

700 

•552547 

•556990 

.561388 

.565742 

.570052 

800 
900 

•595055 
•633771 

.599086 
.637460 

•603079 
.641117 

•607037 
.644744 

.610958 
.648341 

1000 

0.669317 

0.672717 

0.676090 

0.679437 

0.682759 

IIOO 

.702172 

•705325 

•708455 

•7"563 

.714648 

1  200 

•732715 

•735655 

•738575 

•74M75 

•744356 

1300 

.761251 

.764004 

.766740 

•769459 

.772160 

1400 

.788027 

.790616 

.793190 

•795748 

.798292 

1500 

1600 

0.813247 
.837083 

0.815691 

•839396 

0.818120 
.841697 

0.820536 

0.822939 
.846263 

1700 

.839679 

.861875 

.864060 

.866234 

.868398 

1800 
1900 

.881156 

.901622 

.883247 

.903616 

.885327 
.905602 

.887398 
.907578 

.889459 
•909545 

t 

50 

60 

70 

80 

90 

400 

0.423492 

0.429462 

0.435351 

0.441161 

0.446894 

500 

600 

0.479791 
.529623 

0.485040 
•534303 

0.490223 
•538938 

0.495350 

.543522 

0.500415 
.548058 

700 
800 

•574321 
.614845 

« 

•582734 
.622515 

.626299 

.590987 
.630051 

900 

.651908 

•655446 

•658955 

.662437 

.665890 

1000 

IIOO 

0.686055 
.717712 

0.689327 

•720755 

0-692574 
.723776 

0.695797 
.726776 

0.698996 
•729756 

1  200 

.747218 

.750061 

.752886 

•755692 

.758480 

1300 
1400 

•774845 
.800820 

•777514 
•803334 

.780166 
.805834 

.782802 
.808319 

.785422 
.810790 

1500 

1600 
1700 
1800 

0.825329 

.870550 
.891510 

0.827705 
.850781 
.872692 
•893551 

0.830069 

.853023 
.874824 
.895583 

0.832420 
•855253 
•876945 
.897605 

0.834758 

•857471 
.879056 
.899618 

1900 

.911504 

•913454 

•915395 

.917327 

.919251 

SMITHSONIAN  TABLES. 


TABLES  113-114. 


133 


RELATIVE  DENSITY  OF   MOIST  AIR  FOR  DIFFERENT  PRESSURES 

AND   HUMIDITIES. 

TABLE  113.— Values  of  ^,  from  h  =  1  to  h  =  9,  for  the  Computation  of  Different  Valuei 
of  the  Ratio  of  Actual  to  Normal  Barometric  Pressure. 

This  gives  the  density  of  moist  air  at  pressure  h  in  terms  of  the  same  air  at  normal  atmosphere  pres- 
sure. When  air  contains  moisture,  as  is  usually  the  case  with  the  atmosphere,  we  have  the 
following  equation  for  pressure  term:  h=B  —  0.378^,  where  e  is  the  vapor  pressure,  and  B  the 
corrected  barometric  pressure.  When  the  necessary  psychrometric  observations  are  made  the  value 
of  e  may  be  taken  from  Tabl*  189  and  then  0.3782  from  Table  115,  or  the  dew-point  may  be  found 
and  the  value  of  0.378*  taken  from  Table  115. 


h 

h 
760 

1 

2 

3 

0.0013158 
.0026316 
.0039474 

4 

I 

0.0052632 
.0065789 
.0078947 

7 

8 
9 

0.0092105 
.0105263 
.0118421 

EXAMPLES  OF  USE  OF  THE  TABLE. 

To  find  the  value  of  —  when  h  =  754.3 
760 

h  =:  700  gives  .92105 
50        '      .065789 
4  .005263 

vJ  .000395 

754-3  -992497 


To  find  the  value  of  —  when  h  —  5.73 
760 

k  =  5  gives  .0065789 
.7  ' ;  .0009210 
.03  "  .0000395 


5-73 


.0075394 


TABLE  114.  —Values  of  the  logarithms  of    *Q  for  values  of  h  between  80  and  340. 

Values  from  8  to  80  may  be  got  by  subtracting  i  from  the  characteristic,  and  from  0.8  to  8  by  subtracting  2  from  the 

characteristic,  and  so  on. 


h 

Values  of  log  A. 
760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

80 

90 

T.O2228 
•07343 

7.02767 
.07823 

7.03300 
.08297 

7.03826 
.08767 

7.04347 
.09231 

7.04861 
.09691 

7.05368 
.10146 

7.0587  1 
.10596 

7.06367 
.11041 

7.06858 
.11482 

100 

1.11919 

1.12351 

7.12779 

7.13202 

7.13622 

7.14038 

7.14449 

7.14857 

7.15261 

7.15661 

no 

.16058 

.16451 

.16840 

.17226 

.17609 

.17988 

.18364 

•18737 

.19107 

•19473 

120 

.19837 

.20197 

•20555 

.20909 

.21261 

.21611 

.21956 

.22299 

.22640 

.22978 

130 

140 

•23313 
.26531 

.23646 
.26841 

•23976 
.27147 

•24304 
•27452 

.24629 

•27755 

.24952 
•28055 

•2^273 
•28354 

•25591 
.28650 

•25907 
.28945 

.26220 
.29237 

150 

160 

1.29528 
•3233! 

1.29816 
.32601 

7.30103 
.32870 

7.30388 
•33J37 

7.30671 

•33403 

7.30952 
•33667 

7.31231 
•33929 

7.31509 
.34190 

7.31784 
•34450 

7.32058 
•34707 

170 
1  80 

.34964 
•37446 

.35218 
.37686 

•35471 
.37926 

.35723 
.38164 

•35974 
.38400 

.36222 
•38636 

.36470 
•38870 

.36716 
.39128 

.36961 
•39334 

•37204 
•39565 

190 

•39794 

.40022 

.40249 

.40474 

.40699 

.40922 

.41144 

•41365 

•41585 

.41804 

200 

1.42022 

7.42238 

7.42454 

7.42668 

7.42882 

7.43094 

7.43305 

7.43516 

7.43725 

7-43933 

2IO 

.44141 

•44347 

•44552 

•44757 

.44960 

.45162 

45364 

•45565 

.45764 

•45963 

220 
230 

.46161 
.48091 

.46358 
.48280 

.46^4 
.48467 

•46749 
•48654 

•46943 
.48840 

•47137 
.49025 

•47329 
.49210 

•47521 
•49393 

.47712 
49576 

.47902 
•4975s 

240 

.49940 

.50120 

.50300 

•50479 

.50658 

•50835 

.51012 

.51188 

•5I364 

•51539 

250 

i-S'713 

7.51886 

7.52059 

7.52231 

7.52402 

7.52573 

7.52743 

7.52912 

7.53081 

7.53249 

260 

•534i6 

•53583 

•53749 

•S39I4 

•54079 

.54243 

•54407 

•54570 

•54732 

.54894 

270 

•55055 

.55216 

•55376 

•55535 

•55694 

•55852 

.56010 

.56167 

•56?2 

•56479 

o         o 

280 
290 

.56634 
.58158 

.58308 

.56944 
•58457 

•57097 

•57250 
•58753 

•57403 
.58901 

•57555 
.59048 

.57707 
.59194 

•57858 
•59340 

.58008 
.59486 

300 

1.59631 

T-59775 

7.59919 

7.60063 

7.60206 

7.60349 

7.60491 

7.60632 

7.60774 

7.60914 

3*o 

•61055 

.61195 

•61334 

•61473 

.61611 

.61750 

.61887 

.62025 

.62161 

.62298 

320 

.62434 

.62569 

.62704 

.62839 

.62973 

•63107 

.63240 

•63373 

•63506 

.63638 

330 
340 

.63770 
.65067 

.63901 
.65194 

.64032 
•65321 

.64163 
•65448 

.64293 
•65574 

.64423 
.65701 

•64553 
.65826 

.64682 
•65952 

.64810 
.66077 

•64939 
.66201 

SMITHSONIAN  TABLES. 


34 


TABLE   114  (contimud). 
DENSITY   OF   AIR. 


Values  of  logarithms  of  -J-   for  values  of  h  between  350  and  800. 


/* 

Values  of  log  A. 
6  760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

350 

7.66325 

7.66449 

7.66573 

7.66696 

7.66819 

7.66941 

7.67064 

7.67185 

7.67307 

7.67428 

36o 

•67549 

.67669 

.67790 

.67909 

.68029 

.68148 

.68267 

.68385 

.68503 

.68621 

370 

•68739 

.68856 

•68973 

.69090 

.69206 

.69322 

•69437 

•69553 

.69668 

.69783 

•69897 

.70011 

.70125 

.70239 

•70352 

•70465 

.70577 

.70690 

.70802 

.70914 

390 

•7*025 

.71136 

.71247 

•71358 

.71468 

•7*578 

.71688 

.71798 

.71907 

.72016 

400 

7.72125 

7.72233 

7.72341 

7.72449 

7.72557 

7.72664 

7.72771 

7.72878 

7.72985 

7.73091 

410 

•73*97 

•73303 

.73408 

•735*4 

.73723 

.73828 

•73932 

.74036 

•74*40 

420 

•74244 

•74347 

•74450 

•74553 

^4655 

•7475s 

.74860 

.74961 

•75063 

•75*64 

43° 
440 

.76264 

•76362 

.75467 
.76461 

•75567 
•76559 

•76657 

.75768 
.76755 

.75867 
.76852 

•75967 
.76949 

.76066 
.77046 

.76165 
•77*43 

450 

7.77240 

7-77336 

777432 

7.77528 

7.77624 

7.77720 

7.77815 

7.77910 

7.78005 

7.78100 

460 

.78194 

.78289 

•78383 

.78477 

•78570 

.78664 

.78757 

•78850 

•78943 

•79036 

470 
480 

.79128 
.80043 

.79221 
•80133 

•793*3 
.80223 

•79405 
•80313 

•79496 
.80403 

.79588 
•80493 

.79770 
.80672 

.79861 
.80761 

•79952 
.80850 

490 

.80938 

.81027 

.81115 

.81203 

.81291 

.81379 

.81467 

.81554 

.81642 

.81729 

500 

7.8i8i6 

7.81902 

7.81989 

7.82075 

7.82162 

7.82248 

7.82334 

7.82419 

7.82505 

7.82590 

5*° 

.82676 

.82761 

.82846 

.82930 

•83015 

.83099 

.83184 

.83268 

•83352 

•83435 

520 

.835*9 

.83602 

.83686 

.83769 

.83852 

.83935 

.84017 

.84100 

.84182 

.84264 

53° 

•84346 

.84428 

•84510 

.84591 

.84673 

.84754 

•84833 

.84916 

.84997 

.85076 

540 

.85158 

•85238 

•853*9 

•85399 

•85479 

.85558 

•85638 

•857*7 

•85797 

.85876 

550 

7.85955 

7.86034 

7.86113 

7.86191 

7.86270 

7.86348 

7.86426 

7.86504 

7.86582 

1.86660 

560 

•86737 

.86815 

.86892 

.86969 

.87047 

.87*23 

.87200 

.87277 

•87353 

.87430 

570 

.87506 

•87582 

•87658 

•87734 

.87810 

.87885 

.87961 

.88036 

.88111 

.88186 

580 
590 

.88261 
.89004 

•88336 
.89077 

.88411 
.89151 

.88486 
.89224 

.88560 
•89297 

.88634 
•89370 

.88708 
•89443 

.88782 
.895*6 

.88856 
.89589 

38? 

600 

7.89734 

7.89806 

7.89878 

7.89950 

7.90022 

7.90094 

7.90166 

7.90238 

7.90309 

7.90380 

610 

.90452 

•90523 

.90594 

.90665 

•90735 

.90806 

•90877 

•90947 

.91017 

.91088 

620 

.91158 

.91228 

.91298 

•9*367 

•9*437 

•9*507 

•9*576 

•9*645 

•9*7*5 

.91784 

630 

•9*853 

.91922 

.91990 

•92059 

.92128 

.92196 

.92264 

•92333 

.92401 

.92469 

640 

•92537 

.92604 

.92672 

.92740 

.92807 

•92875 

.92942 

•93009 

.93076 

•93*43 

650 

7.93210 

7.93277 

7-93343 

7.93410 

7.93476 

7-93543 

7.93609 

7.93675 

7-9374* 

7.93807 

660 
670 

.93873 
.94526 

•93939 
•9459* 

.94004 
•94656 

.94070 
•94720 

•94*35 
•947»5 

.94201 
•94849 

.94266 
•949*3 

•9433* 
.94978 

•94396 
.95042 

.94461 
.95106 

680 

•95*70 

•95233 

•95297 

•9536* 

•95424 

•95488 

•9555* 

•956*4 

•95677 

•9574* 

690 

.95804 

.95866 

.95929 

.95992 

•96055 

.96117 

.96180 

.96242 

•96304 

.96366 

700 

7.96428 

7.96490 

7.96552 

7.96614 

7.96676 

7.96738 

7.96799 

7.96861 

7.96922 

7.96983 

710 

•97044 

.97106 

.97167 

.97228 

.97288 

•97349 

•974*o 

•9747* 

•9753* 

•97592 

720 

•97652 

•977*2 

•97772 

•97832 

.97892 

•9795* 

.98012 

.98072 

.98132 

.98191 

730 

.98251 

•983*0 

•98370 

.98429 

.98488 

.98547 

•  .98606 

.98665 

.98724 

.98783 

740 

.98842 

.98900 

•98959 

.99018 

.99076 

•99*34 

•99*93 

.99251 

•99309 

•99367 

750 

7.99425 

7.99483 

7.99540 

7.99598 

7.99656 

7-997*3 

7.99771 

7.99828 

7.99886 

7-99942 

760 

o.ooooo 

0.00057 

o.ooi  14 

0.00171 

0.00228 

0.00285 

0.00342 

0.00398 

0.00455 

0.00511 

770 

.00568 

.00624 

.00680 

•00737 

.00793 

.00849 

.00905 

.00961 

.01017 

.01072 

780 

.01128 

.01184 

.01239 

.01295 

•0135° 

.01406 

.01461 

.01516 

.01571 

.01626 

790 

.01681. 

•01736 

.01791 

.01846 

.01901 

•01955 

.02010 

.02064 

.02119 

.02173 

SMITHSONIAN  TABLES. 


TABLES  115-116. 
TABLE  115.  -  Values  of  0.378e.* 

This    table   gives    the   humidity  term   0.3786,    which   occurs  in   the   equation    5  =  60 


135 


760 


=  80 -^- —  for  the  calculation  of  the  density  of  air  containing  aqueous  vapor  at  pressure 

e;  do  is  the  density  of  dry  air  at  normal  temperature  and  barometric  pressure,  B  the  ob- 
served  barometric  pressure,  and  h  =  B  —  0.3  78^,  the  pressure  corrected  for  humidity.    For 

values  of  '—,  see  Table  113.     Temperatures  are  in  degrees  Centigrade,  and  pressures  in  milli- 
meters of  mercury. 


Dew 
point. 

Vapor 
pressure 

(ice). 

0.378e 

Dew 
point. 

e 
Vapor 
pressure 

(water). 

0.378* 

Dew 
point. 

Vapor 
pressure 
(water). 

0.378* 

C 

mm 

mm 

C 

mm 

mm 

C 

mm 

mm 

-50° 

0.029 

O.OI 

0° 

4-58 

i-73 

30° 

31-86 

12.0 

-45 

0.054 

O.O2 

I 

4.92 

1.86 

31 

33-74 

12.8 

-40 

0.096 

O.O4 

2 

5-29 

2.OO 

32 

35-70 

J3-5 

-35 

o.  169 

O.O6 

3 

5-68 

2.15 

33 

37-78 

14-3 

-30 
-25 

0.288 
0.480 

O.II 

0.18 

4 
5 

6.  10 
6-54 

2.31 
2.47 

H 

39-95 
42.23 

16.0 

24 

0-530 

0.20 

6 

7.01 

2.66 

36 

44.62 

16.9 

23 

0.585 

0.22 

7 

7.51 

2.84 

37 

47-13 

17-8 

22 

0.646 

o.  24 

8 

8.04 

3-04 

38 

49.76 

18.8 

21 

-20 

o.  712 

0.783 

0.27 
0.30 

18 

8.61 

9.  21 

3-25 

3.48 

39 
40 

52-51 
55-40 

19.8 
20.9 

19 

0.862 

0-33 

ii 

9-85 

3.72 

41 

58.42 

22.1 

18 

0.947 

0.36 

12 

10.52 

3-98 

42 

61.58 

23-3 

17 

.041 

0-39 

13 

II.  24 

4-25 

43 

64.89 

24.5 

16 

.142 

0-43 

14 

11.99 

4-53 

44 

68-35 

25.8 

-15 

.252 

o-47 

15 

12.79 

4.84 

45 

71.97 

27.2 

14 

•373 

0.52 

16 

5.16 

46 

75-75 

28.6 

13 

•503 

0-57 

17 

14-54 

5-50 

47 

79.70 

30.1 

12 

.644 

0.62 

18 

15.49 

5-85 

48 

83-83 

31-7 

II 

.798 

0.68 

16.49 

6.23 

49 

88.14 

33-3 

-10 

.964 

0.74 

20 

17-55 

6.63 

50 

92.6 

35-o 

9 

2.144 

0.81 

21 

18.66 

7.06 

51 

97-3 

36.8 

8 

2.340 

0.88 

22 

19.84 

7-50 

52 

IO2.  2 

38.6 

7 

2-550 

0.96 

23 

21.09 

7-97 

53 

107.3 

40.6 

6 

2.778 

•05 

24 

22.4O 

8-47 

54 

II2.7 

42.6 

-5 

3-025 

•14 

25 

23.78 

8-99 

55 

118.2 

44-7 

4 

3.291 

.24 

26 

25.24 

9-54 

56 

I24.O 

46.9 

3 

3-578 

•35 

27 

26.77 

10.  12 

57 

130.0 

49-1 

2 

3.887 

•47 

28 

28.38 

10.73 

58 

136.3 

I 

0 

4.  220 
4.580 

.60 
•73 

29 
30 

30.08 
31-86 

n-37 
12.04 

8 

142.  8 
149.6 

54-0 
56-5 

*  Table  quoted  from  Smithsonian  Meteorological  Tables. 
TABLE  116.  —  Maintenance  of  Air  at  Definite  Humidities. 

Taken  from  Stevens,  Phytopathology,  6,  428,  1916;  see  also  Curtis,  Bui.  Bur.  Standards,  11, 
359,  1914;  Dieterici,  Ann.  d.  Phys.  u.  Chem.,  50,  47,  1893.  The  relative  humidity  and  vapor 
pressure  of  aqueous  vapor  of  moist  air  in  equilibrium  conditions  above  aqueous  solutions  of  sul- 
phuric acid  are  given  below. 


Density  of 
acid  sol. 

Relative 
humidity. 

Vapor  pressure. 

Density  of 
acid  sol. 

Relative 
humidity. 

Vapor  pressure. 

20°  C 

30°  C 

20°  C 

30°  C 

mm 

mm 

mm 

mm 

.OO 

100.  0 

17.4 

31-6 

•30 

58.3 

IO.  I 

18.4 

•05 

97-5 

17.0 

30.7 

•35 

47.2 

8-3 

15-0 

.  IO 

93-9 

I6.3 

29.6 

.40 

37-i 

6-5 

11.9 

•  15 

88.8 

15-4 

28.0 

•50 

18.8 

3-3 

6.0 

.  20 

80.5 

14.0 

25-4 

.60 

8-5 

i-5 

2-7 

•25 

70.4 

12.  2 

22.  2 

.70 

3-2 

0.6 

1.0 

SMITHSONIAN  TABLES. 


136 


TABLE    117. 


PRESSURE    OF    COLUMNS    OF    MERCURY    AND   WATER, 

British  and  metric  measures.     Correct  at  o°  C.  for  mercury  and  at  4°  C.  for  water. 


METRIC  MEASURE. 

BRITISH  MEASURE. 

Cms.  of 

Hg. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
Hg. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I3-5956 

0.193376 

1 

34-533 

0.491174 

2 

27.1912 

0.386752 

2 

69.066 

0.982348 

3 

40.7868 

0.580128 

3 

103.598 

1.473522 

4 

54.3824 

0.773504 

4 

138-131 

1.964696 

5 

67.9780 

0.966880 

5 

172.664 

2.455870 

6 

81.5736 

1.160256 

6 

207.197 

2.947044 

7 

95.1692 

1-353632 

7 

241.730 

3.438218 

8 

108.7648 

1.547008 

8 

276.262 

3.929392 

9 

122.3604 

1.740384 

9 

310.795 

4.420566 

10 

I35-9560 

1.933760 

10 

345'328 

4.911740 

Cms.  of 
H,0. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
H20. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I 

0.0142234 

1 

2-54 

0.036127 

2 

2 

0.0284468 

2 

S.08 

0.072255 

3 

3 

0.0426702 

3 

7.62 

0.108382 

4 

4 

0.0568936 

4 

10.16 

0.144510 

5 

5 

0.0711170 

5 

12.70 

0.180637 

6 

6 

0.0853404 

6 

15.24 

0.216764 

7 

7 

0'0995638 

7 

17.78 

0.252892 

8 

8 

0.1137872 

8 

20.32 

0.289019 

9 

9 

O.I280I06 

9 

22.86 

0.325147 

10 

10 

0.1422340 

10 

25.40 

0.361274 

SMITHSONIAN  TABLES. 


TABLE    118. 
REDUCTION  OF  BAROMETRIC  HEIGHT  TO   STANDARD   TEMPERATURE.' 


Corrections  for  brass  scale  and 
English  measure. 

Corrections  for  brass  scale  and 
metric  measure. 

Corrections  for  glass  scale  and 
metric  measure. 

Height  of 
barometer  in 
inches. 

a 

in  inches  for 
temp.  F. 

Height  of 
barometer  in 
mm. 

a 
in  mm.  for 
temp.  C. 

Height  of 
barometer  in 
mm. 

a 
in  mm.  for 
temp.  C. 

150 

0.00135 

400 

0.0651 

50 

0.0086 

16.0 

.00145 

410 

.0668 

100 

•  OI72 

17.0 

.00154 

420 

.0684 

/ 
.0258 

'7-5 

18.0 
18.5 
19.0 
19-5 

.00158 
.00163 
.00167 
.00172 
.00176 

430 
440 

460 
470 

.0700 
.0716 
.0732 
.0749 
.0765 

200 

250 
300 

35° 

•0345 
.0431 

•0517 
.0603 

200 

20.5 

O.OOlSl 
.00185 

480 
490 

.0781 
.0797 

400 

45° 
500 

0.0689 

•0775 
.0861 

21.0 

.00190 

500 

0.0813 

520 

.0895 

21.5 

.00194 

510 

.0830 

540 

.0930 

22.0 

.00199 

520 

.0846 

560 

.0965 

22.5 

.00203 

530 

.0862 

580 

.0999 

23.0 

.OO2O8 

540 

.0878 

23-5 

.OO2I2 

550 

.0894 

600 

0.1034 

560 

.0911 

610 

.1051 

24.0 

O.OO2I7 

570 

.0927 

620 

.1068 

24-5 

.OO22I 

580 

•0943 

630 

.1085 

25.0 

.00226 

590 

.0959 

640 

.1103 

25-5 
26.0 

.00231 
.00236 

600 

0.0975 

650 
660 

.II2O 

•"37 

26.5 

.00240 

610 

.0992 

27.0 

.00245 

620 

.1008 

670 

0.1154 

27-5 

.00249 

630 

.1024 

680 

.1172 

640 

.1040 

690 

.1189 

28.0 

0.00254 

650 

.1056 

700 

.1206 

28.5 

.00258 

660 

•1073 

710 

.1223 

29.0 

.00263 

670 

.1089 

720 

.1240 

29.2 

.00265 

680 

.1105 

730 

.1258 

29.4 

.00267 

.     690 

.1121 

29.6 

.00268 

740 

0.1275 

29.8 

.00270 

700 

O.II37 

75° 

.1292 

30.0 

.00272 

710 

•1154 

760 

.1309 

720 

.1170 

770 

•1327 

30.2 

0.00274 

730 

.1186 

780 

•1344 

3°-4    • 

.00276 

740 

.I2O2 

790 

.1361 

30.6 

.00277 

75° 

.1218 

800 

•1378 

30-8 

.00279 

760 

•I235 

31.0 
31.2 

.00281 
.00283 

770 
780 

.1267 

850 

900 

o.  1  464 

3M 

.00285 

790 

.1283 

95° 

.1639 

31.6 

.00287 

800 

.1299 

IOOO 

•1723 

1 

*The  height  of  the  barometer  is  affected  by  the  relative  thermal  expansion  of  the  mercury  and 
the  glass,  in  the  case  of  instruments  graduated  on  the  glass  tube,  and  by  the  relative  expansion  of 
the  mercury  and  the  metallic  inclosing  case,  usually  of  brass,  in  the  case  of  instruments  graduated 
on  the  brass  case.  This  relative  expansion  is  practically  proportional  to  the  first  power  of  the  tem- 
perature. The  above  tables  of  values  of  the  coefficient  of  relative  expansion  will  be  found  to  give 
corrections  almost  identical  with  those  given  in  the  International  Meteorological  Tables.  The 
numbers  tabulated  under  a  are  the  values  of  a  in  the  equation  //>  =  Hf  —  a  (/'—/)  where  Ht  is  the 
height  at  the  standard  temperature,  Ht'  the  observed  height  at  the  temperature/',  and  a  (t'  —  /)  the 
correction  for  temperature.  The  standard  temperature  is  o°  C.  for  the  metric  system  and  28°.  5  F. 
for  the  English  system.  The  English  barometer  is  correct  for  the  temperature  of  melting  ice  at  a 
temperature  of  approximately  28°.s  F.,  because  of  the  fact  that  the  brass  scale  is  graduated  so  as 
to  be  standard  at  62°  F.,  while  mercury  has  the  standard  density  at  32°  F. 

EXAMPLE.— A  barometer  having  a  brass  scale  gave  H '  =  765  mm.  at  25°  C.  ;  required,  the  cor- 
responding reading  at  o°  C.  Here  the  value  of  a  is  the  mean  of  .1235  and  .1251,  or  .1243  ;  .  • .  a(t'  —  t) 
=  .1243  X  25  =  3.11.  Hence  ff0  =  765  —  3.1 1  -=  761.89 

N.  B.— Although  a  is  here  given  to  three  and  sometimes  to  four  significant  figures,  it  is  seldom 
worth  while  to  use  more  than  the  nearest  two-figure  number.  In  fact,  all  barometers  have  not  the 
same  values  for  a,  and  when  great  accuracy  is  wanted  the  proper  coefficients  have  to  be  deter- 
mined by  experiment. 

SMITHSONIAN  TABLES. 


138 


TABLE  119. 

REDUCTION   OF   BAROMETER  TO  STANDARD   GRAVITY. 
Free-air  Altitude  Term.    Correction  to  be  subtracted. 


The  correction  to  reduce  the  barometer  to  sea-level  is  (gi  —  g)/g  X  B  where  B  is  the  barometer  reading  and  g  and 
|i  the  value  of  gravity  at  sea-level  and  the  place  of  observation  respectively.  The  following  values  were  computed  for 
free-air  values  of  gravity  gi  (Table  565).  It  has  been  customary  to  assume  for  mountain  stations  that  the  value  of 
gi  =  say  about  J  the  free-air  value,  but  a  comparison  of  modern  determinations  of  gi  in  this  country  shows  that  little 
reliance  can  be  placed  on  such  an  assumption.  Where  gi  is  known  its  value  should  be  used  in  the  above  correction 
term.  (See  Tables  566  and  567.  Similarly  for  the  latitude  term,  see  succeeding  tables,  the  true  value  of  g  should  be 
used  if  known;  the  succeeding  tables  are  based  on  the  theoretical  values,  Table  565.) 


Height 

Observed  height  of  barometer  in  millimeters. 

above 

Si—  g 

sea-level. 

400 

450 

500 

550 

600 

650 

700 

7*50 

800 

meters. 

IOO 

0.031 

Correction  in  mm  to  be  subtracted  for 

.02 

.02 

.02 





200 

0.062 

height  above  sea-level  in  first  column  and 

.04 

•  05 

•05 

_ 



300 

0.093 

barometer  reading  in  the  top  line. 

.07 

.07 

•07 

— 

•  — 

400 

0.123 

.09 

.10 

.IO 

— 



500 

0.154 

_. 

— 

— 

MM 



—. 

.11 

.12 

•13 

MM 

MM 

600 

0.185 

— 

— 

— 

— 

— 

.12 

•13 

.14 

_ 



700 

0.216 

— 

— 

— 

— 

— 

.14 

•15 

.16 







800 

0.247 

— 

— 

— 

— 

— 

.16 

.18 

.19 





_ 

000 

0.278 

— 

— 

— 

— 

— 

.18 

.  20 

.  22 







1000 

0.309 

— 

— 

— 

.18 

.19 

.20 

.22 

.24 







IIOO 

0-339 

— 

— 

— 

.19 

.21 

.22 

.24 









I2OO 

0.370 

— 

— 

— 

.21 

•23 

.24 

.26 









1300 

0.401 

— 

— 

^— 

.22 

•24 

.26 

•29 



— 

MM 

MM 

1400 

0.432 

— 

— 

— 

•24 

.26 

.28 

•31 









1500 

0.463 

— 

— 

.24 

.26 

.28 

•30 

•  33 









1600 

0.494 

— 

— 

•25 

.28 

•30 

•32 









1700 
1800 

0.525 
0.555 





:3 

•30 
•31 

•32 

•34 

•34 
.36 





.020 

.0463 

I5OOO 

IOOO 

0.586 

— 

— 

•  30 

•33 

•36 

•39 

— 



.OI9 

.0447 

14500 

2000 

0.617 

— 

.28 

•  31 

•34 

•  38 

.41 

— 

.021 

.019 

.0432 

14000 

2IOO 

0.648 

— 

•  30 

•  33 

•  36 

.40 

— 

.021 

.018 

.04l6 

13500 

220O 

0.679 

— 

•  3i 

•  35 

.38 

.41 

— 

— 

.O2O 

.017 

.O40I 

13000 

230O 

0.710 

— 

•  32 

.36 

.40 

•43 

— 

.021 

.019 

.017 

.0386 

12500 

24OO 

0.740 

— 

•34 

.38 

.42 

•45 

— 

.021 

.018 

.Ol6 

.0370 

12000 

2500 

0.771 

•  31 

•35 

•  39 

•43 

•47 

— 

.O2O 

.Ol8 

•  015 

•0355 

II500 

26OO 

0.802 

•  33 

•37 

.41 

.021 

.019 

.017 

.015 

•0339 

IIOOO 

27OO 

0.833 

•  34 

.38 

.42 

— 

— 

.O2O 

.018 

.Ol6 

.014 

.0324 

10500 

2800 

0.864 

•35 

.40 

•44 

— 

— 

.OI9 

.017 

•015 

•  013 

.0308 

1  0000 

2OOO 

0-895 

.36 

.41 

.46 

— 

.020 

.018 

.Ol6 

•015 

•013 

.0293 

9500 

3000 

0.926 

.38 

.42 

•  47 

— 

.019 

.017 

.Ol6 

.014 

.012 

.O278 

9000 

3100 

0-957 

•39 

•44 

— 

— 

.018 

.Ol6 

•015 

.013 



.0262 

8500 

3200 

0.988 

.40 

.46 

— 

— 

.017 

-015 

.OI4 

.012 



.0247 

8000 

3300 

1.019 

.42 

•47 

— 

.017 

.016 

.014 

•  013 





.O23I 

7500 

3400 

1.049 

•  43 

.48 

— 

.016 

•  015 

.013 

.012 





.0216 

7000 

3500 

1.080 

•44 

•49 

— 

.015 

.014 

.012 

.Oil 





.0200 

6500 

3600 

i.  in 

•45 

— 

— 

.014 

•  013 

.Oil 







.0185 

6000 

3700 

1.142 

.46 

— 

— 

.013 

.012 

.Oil 







.0170 

5500 

3800 

1.  173 

.48 

— 

.012 

.Oil 

.Oil 

.OIO 







•0154 

5000 

3900 

1.204 

•  49 

— 

.Oil 

.010 

.010 









.0139 

4500 

4000 

1.235 

•  50 

— 

.010 

.009 

.009 









.0123 

4000 



— 



.008 

.008 

.007 

.007 

Corrections  in  in.  to  be 

.OO92 

3000 



— 

.006 

-005 

.005 

.0041 

subtracted  for  height  above 

.0062 

20OO 



— 

.003 

.003 

.003 

— 



sea-level  in  last  column  and 

.O03I 

IOOO 

barometer  reading  in  bot- 

tom line. 

feet. 

30 

28 

26 

24 

22 

20 

18 

16 

J4 

Height 

Observed  height  of  barometer  in  inches. 

above 
sea-level. 

SMITHSONIAN  TABLES. 


TABLE  1  2O. 

REDUCTION   OF    BAROMETER  TO  STANDARD  GRAVITY.* 

METRIC  MEASURES. 
From  Latitude  oe  to  45°,  the  Correction  is  to  be  Subtracted. 


'39 


Lati- 
tude 

520 

540 

560 

580 

600 

620 

640 

660 

680 

700 

720 

740 

760 

780 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

nun* 

mm. 

mm. 

0 

—1-39 

—1-45 

—1-50 

—1-55 

—  1.61 

—1.66 

—1.71 

—1.77 

—1.82 

-!.87 

—1-93 

-1.98 

—2.04 

—2.09 

5 

—1-37 

—  .42 

—  1.48 

—1-53 

-  .58 

—  1.64 

-1.69 

—  -74 

—  -79 

—1.85 

—  .90 

ri.95 

—  2.OO 

—2.06 

6 

1.36 

.42 

1.47 

1.52 

•57 

1.63 

1.68 

•73 

•78 

1.83 

.89 

1.94 

•99 

2.04 

7 

1-35 

.40 

1.46 

I-5I 

•56 

1.61 

1.66 

.72 

•77 

1.82 

•87 

1.92 

.98 

2.03 

8 

1-34 

«  3^ 

1.44 

1.49 

•  55 

i.  60 

1.65 

•70 

•75 

1.  80 

•85 

1.91 

.96 

2.01 

9 

1-33 

.38 

1-43 

1.48 

•53 

1.58 

1.63 

.68 

•73 

1.78 

.84 

1.89 

•94 

1.99 

10 

—I-3I 

-  .36 

—1.41 

-1.46 

—  -51 

—1.56 

—  1.61 

—  .66 

—  -7i 

—1.76 

—  .81 

-1.86 

—  .92 

—  .97 

II 

1.29 

•34 

i-39 

1.44 

•49 

i-54 

i-59 

.64 

.69 

1.74 

•79 

1.84 

.89   .94 

12 

1.27 

•  32 

1-37 

1.42 

•47 

1.52 

i-57 

.62 

•67 

1.72 

•76 

1.81 

.86   .91 

13 

1.25 

•  30 

i-35 

1.40 

•45 

1.50 

1-54 

•59 

.64 

1.69 

•74 

1.78 

•83 

.88. 

14 

1.23 

.28 

1-33 

1.38 

.42 

1.47 

1.52 

•56 

.61 

1.66 

•7i 

i.-  75 

.80 

•85 

15 

—1.  21 

—  .26 

—1.30 

—1.35 

—  .40 

—1.44 

—  j.49 

—  -54 

-  -58 

—1.63 

-  -67 

—1.72 

—  -77 

-  .81 

16 

I.I9 

.23 

1.28 

1.32 

•37 

1.41 

1.46 

•50 

•55 

i.  60 

.64 

1.69 

•73 

.78! 

17 

1.16 

.20 

1.25 

1.29 

•34 

1.38 

1-43 

•47 

•52 

1.56 

.60 

1.65 

.69   .74 

18 

1.  13 

.18 

1.22 

1.26 

.31 

1-35 

1-39 

•44 

.48 

1.52 

•57 

1.61 

.65 

•  70, 

19 

1.  10 

•15 

I.I9 

1.23 

.27 

1.32 

1.36 

.40 

•44 

1.48 

•53 

i-57 

.61 

•65 

20 

—1.07 

—1.  1  1 

—  I.I6 

—  1.20 

—  .24 

—1.28 

—1.32 

—  .36 

—  .40 

—1.44 

—  -49 

-1-53 

—  -57 

-  .61 

21 

1.04 

1.  08 

1.  12 

1.16 

.20 

1.24 

1.28 

•32 

•  36 

.40 

•  44 

1.48 

•52 

•56; 

22 

I.  01   I.  OS 

1.09 

1.13 

.16 

i.  20 

1.24 

.28 

•32 

•  36 

.40 

1.44 

.48 

•  51 

23 

0.98 

1.  01 

1.05 

1.09 

•13 

1.16 

1.20 

.24 

.28 

•  3i 

•35 

i-39 

•43 

•46 

24 

0.94 

0.98 

1.  01 

1.05 

.08 

I.  12 

1.16 

•19 

.23 

.27 

•30 

1-34 

•37   -4i 

25 

—  0.90 

—0.94 

—0.97 

—1.  01 

—  .04 

—1.08 

—  1.  1  1 

—  .15 

—  .18 

—  .22 

—  -25 

—1.29 

—  -32—  .36; 

26 

0.87 

0.90 

0.93 

0.97 

.00 

1.03 

1.07 

.10 

.13 

•17 

.20 

1.23 

.27 

•30. 

27 

0.83 

0.86 

0.89 

0.96 

0.99 

i.  02 

•05 

.08 

.12 

•15 

1.18 

.21 

.24 

28 

0.79 

0.82 

0.85 

o.88|  0.91 

0-94 

0.97 

.00 

1.03 

.06 

.09 

1.  12 

•*£ 

.18 

29 

0.75 

0.78 

0.81 

0.84  0.86 

0.89 

0.92 

0.95 

0.98 

.OI 

.04 

1.07 

.IO 

.12 

30 

31 

—0.71 

0.67 

—0.74 
0.69 

—  0.76 
0.72 

—0.79  —  0.82 
0.74  0.77 

—0.85 
0.80 

—0.87 
0.82 

—0.90 
0.85 

—  0.93 
0.87 

—0.95 
0.90 

—  0.981—  i.  oi 

O.92   0.95 

—1.04 
0.08 

—  .06 
.00 

32 

0.62 

0.65 

0.67 

0.70  0.72 

9-74 

0.77 

0.79 

0.82 

0.84 

0.86 

0.89 

0.91 

0.04 

33 

0.58 

0.60 

0.63 

0.65  0.67 

0.69 

0.72 

0.74 

0.76 

0.78 

0.80 

0.83 

0.85 

0.87 

34 

0.54 

0.56 

0.58 

o.6oj  0.62 

0.64 

0.66 

0.68 

0.70 

0.72 

0.74 

0.76 

o-79 

0.81 

35 

—0.49 

—0,51 

—0-53 

-HJ.55 

—0.57 

—0.59 

—  0.61 

—0.63 

—  0.64 

—0.66 

—0.68 

—O.7O 

—0.72 

—0.74 

36 

0.45 

0.46 

0.48 

0.50 

0-52 

0.53 

o.55 

0-57 

0.58 

0.60  0.62 

0.64 

0.65 

0.67 

37 

0.40 

0.42 

o.43  0.45 

0.46 

0.48 

0.49 

0.51 

0.52 

0-54 

0.56 

0-57 

0-59 

0.60 

38 

0.36 

0.37 

0.38 

O.40 

O.4I 

0.42 

0.44 

0-45 

0.46 

0.48 

0.49 

0.51 

0.52 

0-53 

39 

0.31 

0.32 

0-33 

0-34 

0.36 

o.37 

0.38 

0.39 

0.40 

0.42 

0-43 

0.44 

0-45 

0.46 

40 

—  0.26 

—0.27 

—0.28 

0.29 

—0.30 

—0.31 

—  0.32 

—0.33 

—  o.  34 

—0.35 

—0.36 

—0.37 

—0.38 

—0-39 

41 

0.21 

O.22 

0.23 

O.24 

0.25 

0.26 

0.26 

0.27 

0.28 

0.29 

0.30 

0.30 

0.31 

0.32 

42 

0.17 

0.17 

0.18 

O.I9 

0.19 

0.20 

O.2I 

O.2I 

0.22 

O.22 

0.23 

O.24 

0.24 

0.25 

43 

0.12 

0.12 

0.13 

0.13 

O.I4 

0.14 

0.15 

0.15 

0.16 

0.16 

0.16 

0.17 

0.17 

0.18 

44 

O.07 

0.07 

0.08 

0.08 

0.08 

0.08 

0.09 

0.09 

0.09 

O.IO 

O.IO 

O.IO 

O.IO 

O.II 

45  j—  0.02 

—  O.O2 

—0.03 

—0.03 

—0.03 

—0.03 

—  0.03 

—0.03 

—  0.03 

—0.03—0.03 

—  0.03 

—0.03 

—0.04 

"  Smithsonian   Meteorological  Tables.' 


SMITHSONIAN  TABLES 


140 


TABLE  121. 


REDUCTION   OF    BAROMETER  TO   STANDARD  GRAVITY.* 

METRIC  MEASURES. 
From  Latitude  46*  to  90",  the  Correction  is  to  be  Added. 


Lati- 
tude. 

520 

540 

560 

580 

600       620 

640 

660 

680 

700 

720 

740 

760 

780 

mm. 

mm. 

mm. 

iniii.        mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm* 

45 

—0.02 

—  O.O2 

—  O.O3 

—0.03—0.03—0.03 

—  O.O3 

—  O.O3 

—0.03 

—0.03 

—0.03 

—  O.O3 

—  O.O3 

—  0.04 

46 

+O.02+O.03 

+0.03 

+0.03+0.03+0.03 

+0.03 

+0.03 

+0.03 

+0.03 

+0.03 

+0.03 

+0.04 

+0.04 

47 

O.O7 

0.08 

0.08 

0.08 

0.08 

0.09 

0.09 

0.09 

0.09 

0.10 

0.10 

0.10 

O.IO 

O.II 

48 

O.I2 

0.12 

0.13 

0.13 

0.14 

0.14 

0.15 

0.15 

0.16 

0.16 

0.17 

0.17 

0.18 

0.18 

49 

0.17 

0.17 

o.  18 

0.19 

0.19 

0.20 

0.21 

O.2I 

0.22 

0.23 

0.23 

O.24 

0.25 

0.25 

50 

0.22 

O.22 

0.23 

0.24 

0.25 

0.26 

0.26 

0.27 

0.28 

0.29 

0.30 

0.31 

0.31 

0.32 

51 

+0.26 

+0.27 

+0.28 

+0.29 

+0.30 

+0.31 

+0.32 

+0.33 

+0.34 

+0.35 

+0.36 

+0-37 

+0.38 

+0.39 

52 

0.31       0.32 

0.33 

0.34 

0.36 

0-37 

0.38 

0-39 

O.4O 

0.42 

0.43 

0.44 

0.45 

0.46 

53 

0.36 

0.37 

0.38 

0.40 

0.41 

O.42 

0-44 

0.45 

0.46 

0.48 

0.49 

0.51 

0.52 

0-53 

54 

0.40 

0.42 

o.43 

0.45 

0.46 

0.48 

0-49 

0.51 

0.52 

o.54 

0.56 

.057 

0.59 

0.60 

55 

0-45 

0-46 

0.48 

0.50 

0.52 

0-53 

0.55 

0-57 

0.58 

0.60 

0.62 

0.64 

0.65 

0.67 

56 

+0.49 

+0.51+0.53 

+0.55 

+0-57 

+0-59 

+0.60 

+0.62 

+0.64 

+0.66 

+0.68 

+  0./0 

+0.72 

+0-74 

57 

0.54!    0.56^    0.58 

0.60 

0.62 

0.64 

0.66 

0.68 

0.70 

0.72 

0.74 

0.76 

0.78 

0.80 

58 

0.58'    0.60     0.62 

0.65 

0.67 

0.69 

0.71 

0.74 

0.76 

0.78 

0.80 

0.82 

0-85 

0.87 

59 

0.62     0.65     0.67 

0.69 

0.72 

o-74 

o-77 

o.79 

0.81 

0.84 

0.86 

0.89 

0.91 

o-93 

60 

0.66    0.69    0.72 

0.74 

0.77 

o-79 

0.82 

0.84 

0.87 

0.89 

0.92 

0-94 

o-97 

I.OO 

61 

+0.71+0-73 

+0.76 

+0.79 

+0.81 

+0.84 

+0.87 

+0.89 

+0.92 

+0-95 

+0.98 

+  I.OO 

+1.03 

+1.06 

62 

0.74    0.77 

0.80 

0.83 

0.85 

0.88 

0.91 

o-94 

0-97 

.00 

1.02 

1.05 

i.  08 

i.  ii 

63 

0.78    0.81 

0.85 

0.88 

0.91 

0.94 

o-97 

I.OO 

1-03 

.06 

1.09 

1.  12 

1-15 

1.18 

64 

0.82    0.85 

0.89 

0.92 

0-95 

0.98 

.01 

1.04 

i.  08 

.11 

I.I4 

1.  17 

1.20 

1-23 

65 

0.86    0.89 

o-93 

0.96 

0-99 

1.03 

.06 

1.09 

1-13 

.16 

I.I9 

1.22 

1.26 

1.29 

66 

+0.90+0.93 

+0.97 

+  1.00 

+1.04 

+1-07 

+    .10 

+  1.14 

+  1.17 

+    .21 

+  1.24 

+  1.28 

+  I.3I 

+  1-35 

67 

0-93 

0-97 

I.OO 

.04 

i.  08 

.11 

•  15 

1.18 

1.22 

•25 

1.29 

1-33 

1.36 

1.40 

68 

0.97 

I.OO 

1.04 

.08 

i.  ii 

.15 

.19 

1.23 

1.26 

•30 

1-34 

1-37 

I.4I 

i-45 

69 

I.OO 

1.04 

i.  08 

.11 

I-I5 

.19 

•23 

1.27 

I-3I 

•34 

1.38 

1.42 

1.46 

1.50 

1.03 

1.07 

i.  ii 

•15 

1.19 

•23 

•27 

i-35 

•39 

1-43 

1.47 

i-55 

71 

+  1.06 

+  I.IO 

+  1.14 

+  .18 

+  1.22 

+  .26 

+1.31 

+  I.35 

+  1-39 

+  I-43 

+1-47 

+  I-5I 

+  1-55 

+  1.59 

72 

1.09 

I  •  13 

1.17 

.22 

1.26 

•30 

i-34 

1.38 

1.42 

1.47 

i  .  51 

i-55 

i-59 

1.63 

73 
74 

I.  12 

1.  14 

1.  10 

1.19 

1.20 

1.23 

3 

1.29 
1-32 

ia 

i-37 
1,41 

1.42 

i-45 

1.46 
1-50 

1.50 
i-54 

'•55 
1-58 

I  -50 

1-63 

1.63 
1.67 

1.67 
1.72 

75 

1.17 

I.  21 

1.26 

.30 

i-35 

•  39 

1-44 

1.48 

1-53 

1-57 

1.62 

1.66 

1.71 

i-75 

76 

+1.19 

+  1.24 

+  1.28 

+    -33 

+  1.37 

+    -42 

+  L47 

+  1.51 

+1.56 

+  1.60 

+  1.65 

+  1.70 

+  1-74 

+  1.79 

77 

1.  21 

1.26       I.3I 

•  35 

1.40 

•45 

.49 

1.54 

1.59 

1.63 

1.68 

1.73 

1.77 

1.82 

78 

1.23 

1.28     1.33 

•  38 

1.42 

•  47 

•52 

1-57 

1.61 

.66 

•  71 

1.76 

i.  80 

1.85 

79 

1.25 

1.30 

1-35 

.40 

1-45 

•  49 

•  54 

i-59 

1.64 

.69 

.73 

1.78 

1.83 

1.88 

80 

1.27 

1.32 

1-37 

.42 

1-47 

•  51 

•  56 

1.61 

1.66 

•  71 

.76 

1.81 

1.86 

1.90 

81 

+1.29 

+  1.33 

+  1.38 

+   -43 

+  1.48 

+   .53 

+   .58 

+  1.63 

+  1.68 

+   .73 

+   .78 

+  1.83 

+1.88 

+  1-93 

82 
83 

1.30 

i.  31 

1.35 
1.36 

1.40 
1.41 

'.46 

1.50 
I.5I 

1 

.60 
.61 

1.65 
1.67 

1.70 
1.72 

.75 
•  77 

.80 
.82 

1.85 
1.87 

1.90 
1.92 

1-95 
1.97 

84 

1.32 

1-37      1-42 

.48 

1-53 

.58 

1.63 

1.68 

i-73 

.78 

.83 

1.88 

1.98 

85 

1-33 

1.38 

1.43 

•49 

1-54 

.59 

1.64 

1.69 

1-74 

•79 

.84 

1.90 

1-95 

2.OO 

90 

+  1.35 

+  1.41 

+  1.46  +  1.51+1.56 

+  1.61 

+  1.67+1.72 

+  1-77 

+  1.82 

+  1.87 

+I.93 

+1.98 

+2.03 

SMITHSONIAN  TABLE*. 


"  Smithsonian   Meteorological  Tables." 


TABLE  122. 


REDUCTION  OF    BAROMETER  TO  STANDARD  GRAVITY.41 

ENGLISH  MEASURES. 
From  Latitude  o*  to  45°,  the  Correction  is  to  be  Subtracted. 


Lati- 
tude. 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0 

—0.051 

—0.054 

—0.056 

—0.059 

—  0.062 

—0.064 

—  O.O67 

—  0.070 

—0.072 

—0.075 

—0.078 

—O.OSO 

5 

—0.050 

—0.053 

—0.055 

—0.058 

—  0.061 

—0.063 

—0.066 

—  0.069 

—0.071 

—0.074 

—0.077 

—  0.079 

6 

0.050 

0.052       0.055 

0.058 

O.OOO 

0.063 

0.066 

O.068 

0.071 

0.073 

0.076 

0.075 

7 

0.049 

0.052 

0.055 

0.057 

O.O60 

O.062 

0.065 

o.o68i    0.070 

0.073 

0.075 

O.O7fi 

8 

O.O49 

0'052 

0.054 

0.057 

0.059 

O.062 

0.064 

0.067 

0.070 

0.072 

0.075 

0.077 

9 

0.048 

0.051 

0.054 

0.056 

0.059 

0.061 

0.064 

0.066 

0.069 

0.071 

0.074 

0.076 

10 

—0.048 

—0.050 

—0.053 

—0.055 

—0.058 

—  O.O60 

—0.063 

-0.066 

—0.068 

—0.071 

—0.073 

—0.076 

ii 

0.047 

0.050 

0.052 

0.055 

0.057 

0.060 

O.O62 

0.065 

0.067 

0.070 

0.072 

O.O75 

12 

0.047 

O.O49 

0.051 

0.054 

0.056 

0.059 

0.061 

0.064 

0.066 

0.069 

0.071 

0.07] 

13 

0.046 

0.048 

0.051 

0.053 

0-055 

0.058 

0.060 

0.063 

0.065 

0.068 

0.070 

0.072 

14 

0.045 

0.047 

0.050 

0.052 

0.055 

0.057 

0.059 

0.062 

0.064 

0.066 

0.069 

0.071 

15 

—  0.044 

—0.047 

—0.049 

—0.051 

—0.053 

—0.056 

—0.058 

—0.060 

—0.063 

—0.065 

—0.067 

—0.070 

16 

0.043 

0.046 

0.048      0.05O 

0.052 

0.055 

0.057 

0.059 

0.062 

0.064    0.066 

0.068 

17 

0.042 

0.045 

0.047 

0.049 

0.051 

0.053 

0.056 

0.058 

0.060 

0.062!    0.065 

0.067 

18 

0.041 

0.044 

0.046 

0.048 

0.050 

0.052 

0.054 

0.057 

0.059 

0.061     0.063 

0.065 

19 

0.040 

0.042 

0.045 

0.047 

0.049 

0.051 

0-053 

0.055 

0.057 

0.059    0.062 

O.O6^ 

20 

—0.039 

—0.041 

—0.043 

—  0.045 

—0.047 

—0.050 

—0.052 

—0.054 

—0.056 

—0.058—0.060 

—  O.o62 

21 

0.038     0.040 

O.O42 

0.044 

0.046 

0.048 

0.050 

0.052 

0.054 

0.056 

0.058     o.ooo 

22 

0.037 

0.039 

O.04I 

0.043 

0.045 

0.047 

0.049 

0.050 

0.052 

0.054 

0.056!    0.05* 

23 

0.036 

0.038 

0.039 

0.041 

0.043 

0.045 

0.047 

0.049 

0.051 

0.053 

0.054!    0.056 

*4 

0.034 

0.036 

0.038 

0.040 

0.042 

0.043 

0.045 

0.047 

0.049 

0.051 

0.052     0.054 

25 

-0.033 

—0.035 

—0.037 

—0.038 

—  0.040 

—  0.042 

—0.043 

—0.045 

—0.047 

—0.049 

—  0.050  —  0.052 

26 

0.032 

0.033     0.035 

0.037 

0.038 

0.040 

0.042 

0.043 

0.045 

0.047 

0.048}    0.050 

27 

0.030 

0.032 

0.033 

0.035 

0.037 

0.038 

0.040 

0.041 

0.043 

0.045 

0.046;    0.048 

28 

0.029     0.030 

0.032 

0.033 

0.035 

0.036 

0.038 

0.039 

0.041 

0.043 

0.044     0.046 

29 

0.027     0.029 

0.030 

0.032 

0.033 

0.035 

0.036 

0.037 

0.039 

0.040 

0.042     0.043 

30 

—  0.0261  —  0.027 

—0.029 

—0.030 

—0.031 

—0.033 

—0.034 

—0.035 

—0.037 

—0.038 

—  0.040;  —  0.041 

3i 

0.024 

O.020 

0.027 

0.028     0.030 

0.031 

0.032     0.033 

0.035 

0.036 

0.037 

0.038 

32 

0.023 

O.O24 

0.025 

0.026 

0.028 

0.029 

0.030!    0.031 

0.032 

o  034 

0.035 

0.036 

33 

O.O2I 

O.O22 

0.023 

0.025 

0.026 

0.027 

0.028 

0.029 

0.030 

0.031 

0.032 

0.034 

34 

O.O2O 

0.021 

O.O22 

0.023 

0.024 

0.025 

0.026 

0.027 

0.028 

0.029 

0.030 

0.031 

35 

—O.OlS 

-0.019 

—  O.02O 

—  O.02I 

—  0.022 

—  0.023 

—  0.024 

—  0.025 

—  0.026 

—  0.027 

—  0.027 

—0.028 

36 

0.016 

O.OI7       O.OlS 

O.OI9 

O.020 

O.02I 

0.022 

0.022 

0.023 

0.024 

0.025!    0.026 

37 

0.015 

0.015 

0.016 

0.017 

0.018 

O.OI9 

O.OI9 

O.O20 

O.O2I 

O.O22 

O.O22       0.023 

38 

0.013 

O.OI4 

O.OI4 

0.015 

0.016 

0.016 

O.OI7 

0.018 

0.018 

O.OI9 

O.O2O 

0.020 

39 

O.OII 

O.OI2 

0.012 

O.OI3 

0.014 

0.014 

O.OI5 

0.015 

0.016 

0.017 

O.OI7 

0.018 

40 

—  0.010 

—  O.OIO 

—  O.OII 

—  O.OII 

—  0.012 

—  0.012 

—  O.OI3 

—0.013 

—  0.014 

—  O.OI4 

—  0.015 

—  0.015 

41 

0.008!    0.008 

0.009 

O.O09 

0.009 

O.OIO 

O.OIO 

O.OII 

O.OII 

0.012 

O.OI2J      O.OI2 

42 

0.006     0.006 

O.OO7 

O.OO7 

0.007 

0.008 

0.008 

O.OOS      O.O09 

0.009    0.009     0.010 

43 

0.004 

0.005 

O.O05 

0.005 

0.005 

0.005 

O.OO6 

o.oo6i    0.006 

o.oooj    0.007     0.007 

44 

0.003 

0.003 

0.003 

0.003 

0.003 

0.003 

0.003 

o  .  004    o  .  004 

0.004      0.004 

0.004 

45 

—  O.OOI 

—  O.OOI 

—  O.OOIi-  —  O.OOI 

—  O.OOI 

—  O.OOI 

—  O.OOI 

! 
—  O.OOI  —  O.OOI  —  O.OOI,  —  O.OOI  —  O.OOI 

Smithsonian   Meteorological   Tables.' 


SMITHSONIAN  TABLES. 


1 42 


TABLE  123. 


REDUCTION   OF    BAROMETER  TO   STANDARD  GRAVITY.* 

ENGLISH  MEASURES. 
From  Latitude  46°  to  90°  the  Correction  is  to  be  Added. 


'Lati- 
tude. 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

45 

—O.OOI 

—  O.OOI 

—  O.OOI 

—  O.OOI 

—O.OOI 

—  O.OOI 

—  O.OOI 

—O.OOI 

—  O.OOI 

—  O.OOI 

—  O.OOI 

—  O.OOI 

46 

+0.001 

+0.001 

+O.OOI 

+0.001 

+0.001 

+0.001 

+O.OOI 

+O.OOI 

+O.OOI 

+0.001 

+O.OOI 

+O.OOI 

47 

0.003 

0.003 

0.003 

O.OO3 

0.003 

0.003 

0.003 

0.004 

0.004 

0.004 

0.004 

0.004 

48 

0.004    0.005 

0.005 

O.OO5 

0.005 

0.006      O.OO6 

O.OO6 

0.006 

0.006 

0.007 

0.007 

49 

0.006    o.octf 

0.007 

O.OO/ 

O.OO7 

0.008 

0.008 

0.008 

0.009 

0.009 

0.009 

O.OIO 

50 

0.008    0.008 

0.009 

O.O09 

O.OIO 

O.OIO 

O.OIO 

O.OII 

O.OII 

0.012 

O.OI2 

O.OI2 

51 

+O.OIO+O.OIO 

+O.OII 

+O.OII 

+  0.012 

+O.OI2 

+0.013 

+0.013 

+0.014 

+O.OI4 

+0.015 

+0.015 

52 

O.OII 

0.012 

O.OI2 

0.013 

O.OI4 

O.OI4 

0.015 

0.015 

0.016    0.016 

O.OI7 

O.OlS 

53 

0.013 

0.014 

O.OI^ 

0.015 

0.016 

0.016     0.017 

0.018 

O.OlS      0.019      O.O2O 

O.O2O 

54 

0.015 

0.015 

0.016 

O.OI7 

0.018 

O.OI9 

0.019 

O.O2O 

0.021 

O.O22 

O.O22       O.O23 

55 

0.016 

O.OI7 

0.018 

O.OI9 

O.020 

0.021 

O.O2I 

O.O22 

0.023 

0.024 

0.025       O.O26 

56 

+0.018 

+0.019 

+O.O2O 

+O.O2I 

+O.022 

+0.023 

+O.O24 

+O.O24 

+0.026+0.026+0.027  +0.028 

57 

O.020 

O.O2I 

O.O22 

0.023 

O.O24 

O.O25 

O.O26 

0.027 

0.028    0.029    0.030     0.031 

58 

O.O2I 

O.O22 

0.023 

0.025 

0.026 

O.O27 

0.028 

O.029 

0.030    0.031'    0.032 

0.033 

59 

0.023 

0.024 

0.025 

0.026 

O.O28 

O.O29 

0.030 

0.031 

0.032     0.033 

0.035 

0.036 

60 

0.024 

0.026 

O.027 

0.028 

0.029 

0.031 

0.032 

0.033 

0.034 

0.036 

0.037 

0.038 

61 

+0.026 

+0.027 

+0.028 

+0.030 

+  0.031 

+0.033 

+0.034 

+0.035 

+0.037 

+0.038 

+0.039 

+0.041 

62 

0.027    0.029    0.030 

O.O32 

0.033 

0.034 

0.036 

0.037 

0.039    0.040 

o  .  042     o  .  043 

63 

0.029    0.030    0.032 

0.033 

0.035 

0.036 

0.038 

0.039 

0.041     0.042 

0.044     0.045 

64 

0.030 

0.032     0.033 

0.035 

0.036 

0.038 

0.040 

0.041 

0.043     0.044 

0.046    0.047 

65 

0.031 

0.033 

0.035 

0.036 

0.038 

0.040 

0.041 

0.043 

0.045    0.046 

0.048 

0.050 

66 

+0.033 

+0.034 

+0.036 

+0.038 

+0.040 

+0.041 

+0.043 

+0.045 

+o  .  047+0  .  048;+©  .  050 

+0.052 

67 

0.034 

0.036    0.038 

0.039 

0.041 

0.043 

0.045 

0.047 

0.048'    0.050     0.052 

0.054 

68 

0.035 

0.037 

0.039 

0.041 

0.043 

0.045 

0.046 

0.048 

0.050'    0.052     0.054 

0.056 

69 

0.036 

0.038 

0.040 

0.042 

0.044 

0.046 

0.048 

0.050 

0.052     0.054!    0.056 

0.058 

70 

0.038 

0.040 

0.042 

0.044 

0.046 

0.048 

0.050 

0.052 

0.053 

0.055 

0.057 

0.059 

71 

+0.039 

+0.041 

+0.043 

+0.045 

+0.047 

+0.049 

+0.051 

+0.053 

+0.055 

+0.057 

+0.059 

+0.061 

72 

0.040 

0.042 

0.044 

0.046 

0.048 

0.050 

0.052 

0.054 

0.057     0.059 

0.061 

0.063 

73 

0.041 

9.043 

0.045 

0.047 

0.049 

0.052 

0.054 

0.056 

0.058 

O.o6o 

0.062 

0.064 

74 

0.042 

0.044 

0.046 

0.048 

0.051 

0.053 

0.055 

0.057 

0.059 

0.062 

0.064 

0.066 

75 

0.043 

0.045     0.047 

0.049 

0.052 

0.054 

0.056 

0.058 

0.061 

0.063 

0.065 

0.067 

76 

77 

+0.044 
0.044 

+0.046+0.048 
0.047     0.049 

+0.050 
0.051 

+0.053 
0.054 

+0.055 
0.056 

+0.057 
0.058 

+0.060 
0.061 

+0.062 
0.063 

+0.064 
0.065 

0.066 
0.068 

0.069 
0.070 

78 

0.045    0.047    0.050 

0.052 

0-055 

0.057 

0.059 

0.062 

0.064 

O.066      0.069 

0.071 

79 

0.046    0.048    0.051 

0.053 

0-055 

0.058     0.060 

0.063 

0.065 

0.067      O.070 

0.072 

80 

0.046    0.049 

0.051 

0.054 

0.056 

0.059 

0.061 

0.063 

0.066 

0.068 

0.071 

0.073 

81 

+o.047,+o.o49 

+0.052 

+0.054 

+0.057 

+0.059 

+0.062 

+0.064 

+0.067 

+0.069 

+0.072 

+0.074 

82 

0.047     0.050 

0.052 

0.055 

0.057 

0.060 

0.062 

0.065 

0.067     0.070     0.072)    0.075 

83 

0.048     0.050 

0.053 

0.056 

0.058    0.061 

0.063 

0.066 

o.o68|    0.071 

0.073     0.076 

84 

0.048     0.051 

0.053 

0.056 

0.059    0.061     0.064 

0.066 

0.069     0.071 

0.074     0.076 

85 

0.049 

0.051 

0.054 

0.056 

0.059    0.061     0.064 

0.067 

0.069     0.072 

0.074     0.077 

90 

4-0.049+0.052 

+0.055 

+0.057 

+o  .  060+0  .  062+0  .  065 

+0.068 

+0.070+0.073 

+0.075+0.078 

SMITHSONIAN  TABLES. 


*  "  Smithsonian   Meteorological  Tables." 


TABLES  124-125. 
TABLE  124.  —  Correction  oi  the  Barometer  for  Capillarity.* 


143 


i.   METRIC  MEASURE. 

HEIGHT  OF  MENISCUS  IN  MILLIMETERS. 

Diameter 
of  tube 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

in  mm. 

Correction  to  be  added  in  millimeters. 

4 

0.83 

1.22 

i-54 

1.98 

2-37 

_ 

_ 

_ 

•47 

0.65 

0.86 

1.19 

i-45 

i.  80 

— 

— 

6 

.27 

41 

.56 

0.78 

0.98 

1.  21 

i-43 

- 

7 

.18 

.28 

.40 

•53 

.67 

0.82 

0.97 

'•13 

9 

— 

.20 
•15 

.29 

.21 

•38 
.28 

.46 

•33 

.56 

.40 

•65 
.46 

0.77 
•52 

10 

— 

— 

•'5 

.20 

.25 

.29 

•33 

•37 

n 

— 

— 

.IO 

.14 

.18 

.21 

.24 

•27 

12 

- 

- 

.07 

.10 

•13 

•15 

.18 

.19 

13 

" 

.04 

.07 

.10 

.12 

•13 

.14 

2.  BRITISH  MEASURE. 

HEIGHT  OF  MENISCUS  IN  INCHES. 

Diameter 
of  tube 

.01 

.02 

.03 

.04 

.05 

.06 

.    .07 

.08 

in  inches. 

Correction  to  be  added  in  inches. 

•J5 

0.024 

0.047 

0.069 

0.092 

0.116 

_ 

_ 

_ 

.20 

.Oil 

.022 

•033 

•045 

•059 

0.078           - 

— 

•25 

.006 

.OI2 

.019 

.028 

•037 

.047 

0.059 

- 

•30 
•35 
.40 

.004 

.008 
.005 
.004 

.008 
.006 

.018 
.012 
.008 

.023 
.015 
.010 

.029 
.018 
.012 

•035 

.022 
.014 

O.O42 
.026 
.Ol6 

•45 
•5° 

— 

- 

.003 

.002 

.005 
.004 

.007 
.005 

.008    i      .010 
.006    1      .006 

.012 
.007 

•55 

: 

" 

.001 

.002 

.003 

.004 

•005 

.005 

*  The  first  table  is  from  Kohlrausch  (Experimental  Physics),  and  is  based  on  the  experiments  of  Mendelejeff  and 
Gutkowski  (Jour,  de  Phys.  Chem.  Geo.  Petersburg,  1877,  or  Wied.  Beib.  1877).  The  second  table  has  been  calcu- 
lated from  the  same  data  by  conversion  into  inches  and  graphic  interpolation. 


TABLE  125.  —  Volume  of  Mercury  Meniscus  in  Cu.  Mm. 


Height  of 

Diameter  of  tube  in  mm. 

meniscus. 

'4 

'5 

16 

17 

18 

19 

20 

21 

22 

23 

24 

mm. 

1.6 

T57 

185 

214 

245 

280 

318 

356 

398 

444 

492 

54i 

1.8 

2.O 
2.2 
2.4 
2.6 

181 

206 

233 
262 
291 

211 

240 
271 
303 
338 

244 
278 

3*3 
35° 
388 

281 
3i9 
358 
400 

444 

320 
362 
406 
454 
503 

362 
409 

459 
5" 
565 

407 
400 

5«S 

573 
633 

455 
5'3 
574 
639 
706 

§7 
708 
782 

704 
781 
862 

694 
776 
859 
948 

Scheel  und  Heuse,  Annalen  der  Physik,  33,  p.  291,  1910. 


SMITHSONIAN  TABLES. 


144  TABLE 

BAROMETRIC   PRESSURES  CORRESPONDING  TO  THE  TEMPERATURE 
OF  THE  BOILING  POINT  OF  WATER. 

Useful    when    a    boiling-point    apparatus    is    used    in    the   determination    of    heights.      Copied    from 
the  Smithsonian  Meteorological  Tables,  4th  revised  edition. 

(A)  METRIC  UNITS. 


Tem- 
jeraturc. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

c 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

80° 

355-40 

356.84 

358.28 

359-73 

36I.I9 

362.65 

364.11 

365.58 

367.06 

368.54 

81 
82 

370.03 
385-16 

37L52 
386.70 

373-01 
388.25 

374.51 
389-80 

376.02 
39L36 

377-53 

392.92 

379-05 
394-49 

380.57 
396.06 

382.09 
397-64 

383.62 
399-22 

83 

400.8l 

402  .  40 

404  .  oo 

405.61 

407.22 

408.83 

410.45 

4I2.O8 

413.71 

415-35 

84 

416.99 

418.64 

420.29 

421-95 

423.61 

425.28 

426.95 

428.64 

430.32 

432-01 

85 

433-71 

435-41 

437-12 

438.83 

440.55 

442  .  28 

444-01 

445-75 

447-49 

449-24 

86 

450.99 

452-75 

454.51 

456.28 

458.06 

459.84 

461.63 

463-42 

465.22 

467.03 

8? 

468.84 

470.66 

472.48 

474.31 

476.14 

477-99 

479.83 

481.68 

483.54 

485.41 

88 

487.28 

489.16 

491.04 

492.93 

494.82 

496.72 

498.63 

500.54 

502.46 

504.39 

89 

506.32 

508.26 

5I0.2O 

512.15 

514.11 

516.07 

518.04 

520.01 

521-99 

523-98 

90 

91 
92 

525.97 
546.26 
567.20 

527.97 
548.33 
509.33 

529.98 
550.40 
571-47 

53L99 
552.48 
573-61 

534-01 
554.56 
575.76 

536.04 
556.65 
577.92 

538.07 

558.75 
580.08 

540.11 
560.85 
582.25 

5f  .15 
562.96 
584.43 

544-21 
565.08 
586.61 

93 

588.80 

591.00 

593-20 

595.41 

597.63 

599.86 

602  .  09 

604.33 

606.57 

608.82 

94 

611.08 

613.35 

615-62 

617.90 

620.19 

622.48 

624.79 

627.09 

629.41 

63L73 

95 

634.06 

636  .  40 

638.74 

641.09 

643.45 

645-82 

648.19 

650.57 

652.96 

655.35 

96 

657.75 

66o.l6 

662.58 

665.00 

667.43 

669.87 

672.32 

674.77 

677.23 

679.70 

97 

682.18 

684.66 

687.15 

689-65 

692.15 

694.67 

697.19 

699.71 

702.25 

704.79 

98 

707.35 

709.90 

712.47 

715.04 

717.63 

720  .  22 

722.81 

725-42 

728.03 

730.65 

99 

733.28 

635.92 

738.56 

741.21 

743.87 

740-54 

749-22 

75I-90 

754-59 

757-29 

100 

760.00 

762.72 

765-44 

768.17 

770.91 

773-66 

776.42 

779.18 

78i.95 

784.73 

(B)   ENGLISH  UNITS. 


Tem- 
perature- 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

F. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

185° 

17.075 

I7.IT2 

17.150 

I7.I87 

17.224 

17.262 

I7.300 

17.337 

17-375 

17.413 

186 

17.450 

17.488 

17.526 

17.564 

17.602 

17-641 

17-679 

17.717 

17.756 

17.794 

187 

17.832 

17.871 

17.910 

17.948 

17.987 

18.026 

18.065 

I8.I04 

18.143 

I8.I82 

188 

18.221 

l8.26l 

18.300 

18.340 

18.379 

18.419 

18.458 

18.498 

18.538 

18.578! 

189 

18.618 

18.658 

18.698 

18.738 

18.778 

18.818 

18.859 

18.899 

18.940 

i8.980( 

190 

19.021 

19.062 

I9.IO2 

I9.I43 

19.184 

19-225 

19.266 

19.308 

19.349 

19.390 

191 

I9-43I 

19.473 

19.514 

19.556 

19.598 

19.639 

I9.68I 

19.723 

19.765 

19.807 

192 

19-849 

19.892 

19-934 

19.976 

20.019 

20.061 

20.  104 

20.146 

20.189 

20.232 

193 

20.275 

20.318 

20.361 

20.404 

20.447 

20.490 

20.533 

20.577 

20.62O 

20.664 

194 

20.707 

20.751 

20.795 

20.839 

20.883 

20.927 

20.971 

21.015 

21.059 

21.103 

195 

21.148121.192 

21.237 

21.282 

21.326 

21.371 

2I.4l6 

21.461 

21.506 

2I.55I 

196 

21.  597  121.642 

21.687 

21-733 

21.778 

21.824 

21.870 

21.915 

21.961 

22.007 

197 

22.053 

22.099  22.145 

22.192 

22.238 

22.284 

22.331 

22.377 

22.424 

22.471 

198 

22.517 

22.564 

22.611 

22.658 

22.706 

22.752 

22.80O 

22.847 

22.895 

22.942 

199 

22.990 

23.038 

23.085 

23.133 

23.181 

23.229 

23.277 

23.325 

23-374 

23.422 

200 

23.470 

23oI9 

23.568 

23.616 

23.665 

23-714 

23  -  763 

23.812 

23.861 

23.910 

201 

23-959 

24.009 

24.058 

24.108 

24.157 

24.207 

24.257 

24.307 

24-357 

24.407 

202 

24-457 

24.507  24.557 

24.608 

24-658 

24.709 

24.759 

24.810 

24-861 

24.912 

203 

24-963 

25.014 

25.065 

25.116 

25.168 

25.219 

25.271 

25.322 

25-374 

25.426 

204 

25.478 

25.530 

25.582 

25.634 

25.686 

25-738 

25.791 

25.843 

25.948 

205 
206 

26.001 
26.534 

26.054 
26.587 

26.107 
26.641 

26.160 
26.695 

26.213 
26.749 

26.266 
26.803 

26.319 
26.857 

26.373 
26.912 

26.426 
26.966 

26.480 
27.021 

207 
208 
209 

27.075 
27  .  626 
28.185 

27.130 
27.681 
28.242 

27.184 
27.737 
28.298 

27.239 
27-793 
28.355 

27.294 
27.848 
28.412 

27.349 
27.904 
28.469 

27.404 
27.960 
28.526 

27.460 
28.0l6 
28.583 

27.515 
28.073 
28.640 

27.570 
28.  129 
28.697 

210 

28.754 

28.812 

28.869 

28.927 

28.985 

29  .  042 

29.100 

29.158 

29.216 

29-275 

211 

29-333 

29.391 

29.450 

29.508 

29.567 

29.626 

29.685 

29.744 

29.803 

29.862 

212 

29.921 

29.981 

30.040 

30.100 

30.159 

30.219 

30.279 

30-339 

30  .  399 

30.459 

213 

30.519 

30  .  5^O 

30.640 

30.701 

.30.761 

30.822 

7O  &ft7 

7r  nnc 

IT  orVi 

TABLE  127.  145 

DETERMINATION   OF   HEIGHTS   BY  THE   BAROMETER. 


Formula  of  Babinet :  Z  =  C 


C  (in  meters)  =  16000   fi  -f-  ii£l+J)~j  metric  measures. 
I-  1000      -I 

In  which  Z  =  difference  of  height  of  two  stations  in  feet  or  meters. 
0)  B  —  barometric  readings  at  the  lower  and  upper  stations  respectively,  corrected  for  all 

sources  of  instrumental  error. 
t0,  t  =r  air  temperatures  at  the  lower  and  upper  stations  respectively. 

Values  of  C. 


ENGLISH  MEASURES. 

METRIC  MEASURES. 

i  ('<>  +  *). 

C 

LogC 

H'o  +  4 

C 

LogC 

Fahr. 

Feet. 

Cent. 

Meters. 

10° 

49928 

4.69834 

—10° 

'5360 

4.18639 

15 

505H 

•70339 

—8 

15488 

.19000 

—6 

15616 

•J9357 

20 

5I094 

4.70837 

—4 

T5744 

.19712 

25 

5l677 

•71330 

—  2 

15872 

.20063 

30 

52261 

4.71818 

0 

16000 

4.20412 

35 

52844 

.72300 

+  2 

16128 

•20758 

4 

16256 

.2IIOI 

40 

53428 

4.72777 

6 

16384 

.21442 

45 

54011 

.73248 

8 

16512 

.21780 

50 

54595 

4737I5 

10 

16640 

4.22IIC 

55 

55178 

.74177 

12 

16768 

.22448 

H 

16896 

.22778 

60 

5576i 

474633 

16 

17024 

.23106 

65 

56344 

•75085 

18 

17152 

•23431 

70 

56927 

4-75532 

20 

17280 

4-23754 

75 

57511 

•75975 

22 

17408 

.24075 

80 

58094 

4.76413 

24 
26 

17664 

•24393 
.24709 

85 

58677 

.76847 

28 

17792 

.25022 

90 

59260 

4-77276 

30 

17920 

4-25334 

95 

59844 

.77702 

32 

18048 

•25643 

34 

18176 

•2595° 

100 

60427 

4.78123 

36 

18304 

.26255 

Values  only  approximate.     Not  good  for  great  altitudes.    A  more  r  ccurate  formula  with 
corresponding  tables  may  be  found  in  Smithsonian  Meteorological  Tables. 

SMITHSONIAN  TABLES. 


146 


TABLE  128. 
VELOCITY  OF  SOUND   IN  SOLIDS. 


The  velocity  of  sounds  in  solids  varies  as  VE/P,  where  E  is  Young's  Modulus  of  elasticity  and  p  the 
density.  These  constants  for  most  of  the  materials  given  in  this  table-  vary  through  a  somewhat 
wide  range,  and  hence  the  numbers  can  only  be  .taken  as  rough  approximations  to  the  velocity 
which  may  be  obtained  in  any  particular  case.  When  temperatures  are  not  marked,  between  10* 
and  20°  is  to  bo  understood. 


Substance. 

Temp.  C. 

Velocity  in 
meters  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Metals:  Aluminum 

o 

5104 

16740 

Masson. 

Brass          .... 

_ 

3500 

11480 

Various. 

Cadmium  .... 

- 

2307 

7570 

Masson. 

Cobalt        .... 

- 

4724 

15500 

11 

Copper       .... 

2O 

356° 

11670 

Wertheim. 

"            .... 

IOO 

3290 

IO8OO 

H 

"            .... 

200 

2950 

9690 

u 

Gold  (soft) 

20 

1743 

5717 

" 

"     (hard) 

— 

2IOO 

6890 

Various. 

Iron  and  soft  steel 

— 

5OOO 

16410 

« 

Iron    ..... 

2O 

r  j  -JQ 

16820 

Wertheim. 

IOO 

5300 

17390 

"..... 

200 

4720 

15480 

" 

"   cast  steel     . 

20 

4990 

16360 

" 

"      ''      " 

2OO 

4790 

I57IO 

" 

Lead  

2O 

1227 

4026 

M 

Magnesium 
Nickel         .... 

- 

46O2 

4973 

I5IOO 
16320 

Melde. 
Masson. 

Palladium  .... 

— 

3K50 

10340 

Various. 

Platinum     .... 

2O 

2690 

8815 

Wertheim. 

. 

IOO 

2570 

8437 

" 

"             .... 

200 

2460 

8079 

u 

Silver          .... 

2O 

2610 

8553 

" 

"              .... 

IOO 

2640 

8658 

« 

Tin     

- 

2500 

8200 

Various. 

Zinc    

- 

3700 

I2I40 

« 

Various:  Brick         .... 

_ 

f 

3652 

11980 

Chladni. 

Clay  rock 
Cork         .... 

: 

3480 
500 

II42O 
1640 

Gray  &  Milne. 
Stefan. 

Granite     .... 
Marble      .... 

- 

395° 
3810 

12960 
12500 

Gray  &  Milne. 
tt 

Paraffin     .... 

15 

1304 

4280 

Warburg. 

Slate          .... 
Tallow      .... 

16 

4510 
390 

14800 
1280 

Gray  &  Milne. 
Warburg. 

Tuff  

— 

2850 

9350 

Gray  &  Milne. 

Glass                        1  from 

- 

5000 

16410 

Various. 

I  to 

— 

6000 

19690 

M 

Ivory         .... 
Vulcanized  rubber            ) 

0 

3OI3 

54 

9886 

177 

Ciccone  &  Campanile. 
Exner. 

(black)  J 

5° 

I  O2 

« 

"     (red)      . 

o 

69 

226 

" 

"                "        "         . 

70 

34 

III 

u 

Wax          .... 

17 

880 

2890 

Stefan. 

Woods  :  Ash,  along  the  fibre  . 

28 

441 
4670 

145° 

M 

Wertheim. 

"    across  the  rings 

— 

'390 

4570 

«» 

"    along  the  rings 

- 

1260 

4140 

« 

Beech,  along  the  fibre 
"      across  the  rings     . 

_ 

3340 
1840 

10960 
6030 

t« 

"      along  the  rings 
Elm,  along  the  fibre 

_ 

1415 
4120 

4640 
13516 

" 

"      across  the  rings 

— 

1420 

4665 

« 

"      along  the  rings 
Fir,  along  the  fibre  . 

_ 

1013 
4640 

3324 
15220 

" 

Maple           "             .         . 

— 

4110 

13470 

« 

Oak 

- 

3850 

12620 

• 

Pine              " 
Poplar 
Sycamore     " 

- 

3320 
4280 
4460 

10900 
14050 
14640 

« 

SMITHSONIAN  TABLES. 

TABLE  129. 
VELOCITY   OF   SOUND    IN    LIQUIDS  AND   GASES. 

For  gases,  the  velocity  of  sound^V^r/P,  where  P  is  the  pressure,  p  the  density,  and  7  the  ratio  of 
specific  heat  at  constant  pressure  to  that  at  constant  volume  (see  Table  253).  For  moderate  tem- 
perature changes  Vt  =  V0d  +  at)  where  0=0.00367.  The  velocity  of  sound  in  tubes  increases  with 
the  diameter  up  to  the  free-air  value  as  a  limit.  The  values  from  ammonia  to  methane  inclusive  are 
for  closed  tubes. 


Substance. 

Temp.  C. 

Velocity  in 
meters  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Liquids  :  Alcohol,  9$%    . 

0 

12.5 

1241. 

4072. 

Dorsing,  1908. 

it 

20.5 

1213- 

3980. 

" 

Ammonia,  cone. 

16. 

1663- 

5456- 

't 

Benzol 

17- 

1166. 

3826. 

a 

Carbon  bisulphide   . 

15- 

1161. 

3809. 

« 

Chloroform 

iS- 

983- 

3225. 

" 

Ether 

iS- 

1032. 

" 

NaCl,  10%  sol. 

iS- 

1470. 

4823. 

<« 

"       15%    ". 

15- 

1530. 

5020. 

" 

20%      "  . 

15- 

1650. 

54I4- 

u 

Turpentine  oil. 

IS- 

1326. 

4351- 

" 

Water,  air-free 

13- 

1441. 

4728. 

" 

«         «        <• 

19. 

1461. 

4794- 

11 

<          «•        a 

31. 

1505- 

4938. 

" 

'       Lake  Geneva 

9- 

1435- 

4708. 

Colladon-Sturm. 

'        Seine  river  . 

15- 

1437- 

4714. 

Wertheim. 

<            •<        <« 

30. 

1528. 

5013. 

11 

<            «         « 

60. 

1724. 

5657- 

" 

Explosive  waves  in  water  : 

Guncotton,  9  ounces    . 

1732. 

5680. 

1  Threlfall,   Adair, 

"               10         "             . 

1775- 

5820. 

L      1889,    see    Bar- 

18     "         . 

1942. 

6372- 

ton's  Sound,  p. 

64      "         .        . 

2013. 

6600. 

J       518. 

Gases  :  Air,  dry,  CO2-free 

0. 

33L78 

1088.5 

Rowland. 

" 

0. 

331-36 

1087.1 

Violle,  1900. 

"     CO2-free      . 

0. 

33I.92 

1089  •  o 

Thiesen,  1908. 

i  atmosphere  . 

0. 

33L7 

1088. 

Mean. 

25            "   .        . 

0. 

332.0 

1089. 

"    (Witkowski). 

50            "  .        . 

0. 

334-7 

1098. 

«              «' 

100                "    . 

o. 

350.6 

1150. 

-»              « 

. 

20. 

344- 

1129. 

. 

100. 

386. 

1266. 

Stevens. 

. 

500. 

553- 

1814. 

'• 

. 

1000. 

700. 

2297. 

Explosive  waves  in  air: 

Charge  of  powder,  0:24  gms. 
3-80     " 
17.40 
45-6o 

336. 
500. 
93i- 

1  102. 
1640. 
3060. 
4l60. 

1  Violle,  Cong.  In- 
tern.    Phys.     i, 
J       243,  1900. 

Ammonia    . 

0. 

415. 

I36l. 

Masson. 

Carbon  monoxide 

0. 

337-1 

1106. 

Wullner. 

"               " 

0. 

337-4 

1107. 

Dulong. 

"        dioxide  . 

0. 

258.0 

846. 

Brockendahl,  1006. 

"        disulphide 

0. 

620. 

Masson. 

Chlorine 

0. 

206.4 

677- 

Martini. 

(i 

0. 

205-3 

674- 

Strecker. 

Ethylene 

0. 

314- 

1030. 

Dulong. 

Hydrogen   . 

0. 

1269.; 

4165- 

" 

" 

0. 

1286.4 

4221. 

Zoch. 

Illuminating  gas 

0. 

490.4 

1609. 

«< 

Methane 

0. 

432. 

1417. 

Masson. 

Nitric  oxide 

0. 

325- 

1066. 

'• 

Nitrous  oxide     . 

0. 

261.8 

859- 

Dulong. 

Oxygen 

0. 

317-2 

1041. 

'* 

Vapors  :  Alcohol 

0. 

230.6 

756. 

Masson. 

Ether 

0. 

179.2 

588. 

'' 

Water        . 

0. 

401. 

1315- 

i< 

tt 

IOO. 

404.8 

1328. 

Treitz,  1903. 

ti 

130. 

424.4 

1392. 

•• 

148 


TABLES  13O-131. 
MUSICAL  SCALES, 


The  pitch  relations  between  two  notes  may  be  expressed  precisely  (i)  by  the  ratio  of  their  vibra- 
tion frequencies;  (a)  by  the  number  of  equally-tempered  semitones  between  them  (E-  b.);  also,  les» 
conveniently,  (3)  by  the  common  logarithm  of  the  ratio  in  (i);  (4)  by  the  lengths  of  the  two  portions 
of  the  tense  string  which  will  furnish  the  notes;  and  (5)  in  terms  of  the  octave  as  unity.  The  ratio 
in  (4)  is  the  reciprocal  of  that  in  (i);  the  number  for  (5)  is  1/12  of  that  for  (2);  the  number  for 
(a)  is  nearly  40  times  that  for  (3). 

Table  130  gives  data  for  the  middle  octave,  including  vibration  frequencies  for  three  standards  of 
pitch:  Aa=435  double  vibrations  per  second,  is  the  international  standard  and  was  adopted  by  the 
American  Piano  Manufacturers'  Association.  The  "just-diatonic  scale"  of  C-major  is  usually 
deduced,  following  Chladni,  from  the  ratios  of  the  three  perfect  major  triads  reduced  to  one 


octave,  thus:  4:5:6 

4:5:6  4:5:6 

F  A  C  E  (I  B  D 

16  20  24  30  36  45  54 

24      27      30      32      36      40      45      48 

Other  equivalent  ratios  and  their  values  in  E.  S.  are  given  in  Table  131.  By  transferring  D  to  the 
left  and  using  the  ratio  10  :  12  :  15  the  scale  of  A-minor  is  obtained,  which  agrees  with  that  of  C-major 
except  that  D  =  26  2/3.  Nearly  the  same  ratios  are  obtained  from  a  series  of  harmonics  beginning 
with  the  eighth;  also  by  taking  12  successive  perfect  or  Pythagorean  fifths  or  fourths  and  reducing 
to  one  octave.  Such  calculations  are  most  easily  made  by  adding  and  subtracting  intervals  expressed 
in  E.  S.  The  notes  needed  to  furnish  a  just  major  scale  in  other  keys  may  be  found  by  successive 
transpositions  by  fifths  or  fourths  as  shown  in  Table  131.  Disregarding  the  usually  negligible  differ- 
ence of  0.02  E.  S.,  the  table  gives  the  24  notes  to  the  octave  required  in  the  simplest  enharmonic 
organ;  the  notes  fall  into  pairs  that  differ  by  a  comma,  0.22  E.  S.  The  line  "  mean  tone  "  is  based 
on  Dom  Bedos*  rule  for  tuning  the  organ  (1746).  The  tables  have  been  checked  by  the  data  in 
Ellis'  Helmholtz's  "Sensations  of  Tone." 

TABLE  130. 


Interval. 

Ratios. 

Logarithms. 

Number  of  double  Vibrations  per  second. 

Note. 

Just. 

Tem- 
pered. 

Just. 

Tem- 
pered. 

Just. 

Tem- 
pered. 

Just. 

Just. 

Just. 

Tem- 
pered- 

Tem- 
pered. 

Tem- 
pered 

E.  S. 

E.  S. 

c, 

o. 

0 

I.OO 

1.  00000 

.0000 

.00000 

256 

264 

258-7 

258.7 

261.6 

271-1 

i 

1.05926 

.02509 

274.0 

277.2 

287.3 

o» 

2.04 

2 

1.  125 

1.12246 

•05115 

.05017 

288 

297 

291.0 

290.3 

293-7 

304-3 

3 

1.18921 

•07526 

307-6 

3«.i 

322.4 

£ 

3-86 
4.98 

4 

S 

1.25 
i-33 

1.25992 
1.33484 

.09691 
.12494 

.10034 
•12543 

320 
341.3 

330 
352 

323-4 
344.9 

325-9 
345-3 

329-6 
349-2 

341-6 
361.9 

6 

1.41421 

•15051 

365.8 

370-0 

383-4 

«• 

7.02 

7 

1.50 

1.40831 

.17609 

.17560 

384 

396 

388 

387-5 

392.0 

406.2 

8 

1.58740 

20069 

410.6 

415-3 

430.4 

A, 

8.84 

9 

1.67 

1.68179 

.22185 

•22577 

426.7 

440 

431-  1 

435-0 

440.0 

456.0 

10 

1.78180 

.25086 

460.9 

446.2 

483.1 

B, 

10.88 

II 

1.875       1.88775 

.27300 

•27594 

480 

495 

485-0 

488.3 

493-9 

511.8 

c* 

12.  OO 

12 

2.OO           2.00000 

.30103 

•30103 

512 

528 

5I7.3 

517-3 

523-2 

542.3 

TABLE  131. 


Key  of 

c 

D 

E 

F 

G 

A 

B 

C 

7*s 

C3 

1.14 

0.92 

3.18 
2.96 

4-78 

6.12 

5-9° 

8.16 

7-94 

9.98 
9.76 

12.02 

II.80 

6  " 

FS 

1.14 

2.96 

5-00 

6.12 

8.16 

9.98 

II.IO 

0.92 

2.74 

4.78 

5-90 

7-94 

9.76 

10.88 

c  " 

B^s 

1.14 

2.96 

4.08 

6.12 

7-94 

9.98  j 

'   II.IO 

5 

o.g2v 

2.74^ 

3.  So/ 

5-9<V 

7.72^ 

9.76V 

10.88^ 

4  " 

E  v 

0.92 
0.70^ 

2.96 

2-74/ 

4.08 

6.12 

5-9^ 

7-94, 
7.72 

9.06 

8.84V 

t 

II.IO 

10.  89/ 

3  " 

A* 

0.92 
O-7O/ 

2.04 

1.82^ 

J'.of 
3-86 

5-9<> 
5.68^ 

7-94 
7.72^ 

Lit 

II.IO  > 

10.887 

J 

2    " 

D 

o.9> 

2.04- 

5.90v 

7-02v 

/ 

9.06  <• 

10.88- 

J 

I  # 

G 

o.cxy 

2.04^ 

3.86  v 

f 

5-9°' 

^7.02  v 

/ 

9.06' 

io.88v 

'12.00 

C  * 

o.oo* 

2.04^ 

3  86^ 

4.98 

7.02 

/ 

8.84^ 

S 

lo-SS1" 

12.00 

i  !> 

F  v' 

0.00' 

1.82 

3.86 

4.98, 

7.02 

8.84^ 

9.96 

12.00 

2  i>S 

Bt> 

0.00 

1.82 

2.94 

4.98 

6.80 

8.84 

9.96 

I2.OO 

3" 

E? 

-.22 

1.82 

2.94 

4-98 

6.80 

7.92 

9.96 

11.78 

4" 

A? 

-.22 

0.90 

2.94 

4.76 

6.80 

7.92 

9.96 

11.78 

5  " 

1)7 

-.22 

0.90 

2.94 

4.76     5.88 

7.92 

9-74 

11.78 

6  " 

G? 

0.90 

2.72 

4.76 

5-88 

7.92 

9-74 

10.86 

7" 

c? 

0.90 

2.72 

3-84 

5.88 

770 

9-74 

10.86 

Harmonic  Series 

8 
0.0 

U) 

9 
2.04 

(a!?8) 

IO 

3.86 

/    2,    \ 

\4-70/ 

it 

5-51 

12 

7-02 

/  25  \ 

V7-73/ 

8.41 

'4 
9.69 

15 

10.88 

it 

12.00 

Cycle  of  fifths 

O.O 

1.14 

2.04 

3.18 

4.08 

5-22 

6.12 

7-02 

8.16 

9.06 

IO.2O 

II.IO 

12.24 

Cycle  of  fourths 
Mean  tone 

O.O 
O.O 

0.90 
0.76 

1.  80 

'•93 

2.94 

3-" 

3.86 

4.98 

5-°3 

5.88 
5-79 

6.78 
6-97 

7.92 
7.72 

8.82 
8.90 

9.96 
IO.O7 

10.86 
10.83 

11.76 

I2.OO 

Equal  7  step 

O.O 

1.71 

3-43 

5-M 

6.86 

8.57 

IO.29 

12.00 

SMITHSONIAN  TABLES. 


TABLES  132-135. 
MISCELLANEOUS   SOUND   DATA. 

TABLE  132.  —  A  Fundamental  Tone,  Its  Harmonics  (Overtones)  and  the  Nearest 
Tone  of  the  Equal-tempered  Scale. 


I4Q 


No.  of  partial  

i 

2 

4 

5 

6 

8 

Q 

10 

Frequency                          

129 

259 

388 

Si? 

& 

776 

1030 

I2O? 

Nearest  tempered  note 

C 

c 

ig 

C 

F 

G 

B? 

D 

E 

Corresponding  frequency  

129 

259 

388 

517 

652 

775 

922 

1293 

No.  of  partial  

II 

12 

13 

14 

15 

16 

1^ 

18 

20 

Frequency                    

1423 

1552 

1681 

1811 

1940 

2069 

2328 

2586 

Gb 

G 

G# 

Bi> 

s 

c 

r# 

D 

D/ 

Corresponding  frequency  

1463 

1550 

1642 

1843 

1953 

2O69 

2192 

2323 

NOTE.  —  Overtones  of  frequencies  not  exact  multiples  of  the  fundamental  are  sometimes  called  inharmonic  partials. 
TABLE  133.  —  Relative  Strength  of  the  Partials  in  Various  Musical  Instruments. 

The  values  given  are  for  tones  of  medium  loudness.     Individual  tones  vary  greatly  in  quality  and,  therefore,  in 
loudness. 


Instrument. 

Strength  of  partials  in  per  cent  of  total  tone  strength. 

i 

2 

3 

4 

5 

6 

7 

8 

9 

10 

II 

12 

Tuning  fork  on  box  .  . 
Flute 

100 

66 
26 

2 
12 
36 

6 

24 
25 
2 
0 
26 
II 

4 
9 

4 

10 

i? 
35 

6 

10 

29 
3 

7 

12 

27 
35 
5 
4 
8 

i 
14 
o 
3 
ii 

o 

| 

2 
2 

18 

3 
15 

] 

I 

5 

0 

6 

i 
i 

Violin,  A  string  
Oboe     

Clarinet 

Trombone  

6 

4 

3 

2 

i 

TABLE  134.  —  Characteristics  of  the  Vowels. 

The  larynx  generates  a  fundamental  tone  of  a  chosen  pitch  with  some  20  partials,  usually  of  low  intensity.  The 
particular  partial,  or  partials,  most  nearly  in  unison  with  the  mouth  cavity  is  greatly  strengthened  by  resonance.  Each 
vowel,  for  a  given  mouth,  is  characterized  by  a  particular  fixed  pitch,  or  pitches,  of  resonance  corresponding  to  that 
vowel's  definite  form  of  mouth  cavity.  These  pitches  may  be  judged  by  whispering  the  vowels.  It  is  difficult  to  sing 
vowels  true  above  the  corresponding  pitches.  The  greater  part  of  the  energy  or  loudness  of  a  vowel  of  a  chosen  pitch 
is  in  those  partials  reinforced  by  resonance.  The  vowels  may  be  divided  into  two  classes,  —  the  first  having  one  char- 
acteristic resonance  region,  the  second,  two.  The  representative  pitches  of  maximum  resonance  of  a  mouth  cavity 
for  selected  vowels  in  each  group  are  given  in  the  following  table. 


Vowel  indicated  by  italics  in 
the  words. 

Pitch  of  maxi- 
mum resonance. 

Vowel  indicated  by  italics  in 
the  words. 

Pitch  of  maxi- 
mum resonance. 

father,    far,        guard  
raw,        fall,        haul  .    . 

910 

732 

mat,     add,          cat  
pet        feather,    bless 

800  and  1840 
691  and  1953 

461 

488  and  2461 

gloom,     move,     group  

326 

bee,      pique,      machine  

308  and  3100 

TABLE  135.  —  Miscellaneous  Sound  Data. 

Koenig's  temperature  coefficient  for  the  frequency  (n)  of  forks  is  nearly  the  same  for  all  pitches.  nt  — 
«o(i  —  o.opoii*0  C),  Ann.  d.  Phys.  9,  p.  408,  1880. 

Vibration  frequencies  for  continuous  sound  sensations  are  practically  the  same  as  for  continuous  light  sensation, 
10  or  more  per  second.  Helmholtz'  value  of  32  per  sec.  may  be  taken  as  the  flicker  value  for  the  ear.  Moving  pictures 
use  16  or  more  per  sec.  For  light  the  number  varies  with  the  intensity. 

Pitch  limits  of  voice:  60  to  1200  vibrations  per  second. 

Piano  pitch  limits:  27.2  to  4138.4  v.  per  sec.  (over  7  octaves). 

Organ  pitch  limits:  16  (32  ft.  pipe),  sometimes  8  (64  ft.)  to  4138  (ij  in.)  (9  octaves). 

Ear  can  detect  frequencies  of  20,000  to  30,000  v.  per  sec.  Koenig,  by  means  of  dust  figures,  measured  sounds  from 
steel  forks  with  frequencies  up  to  90,000. 

The  quality  of  a  musical  tone  depends  solely  on  the  number  and  relative  strength  of  its  partials  (simple  tones)  and 
probably  not  at  all  on  their  phases. 

The  wave-lengths  of  sound  issuing  from  a  closed  pipe  of  length  L  are  *L,  4^/3,  4^/5,  etc.,  and  from  an  open  pipe, 
2L,  2L/2,  2L/3,  etc.  The  end  correction  for  a  pipe  with  a  flange  is  such  that  the  antinode  is  0.82  X  radius  of  pipe 
beyond  the  end;  with  no  flange  the  correction  is  0.57  X  radius  of  pipe. 

The  energy  of  a  pure  sine  wave  is  proportional  to  n*A2;  the  energy  per  cm3  is  on  the  average  2pir*U*A-/\'1;  the  energy 
passing  per  sec.  through  i  cm*  perpendicular  to  direction  of  propagation  is  2pir*U3A*/\*;  the  pressure  is  \(y  +  i) 
(average  energy  per  cm3);  where  n  is  the  vibration  number  per  sec.,  X  the  wave-length,  A  the  amplitude,  V  the  veloc- 
ity of  sound,  p  the  density  of  the  medium,  J  the  specific  heat  ratio.  Altberg  (Ann.  d.  Phys.  n,  p.  405,  1903)  measured 
sound-wave  pressures  of  the  order  of  0.24  dynes/cm2  =  0.00018  mm  Hg. 

SMITHSONIAN  TABLES. 


1S°  TABLES   1  36-137. 

TABLE  136.  —  Aerodynamics. 
KINETICS  OF  BODIES  IN  RESISTING  MEDIUM. 

The  differential  equation  of  a  body  falling  in  a  resisting  medium  is  diifdt  =  g  —  ku*.  The  ve- 
locity tends  asymptotically  to  a  certain  terminal  velocity,  V  '=  \/g/&-  Integration  gives  u  = 
V-  tanh  (gt/Y),  x  =—  "  log  cosh  (gt/T)  if  w  =  x  =  /  =  o. 

When  body  is  projected  upwards,  du/df  =  —g  —  &u2,  and  if  u0  is  velocity  of  projection,  then 
tan"1  u/V  =  tan"1  (uQ/Y)  -gtlV,  x  =  (V*/2g)  log  (V*  +  u0*)  (V*  +  «2).  The  particle  comes  to 
rest  when  /  =  (V/g)  tan"1  (u0/V)  and  x  =  (P/2g)  log  (i  -  «o2/72). 

For  small  velocities  the  resistance  is  more  nearly  proportional  to  the  velocity. 

Stokes'  Law  for  the  rate  of  fall  of  a  spherical  drop  of  radius  a  under  gravity  g  gives  for  the 
velocity,  t>, 


where  a  and  p  are  the  densities  of  the  drop  and  the  medium,  t]  the  viscosity  of  the  medium. 
This  depends  on  five  assumptions:  (i)  that  the  sphere  is  large  compared  to  the  inhomogeneities 
of  the  medium;  (2)  that  it  falls  as  in  a  medium  of  unlimited  extent;  (3)  that  it  is  smooth  and 
rigid;  (4)  that  there  is  no  slipping  of  the  medium  over  its  surface;  (5)  that  its  velocity  is  so 
small  that  the  resistance  is  all  due  to  the  viscosity  of  the  medium  and  not  to  the  inertia  of  the 
latter.  Because  of  5,  the  law  does  not  hold  unless  the  radius  of  the  sphere  is  small  compared 
with  rj/vp  (critical  radius).  Arnold  showed  that  a  must  be  less  than  0.6  this  radius. 

If  the  medium  is  contained  in  a  circular  cylinder  of  radius  R  and  length  Z,,  Ladenburg  showed 
that  the  following  formula  is  applicable  (Ann.  d.  Phys.  22,  287,  1907,  23,  447,  1908): 

2  ga2((7  -  p)  __ 


9  i?(i  +  2.40./R)  (i  -f-  3.*a/£) 

As  the  spheres  diminish  in  size  the  medium  behaves  as  if  inhomogeneous  because  of  its  molec- 
ular structure,  and  the  velocity  becomes  a  function  of  I/a,  where  /  is  the  mean  free  path  of  the 
molecules.  Stokes'  formula  should  then  be  modified  by  the  addition  of  a  factor,  viz.: 

2    trap  (  .  I 

v\  =  -  - —  (ff  -  p)   <  i  +  (0.864  +  o.2ge-*-*S  w*))  - 
(See  chapter  V,  Millikan,  The  Electron,  1917  ;  also  Physical  Review  15,  p.  545,  1920.) 


TABLE  137.  —Flow  of  Gases  through  Tubes.* 

When  the  dimensions  of  a  tube  are  comparable  with  the  mean  free  path  (Z)  of  the  molecules  of 
a  gas,  Knudsen  (Ann.  der  Phys.  28,  75,  199,  1908)  derives  the  following  equation  correct  to  5% 
even  when  D/L  =  0.4:  Q,  the  quantity  of  gas  in  terms  of  PV  which  flows  in  a  second  through  a 
tube  of  diameter  Z>,  length  /,  connecting  two  vessels  at  low  pressure,  difference  of  pressure 


—  PI,  equals  (P%  —  P\)/W\/p  where  p  is  the  density  of  the  gas  at  one  bar  (i  dyne/cm2)  =  (mo- 
ular weight)/(83.i5  X  io67")  and  IV'  which   is  of  the  nature  of  a  resistance,  =  2-394I//Z?3  + 
3-I84/Z?2.     The  following  table  gives  the  cm3  of  air  and  Hat  i  bar  which  would  flow  through  dif- 


ferent sized  tubes,  difference  of  pressure  i  bar,  room  temperature. 

/  =  icm.          D  =  icm.         W  =         5.58         Q,  cm8  of  air,  5200.         cm3  of  J?2,  19700. 

10  i  27.1  1070.  4050. 

i  o.i  2710.  10.7  40.5 

10  o.i  24300.  i. 20  3.60 

Knudsen  derives  the  following  equation,  equivalent  to  Poiseuille's  at  higher,  and  to  the  above  at 
lower  pressures  : 

Q  =  (Pz  -Pi)  {aP  +  b  (i  +  £iP)/(i  +  fZP)}  where  a  =  irD4/i2Si)S  (Poiseuille's  constant) ;  b  = 
i/^\/p,  (coefficient  of  molecular  flow) ;  c^  =  \/~p  Z)/i)-,  and  r2  =  1.24  \/p  D!I\  ;  T?  =  viscosity  coef- 
ficient. The  following  are  the  volumes  in  cm3  at  i  bar,  2O°C,  that  flow  through  tube,  D  =  i  cm, 
/  =  locm,  /'.,-  j\  =  i  bar,  average  pressure  of  /'bars: 

P  =     io.«         Q  =  13,000,000.         P  =  5.         Q  =  1026.  P  =  i.  Q  =  1044.  cm3 

100.  2,227.  4-  1024.  o.i  1065. 

IO.  1,058.  3.  1025.  O.QI  IO7O. 

When  the  velocity  of  flow  is  below  a  critical  value,  /^(density,  viscosity,  diameter  of  tube),  the 
stream  lines  are  parallel  to  the  axis  of  the  tube.  Above  this  critical  velocity,  Vc,  the  flow  is  tur- 
bulent. Fe  =  ki7  pr  for  small  pipes  up  to  about  5  cm  diameter,  where  K  is  a  constant,  and  r  the 
tube  radius.  \Vhcn  these  are  in  cgs  units,  k  is  io3  in  round  numbers.  Below  Fc  the  pressure  drop 
along  the  tube  is  proportional  to  the  velocity  of  gas  flow  ;  above  it  to  the  square  of  the  velocity. 

*  See  Dushman,  The  Production  and  Measurement  of  High  Vacua,  General  Elec.  Rev.  23,  p.  493,  1920 
SMITHSONIAN  TABLES. 


TABLES  138-139. 
AERODYNAMICS. 

TABLE  138.  —  Air  Pressures  upon  Large  Square  Normal  Planes  at  Different  Speeds 

through  the  Air. 

The  resistance  F  of  a  body  of  fixed  shape  and  presentation  moving  through  a  fluid  may  be  written 

F  =  pl?V*f(LV/v) 

in  which  p  denotes  the  fluid  density,  v  the  kinematic  viscosity,  L  a  linear  dimension  of  the  body  F  the  speed  of  trans- 
lation. In  general  /  is  not  constant,  even  for  constant  conditions  of  the  fluid,  but  is  practically  so  for  normal  impact 
on  a  plane  of  fixed  size.  In  the  following,  p  is  taken  as  1.230  g/l  (.0768  lbs./ft3). 

The  mean  pressure  on  thin  square  plates  of  i.i  m2  (12  ft2),  or  over,  moving  normally  through  air  of  standard  density 
at  ordinary  transportation  speeds  may  be  written  P  =.oo6ov2  for  P  in  kg  per  m2  and  v  in  km  per  hour  or  P  =  0032-11* 
for  P  in  Ibs.  per  ft2  and  v  in  miles  per  hour.  The  following  values  are  computed  from  this  formula.  For  smaller  areas 
the  correction  factors  as  given  in  the  succeeding  table  (Table  139)  derived  from  experiments  made  at  the  British  National 
Physical  Laboratory,  may  be  applied. 

Units:  the  first  of  each  group  of  three  columns  gives  the  velocity;  the  second,  the  corresponding  pressure  inkg/m2 
when  the  first  column  is  taken  as  km  per  hour;  the  third  in  pds/ft2  when  in  miles  per  hour. 


Veloc- 
ity. 

Pressure. 

Veloc- 
ity. 

Pressure, 

Veloc- 
ity. 

Pressure. 

Veloc- 
ity. 

Pressure. 

Metric. 

English. 

Metric. 

English. 

Metric. 

English. 

Metric. 

English. 

10 

.60 

0.32 

40 

9.60 

5-12 

70 

29.4 

15-7 

IOO 

60.0 

32.0 

ii 

•73 

o.39 

4^ 

10.09 

5.38 

71 

30.2 

16.1 

101 

61.2 

32.6 

12 

.86 

0.46 

42 

10.58 

5-64 

72 

16.6 

102 

62.4 

33-3 

13 

14 

.01 

.18 

;fj 

43 

44 

11.09 
ii.  6 

5-92 

6.20 

73 
74 

32'© 
32.8 

17.0 
17-5 

103 
104 

63.7 
64.9 

33-9 
34-6 

16 

•  35 
•  54 

.82 

JS 

12.  I 
12.7 

6.48 

6.77 

11 

33-7 
34-7 

18.0 
18.5 

105 
106 

66.1 
67.4 

35-3 
36.0 

17 

•  73 

.92 

47 

13-3 

7.07 

77 

35-6 

19.0 

107 

68.7 

36.6 

18 

•94 

.04 

48 

13-8 

78 

36.5 

19-5 

108 

70.0 

37-2 

19 

•  17 

.16 

49 

14.4 

7.68 

79 

37-4 

20.0 

109 

7i-3 

38.0 

20 

.40 

.28 

50 

15-0 

8.00 

80 

38.4 

20.5 

no 

72.6 

38.7 

21 

•  65 

.41 

Si 

15-6 

8.32 

8l 

39-4 

21.0 

in 

73-9 

39-4 

22 

.90 

•  55 

52 

16.2 

8.65 

82 

40.3 

21.5 

113 

75-3 

40.1 

23 

3-17 

.69 

53 

16.9 

8-99 

83 

41-3 

22.0 

"3 

76.6 

40.9 

24 

3.46 

.84 

54 

17.5 

9-33 

84 

42.3 

22.6 

"4 

78.0 

41.6 

25 
26 

3-75 
4-06 

.00 
.16 

18.1 
18.8 

9.68 
10.04 

8s 
86 

43-3 
44.4 

23-1 
23-7 

"5 
116 

79-3 
80.8 

42.3 
43-1 

27 

4-37 

•  33 

57 

19-5 

10.40 

87 

45-4 

24.2 

117 

82.1 

43-7 

28 

4.70 

•  51 

58 

20.2 

10.76 

88 

46.4 

24.8 

118 

83.5 

44-6 

29 

5-05 

.69 

59 

20.9 

11.14 

89 

47-5 

25-4 

119 

84-9 

45-3 

30 

5-40 

.88 

60 

21.6 

11-52 

90 

48.  6 

25-9 

120 

86.4 

46.1 

31 

5-77 

3-o8 

61 

22.3 

11.91 

49-7 

26.5 

121 

87.8 

46.8 

32 

6.14 

3-28 

62 

23.0 

12.3 

92 

50.8 

27.1 

123 

89-3 

47-6 

33 

6.54 

3-48 

63 

23.8 

12.7 

93 

51-9 

27-7 

123 

90.8 

48.4 

34 

6-93 

3-70 

64 

24.6 

I3-I 

94 

53-0 

28.3 

124 

92.2 

49-2 

11 

7-35 
7-74 

3-92 
4-15 

65 
66 

3:S 

13-5 
13-9 

54-2 

28.9 
29-5 

IS 

93-7 
95-3 

50.0 
50.8 

37 

8.22 

4.38 

67 

26.9 

14.4 

97 

56  5 

30.1 

127 

96.8 

51-6 

38 

8.66 

4.62 

68 

27.7 

14.8 

98 

57-6 

30-7 

128 

98.4 

52.5 

39 

9.12 

4-87 

69 

28.6 

15-2 

99 

58.8 

31-4 

129 

98.7 

53-2 

TABLE  139.  —  Correction  Factor  for  Small  Square  Normal  Planes. 

The  values  of  Table  138  are  to  be  multiplied  by  the  following  factors  when  the  area  of  the  surface  is  less  than  about 
I  m2  (12  ft2). 


Metric. 

English. 

Area,     m2 

Factor. 

Area,    m- 

Factor. 

Area,     ft2 

Factor. 

Area,     ft2 

Factor 

0.03 

O.IO 

0.50 

0.845 
0.859 
0.884 

5-o 
6.0 
7-o 

0.969 
0-975 
0.979 

0.03 

0.  10 

0.50 

0.842 
0-857 
0.884 

S-o 
6.0 

7-0 

0.968 
0-973 
0.977 

0-75 

I.OO 

0.890 
0.898 

8.0 
9-o 

0.984 
0.989 

0.75 

I.OO 

0.889 
0.896 

8.0 
9.0 

0.981 
0.986 

2.00 

0.919 

IO.O 

0-993 

2.OO 

0.917 

IO.O 

0.990 

3-00 

0.933 

II.  0 

0.999 

3-00 

0.930 

II.  0 

0.994 

4.00 

0.950 

12.0 

I.  000 

4.00 

0-943 

12.0 

I.  000 

SMITHSONIAN  TABLES. 


152 


TABLES  140-14J. 

AERODYNAMICS. 

TABLE  140.  —  Effect  of  Aspect  Ratio  upon  Normal  Plane  Pressure  (Eiffel). 


The  mean  pressure  on  a  rectangular  plane  varies  with  the  "aspect  ratio,"  a  name  introduced 
by  Langley  to  denote  the  ratio  of  the  length  of  the  leading  edge  to  the  chord  length.  The  effect 
of  aspect  ratio  on  normally  moving  rectangular  plates  is  given  in  the  following  table,  derived 
from  Eiffel's  experiments. 


Aspect  ratio. 

I.  00 
I.OO 

i-5 
1.04 

3.00 
1.07 

6.00 

I.  10 

IO.OOO 

1.145 

14.60 

1.25 

20.00 

i-34 

30.00 
1.40 

41.500 
1-435 

50.00 
i-47 

Pressure  on  rectangle 

Pressure  on  square 

TABLE  141.  —  Ratio  of  Pressures  on  Inclined  and  Normal  Planes. 

The  pressure  on  a  slightly  inclined  plane  is  proportional  to  the  angle  of  incidence  a,  and 
is  given  by  the  formula  Pa  =  c-P9o-a.  The  value  of  c,  which  is  constant  for  incidences  up  to  about 
12°,  is  given  for  various  aspect  ratios.  The  angle  of  incidence  is  taken  in  degrees. 


Aspect  ratio 

-        .        3 

0.0360.0430.050 

4 
0-053 

5 
0.057 

6 
0.061 

7 
0.065 

8 
0.070 

9 

0.075 

10 

0.080 

Value  of  c.  . 

TABLE  142.  —  Skin  Friction. 


The  skin  friction  on  an  even  rectangular  plate  moving  edgewise  through  ordinary  air  is  given 
by  Zahm's  equation, 


or 


F(pds./ft.2) 


o.  00030  U(m2))°-93{  nkm/hr.)}1-86  in  metric  units 
0.0000082  \A  (ft.2)  }°-93  { 7(ft./sec.) }  1i86, 


where  A  is  the  surface  area  and  V  the  speed  of  the  plane.    The  following  table  gives  the  friction 
per  unit  area  on  one  side  of  a  plate. 


Speed. 

Skin  friction. 
Kg  per  sq.  m. 
Plane. 

Speed. 

Skin  friction. 
Lbs.  per  sq.  ft. 
Plane. 

km/hr. 

i  m  long. 

32  m  long. 

miles/hr. 

ft/sec. 

i  ft.  long. 

32  ft.  long. 

5 

0.0059 

0.0047 

5 

7-3 

0  .  00033 

o  .  00026 

10 

0.0217 

0.0171 

10 

14-7 

O.  001  2  I 

o  .  00095 

15 

o  .  0464 

o  .  0364 

15 

22.  O 

0.00258 

0.002O2 

20 

0.079 

0.062 

20 

29-3 

0.00439 

0.00345 

25 

0.  122 

0.095 

25 

36.7 

0.0068 

0.00530 

30 

o.  169 

0.133 

30 

44-o 

o  .  0094 

O.OO74 

40 

0.288 

0.225 

40 

58-7 

0.0160 

O.OI25 

So 

0-439 

0.346 

50 

73-3 

0.0244 

O.OI92 

00 

0.616 

0.482 

60 

88.0 

0.0342 

0.0268 

70 
80 

0.82 
i.  06 

0.64 
0.83 

70 
80 

102.7 
II7-3 

0.0455 
0.0587 

0.0357 
0.0461 

90 

i-3i 

1.03 

90 

132.0 

0.073 

0.0572 

IOO 

1.58 

1.24 

IOO 

146.7 

0.088 

0.069 

no 

1.89 

1.49 

no 

161.  2 

o.  105 

0.083 

120 

2.20 

1-73 

1  20 

175-8 

O.  122 

0.096 

125 

2-39 

1.87 

125 

183.4 

°-I33 

o.  104 

130 

2.56 

2.01 

130 

190.5 

o.  142 

O.  112 

135 

2.68 

2.  IO 

135 

197.8 

0.149 

o.  117 

140 

2.94 

2.31 

140 

205.4 

o.  164 

0.128 

US 

3  15 

2.47 

145 

212.5 

0.175 

0.137 

150 

3-37 

2.65 

!50 

220.0 

0.188 

0.147 

SMITHSONIAN  TABLES. 


TABLES  143-145. 
AERODYNAMICS.  • 

The  following  tables,  based  on  Eiffel,  show  the  variation  of  the  resistance  coefficient  K,  with 
the  angle  of  impact  i,  the  aspect  (ratio  of  leading  edge  to  chord  length),  shape  and  velocity  V 
in  the  formula 

tf(kg/m2)  =  KS(m2)fF(m/sec.)}2 
The  value  of  K  for  km/hour  would  be  0.77  times  greater. 

TABLE  143.  —  Variation  of  Air  Resistance  with  Aspect  and  Angle. 


Size  of  plane. 

Aspect. 

Values  of  i. 

Max.  ratio. 

6° 

10° 

20°     |        30° 

40° 

45° 

60° 

75° 

Value. 

». 

Values  of  Ki  /Kto. 

15  x  90  cm  
15  X45  cm  
25  x  25  cm  
30  x  15  cm  
45  x  15  cm  

I 

I 

2 

3 
6 

9 

.07 
.  II 
.  20 
.26 
•31 
•37 
•45 

•  13 

.  21 
•36 

•43 
•50 
•58 
.62 

.40 

•51 
.80 
.91 

•77 
.70 

•73 

0.67 
0.89 
1.24 
0.72 
0.77 
0.78 
0.80 

0.92 

I.  20 
I.I7 
0.79 
0.84 
0.84 
0.85 

I.  08 
I  .  22 
I.  08 
0.82 

0.88 
0.88 
0.88 

1.07 
i.  06 
1.03 
0.90 
0.94 

o-93 
0.94 

1.03 
1.02 
1.02 
0-97 
0.99 
0.98 
0.99 

1.07 
1.22 
1.46 
0.91 
0.77 
0.69 

60 

45 
38 
20 

20 
IS 

90  x  15  cm  
90  x  10  cm  

Cylinder,  base  JL  to  wind: 
Diameter  of  base,  30  cm 
Diameter  of  base,  15  cm 
Cylinder,  base 
Cylinder,  base 


TABLE  144.  —  Variation  of  Air  Resistance  with  Shape  and  Size. 

Length,     o  cm      iR*      2R*      *R*      6R*      SR* 


o  cm 

K  =        .0675     .068     .055     .050      —        — 
K=       .066       .066     .055     .051     .051     .0515 
to  wind:  diameter  base,  15  cm,  length,  60  cm  K  =  .040 
to  wind:  diameter  base,  3  cm,  length,  100  cm  K  =  .060 


.059 


Cone,  angle  60°,  diam.  base,  40  cm,  point  to  wind,  solid  K  =  .032 

Cone,  angle  30°,  diam.  base,  40  cm,  point  to  wind,  solid  K  =  .021 

Sphere,  25  cm  diam.  K  =  .on 

Hemisphere,  same  diam.,  convex  to  wind  K  =  .021 

Hemisphere,  same  diam.,  concave  to  wind  K  =  .083 

Sphero-conic  body,  diam.,  20  cm,  cone  20°,  point  forward  K  =  .010 

Sphero-conic  body,  diam.,  20  cm,  cone  20°,  point  to  rear  K  =  .0055 

Cylinder,  120  cm  long,  spherical  ends  to  wind  K  =  .012 

The  wind  velocity  for  the  values  of  this  table  was  10  m/sec. 

Tables  143  and  144  were  taken  from  "The  Resistance  of  the  Air  and  Aviation,"  Eiffel,  trans- 
lated by  Hunsaker,  1913. 

*  In  the  case  of  these  cylinders  the  percentages  due  to  skin  friction  are  2,  3,  6,  8,  n  and  16 
per  cent  respectively,  excluding  the  disk. 

TABLE  145.  —  Variation  of  Air  Resistance  with  Shape,  Size  and  Speed. 

This  table  shows  the  peculiar  drop  in  air  resistance  for  speeds  greater  than  4  to  12  meters  per 
second.    Another  change  occurs  when  the  velocity  approaches  that  of  sound. 


Values  of  K. 

1  Speed,  m/sec. 

4 

6 

8 

10 

12 

14 

16 

20 

32 

Sphere,  16.  2  cm  diameter  

•  033 

.030 

.028 

.027 

.024 

.009 

.0095 

.OIO 

.on 

Sphere,  24.4  cm  diameter  

.025 

.025 

.O2I 

•  013 

.OIO 

.010 

.010 

.OIO 

.OIO 

Sphere,  33  cm  diameter  

.023 

.017 

.OI2 

.010 

.OIO 

.OIO 

.on 

.012 

.012 

Concave  cup,  25  cm  diameter  

.090 

.090 

.089 

.087 

.087 

.088 

.089 

•  095 

.  IOO 

Convex  cup,  25  cm  diameter 

027 

.022 

.021 

.022 

.022 

.021 

.020 

.019 

.018 

Disk,  25  cm  diameter  

.071 

.070 

.070 

.070 

.070 

.070 

.070 

.070 

.068 

Cylinder                                                    cm 

element  _L  to  wind,  d  =  15  cm,  I  =  15.0 

•043 

.042 

•037 

.030 

•025 

.022 

.021 

.022 

.022 

element  JL  to  wind,          30               30.0 

•045 

.032 

.027 

.023 

.024 

.025 

.025 

.025 

.023 

element  _L  to  wind,           15                 7.5 

.035 

•034 

.032 

.031 

.031 

-031 

.030 

.030 

.030 

element  _L  to  wind,           15               12.0 

•  038 

-037 

.036 

.032 

.030 

.028 

.027 

.025 

.025 

element  _L  to  wind,          15              22.5 

.042 

.041 

.038 

•034 

.031 

.028 

.025 

.022 

.O2O 

element  ||  to  wind,            15             105.0 

.069 

.061 

•057 

•055 

•053 

.052 

•051 

.051 

.050 

Spherical  ends,                      15             120.0 

.024 

.022 

.019 

.018 

.018 

.Ol8 

.017 

.Ol6 

•015 

Taken  from  "Nouvelles  Recherches  sur  la  resistance  de  1'air  et  1'aviation,"  Eiffel,  1914. 
SMITHSONIAN  TABLES. 


154 


TABLES  146-148. 
TABLE   146. -Friction. 


The  required  force  F  necessary  to  just  move  an  object  along  a  horizontal  plane  =.fN  where  N  is  the  normal  pressure 
on  the  plane  and  f  the  "  coefficient  of  friction."  The  angle  of  repose  *  (tan  *  =  F/N)  is  the  angle  at  which  the 
plane  must  be  tilted  before  the  object  will  move  from  its  own  weight.  The  following  table  of  coefficients  was  com- 
piled by  Rankine  from  the  results  of  General  Morin  and  other  authorities  and  is  sufficient  for  ordinary  purposes. 


Material. 

/ 

I// 

+ 

Wood  on  wood,  dry       

.25-.50 

4.00-2.00 

14.0-26.5 

"       "       "       soapy   

.20 

5.00 

"•S 

Metals  on  oak,  dry         

•5o-.6o 

2.00-1.67 

26.5-31.0 

"        "      "    wet         

.24-.  26 

4-  17-3-85 

^•S-M-S 

"        "      "    soapy     ...... 

.20 

5.00 

"•5 

"         "    elm,  dry         ..'.... 

.20-.25 

5.00-4.00 

11.5-14.0 

Hemp  on  oak,  dry          

•53 

1.89 

28.0 

"        "      "     wet          

•33 

3.00 

18.5 

Leather  on  oak      .         .         .         . 

27-.  l8 

q.70-2.86 

I  C.O—  IQ  C 

"         "    metals,  dry  

*/    %J" 

•56 

Of        *«w 

179 

j-w     y*j 

29-5 

"         "         "       wet  

•36 

278 

2O.O 

"         "         "       greasy      

•23 

4-35 

I3.0 

"         "         "        oily          

•T5 

6.67 

8-5 

Metals  on  metals,  dry    

.15-.  20 

6.67-5.00 

8.5-11.5 

"wet   

•3 

3-33 

16.5 

Smooth  surfaces,  occasionally  greased  . 
continually  greased   . 

.07-.08 
.05 

14.3-12.50 

20.00 

4.0-4.5 
3-° 

"        best  results         .... 

.O3-.O36 

33-3-27-6 

175-2.0 

Steel  on  agate,  dry  *      

.20 

5.00 

TI-5 

"      "       "       oiled*   

.107 

9-35 

6.1 

Iron  on  stone         
Wood  on  stone      

.30-70 
About  .40 

3-33-1-43 

2.50 

167-35.0 

22.O 

Masonry  and  brick  work,  dry        .... 

.60-70 

1.67-1.43 

33-o-35-o 

''       "        "        damp  mortar 

•74 

J-35 

36-5 

"       on  dry  clay      

•51 

1.96 

27.0 

"         "  moist  clay  
Earth  on  earth       
dry  sand,  clay,  and  mixed  earth    . 
"       "       "      damp  clay     

•33 
.25-1.00 

•38-75 

I.OO 

3-oo 
4.00-1.00 
2-63-1-33 

I.OO 

18.25 
14.0-45.0 
21.0-37.0 
45-o 

"        "        "      wet  clay         

•31 

3-23 

17.0 

"       "       "      shingle  and  gravel 

.81-1.  ii 

1.23-0.9 

39.0-48.0 

*  Quoted  from  a  paper  by  Jenkin  and  Ewing,  "  Phil.  Trans.  R.  S."  vol.  167.  In  this  paper  it  is  shown  that  in 
cases  where  "  static  friction  "  exceeds  "  kinetic  friction  "  there  is  a  gradual  increase  of  the  coefficient  of  friction  as  the 
speed  is  reduced  towards  zero. 

TABLE  147, -Lubricants. 

The  best  lubricants  are  in  general  the  following:      Low  temperatures,  light  mineral  lubricating 

Very  great  pressures,  slow  speeds,  graphite,  soapstone  and  other  solid  lubricants.     Heavy 

ssures  slow  speeds  ditto  and  lard,  tallow  and  other  greases.  Heavy  pressures  and  high  speeds, 

sperm  oil,  castor  oil,  heavy  mineral  oils.    Light  pressures,  high  spee/s,  sperm,  refined  |et£leum 

.rape,  cot  tonsced.      Ordinary  machinery,  lard  oil,  tallow  oil,  heavy  mineral   oils  and  the 

eavier  vegetable  oils.    Steam  cylinders,  heavy  mineral  oils,  lard,  tallow.    Watches  and  delicate 

iisms,  clarified  sperm,  neat's-foot,  porpoise,  olive  and  light  mineral  lubricating  oils. 


TABLE  148.  -Lubricants  For  Cutting  Tools. 


Material. 

Turning. 

Chucking. 

Drilling. 

Tapping 
Milling. 

Reaming. 

Tool  Steel, 
Soft  Steel, 
Wrought  iron 
Cast  iron,  brass 
Copper 
Glass 

dry  or  oil 
dry  or  soda  water 
dry  or  soda  water 
dry 
dry 
turpentine  or  kerosene 

oil  or  s.  w. 
soda  water 
soda  water 
dry 
dry 

oil 
oil  or  s.  w. 
oil  or  s.  w. 
dry 
dry 

oil 
oil 
oil 
dry 
dry 

lard  oil 
lard  oil 
lard  oil 
dry 
mixture 

Mixture  =  X  crude  petroleum,  %  lard  oil.     Oil  =  sperm  or  lard. 
Tables  147  and  i^quoted  from  "Friction  and  Lost  Work  in  Machinery  and  Mill  Work,"  Thurston,  Wiley  and  Sons. 
SMITHSONIAN    TABLES. 


TABLES  149-151. 

VISCOSITY. 
TABLE  149.  —  Viscosity  of  Fluids  and  Solids. 


155 


The  coefficient  of  viscosity  of  a  substance  is  the  tangential  force  required  to  move  a  unit  area  of  a  pkne  surface 
with  unit  speed  relative  to  another  parallel  plane  surface  from  which  it  is  separated  by  a  layer  a  unit  thick  of  the  sub- 
stance. Viscosity  measures  the  temporary  rigidity  it  gives  to  the  substance.  The  viscosity  of  fluids  is  generally  meas- 
ured by  the  rate  of  flow  of  the  fluid  through  a  capillary  tube  the  length  of  which  is  great  in  comparison  with  its  diameter. 
The  equation  generally  used  is 


,  the  viscosity, 


Virgd*t 
X28Q0  +  X) 


where  y  is  the  density  (g/cm3),  d  and  /  are  the  diameter  and  length  in  cm  of  the  tube,  Q  the  volume  in  cm*  discharged 
in  /  sec.,  X  the  Couette  correction  which  corrects  the  measured  to  the  effective  length  of  the  tube,  h  the  average  head 
in  cm,  m  the  coefficient  of  kinetic  energy  correction,  mf/g,  necessary  for  the  loss  of  energy  due  to  turbulent  in  distinc- 
tion from  viscous  flow,  g  being  the  acceleration  of  gravity  (cm/sec/sec),  v  the  mean  velocity  hi  cm  per  sec.  (See  Tech- 
nologic Paper  of  the  Bureau  of  Standards,  100  and  112,  Herschel^igi 7-1918,  for  discussion  of  this  correction  and  X.) 

The  fluidity  is  the  reciprocal  of  the  absolute  viscosity.  The  kinetic  viscosity  is  the  absolute  viscosity  divided  by 
the  density.  Specific  viscosity  is  the  viscosity  relative  to  that  of  some  standard  substance,  generally  water,  at  some 
definite  temperature.  The  dimensions  of  viscosity  are  ML~lT~l.  It  is  generally  expressed  in  cgs  units  as  dyne-seconds 
per  cm2  or  poises. 

The  viscosity  of  solids  may  be  measured  in  relative  terms  by  the  damping  of  the  oscillations  of  suspended  wires 
(see  Table  78).  Ladenburg  (1006)  gives  the  viscosity  of  Venice  turpentine  at  18.3°  as  1300  poises;  Trouton  and 
Andrews  (1904)  of  pitch  at  o°,  51  X  io10,  at  15°,  1.3  X  to10;  of  shoemakers'  wax  at  8°,  4.7  X  io6;  of  soda  glass  at  575°, 
ii  X  io12;  Deeley  (1908)  of  glacier  ice  as  12  X  io13. 


TABLE  150.  —  Viscosity  of  Water  in  Centipoises.    Temperature  Variation. 

Bingham  and  Jackson,  Bulletin  Bureau  of  Standards,  14,  75,  1917. 


Vis- 

Vis- 

Vis- 

Vis- 

Vis- 

Vis- 

Vis- 

°c. 

cosity. 

°C. 

cosity. 

°C. 

cosity. 

°C. 

cosity. 

°C. 

cosity. 

°C. 

cosity. 

°C. 

cosity. 

cp 

cp 

cp 

cp 

cp 

cp 

cp 

o 

.7921 

10 

.3077 

20 

1.0050 

30 

0.8007 

40 

0.6560 

50 

0.5494 

60 

0.4688 

i 

.7313 

ii 

.2713 

21 

0.9810 

3i 

0.7840 

41 

0.6439 

Si 

0.5404 

65 

0.4355 

2 

.6728 

12 

.2363 

22 

0.9579 

32 

0.7679 

42 

0.6321 

52 

0.5315 

70 

0.4061 

3 

.6191 

13 

.2028 

23 

0.9358 

33 

0.7523 

43 

o.  6207 

53 

0.5229 

75 

0.3799' 

4 

•  5674 

14 

.1709 

24 

0.9142 

34 

0-7371 

44 

0.6097 

54 

0.5146 

80 

0.3*65 

| 

.5188 
.4728 

IS 
16 

.1404 
.1111 

25 
26 

0.8937 

0.8737 

35 
36 

0.7225 
0.7085 

45 
46 

0.5988 
0.5883 

55 
56 

0.5064 
0.4985 

85 

00 

0-3355 
0.3165 

7 

.4284 

17 

.0828 

27 

0.8545 

37 

0.6947 

47 

0.5782 

57 

0.4907 

95 

0.2994 

8 

.3860 

18 

•  0559 

28 

0.8360 

38 

0.6814 

48 

0.5683 

S8 

0.4832 

IOO 

0.2838 

9 

.3462 

19 

.0299 

29 

0.8180 

39 

0.6685 

49 

0.5588 

59 

0.4759 

153 

0.181* 

*  de  Haas,  1894.    Undercooled  water:    —2.10°,  1.33  cp;    —4.70°,  2.12  cp;  —6.20°,  2.25  cp;  —8.48°,  2.46  cp; 

—9.30°,  2.55  cp;   White,  Twining,  J.  Amer.  Ch.  Soc.,  50,  380,  1913. 

TABLE  151.  —  Viscosity  of  Alcohol-water  Mixtures  in  Centipoises.    Temperature  Variation. 


Percentage  by  weight  of  ethyl  alcohol. 

°c. 

o 

IO 

20 

30 

39 

40 

45 

50 

60 

70 

80 

90 

IOO 

o 

.792 

3-3II 

5.3I9 

6.94 

7-25 

7.14 

6-94 

6.58 

5-75 

4.762 

3-6oo 

-732 

-773 

5 

10 

•  519 

.308 

•577 
.179 

4.065 
3.I6S 

5-29 

4-05 

5.62 
4-39 

5-59 
4-39 

5-50 
4-35 

5-26 
4.18 

4-63 
3-77 

3-906 
3-268 

3-125 
2.710 

•  309 

.101 

.623 
.466 

15 

.140 

.792 

.6l8 

3-26 

3-52 

3-53 

3-Si 

3-44 

3.14 

2.770 

2.309 

.802 

-332 

20 

.005 

•  538 

.183 

2.71 

2.88 

2.91 

2.88 

2.87 

2.67 

2.370 

2.008 

.610 

.200 

25 

.894 

.323 

.815 

2.18 

•35 

2-35 

2-39 

2.40 

2.24 

2.037 

1.748 

.424 

.006 

30 

.801 

.160 

•  553 

.87 

.00 

2.02 

2.02 

2.02 

1-93 

1.767 

I.53I 

.279 

.003 

35 

.722 

.006 

•  332 

.58 

•  71 

1.72 

1.73 

1.72 

1.66 

1-529 

1-355 

.147 

.914 

40 

.656 

.907 

.160 

.368 

•  473 

1.482 

1-495 

1.499 

1.447 

1-344 

1.203 

•  035 

•834 

45 

•599 

.812 

.015 

.189 

.284 

1.289 

1-307 

1.294 

1.271 

1.189 

1.081 

•939 

.764 

50 

•  549 

•734> 

.907 

.050 

.124 

1.132 

1.148 

I-  155 

1.127 

1.062 

0.968 

.848 

.702 

60 
70 

.469 
.406 

.609 
•  514 

:& 

0.834 
0.683 

0.885 
0.725 

0.893 
0.727 

0.907 
0.740 

0.913 
0.740 

0.902 
0.729 

0.856 
0.695 

0.789 
0.650 

.704 
089 

-592 
-504 

80 

•  356 

•  430 

•  505 

0.567 

0.598 

0.601 

0.609 

0.612 

o.  604 

SMITHSONIAN  TABLES. 


Same  authority  as  preceding  table. 


156 


TABLES  162-164. 

VISCOSITY. 

TABLE  152.  —  Viscosity  and  Density  of  Sucrose  in  Aqueous  Solution. 
See  Scientific  Paper  298,  Bingham  and  Jackson,  Bureau  of  Standards,  1917,  and  Technologic 
Paper  100,  Herschel,  Bureau  of  Standards,  1917. 


-ity  in  centipoises. 

Density  d*. 

Tempera- 
ture. 

Per  cent  sucrose  by  weight. 

Per  cent  sucrose  by  weight. 

0 

20 

40 

60 

0 

20 

40 

60 

0°C 

.7921 

3.804 

14-77 

238. 

0.99987  . 

•  08546 

I  .  18349 

-  29560 

5 

.5188 

3-154 

11.56 

156. 

0.99999 

.  08460 

I  .  l8l92 

.29341 

10 

•3077 

2.652 

9-794 

109.8 

0-99973 

•08353 

I.  l8O2O 

.29117 

15 

.1404 

2.267 

7.468 

74-6 

0.99913 

.08233 

I.I7837 

.  28884 

20 

.0050 

I  .960 

6.  200 

56-5 

0.99823 

.  08094 

I.I7648 

.  28644 

30 

0.8007 

1-504 

4-382 

33.78 

0.99568 

.07767 

I.I72I4 

.  28144 

40 

0.6560 

I-J93 

3-249 

21.28 

0.99225 

.07366 

I.I6759 

.27615 

5° 

0-5494 

0.970 

2-497 

14.01 

0.98807 

.06898 

I.I6248 

.27058 

60 

0.4688 

0.808 

1.982 

9-83 

0.98330 

.06358 

LI5693 

I  .  26468 

70 

0.4061 

0.685 

i.  608 

7-15 

80 

0-3565 

0.590 

1-334 

5-40 

Densities  due  to  Plato. 

TABLE  153.  —  Viscosity  and  Density  of  Glycerol  in  Aqueous  Solution  (20°  C). 


% 

Glycerol. 

* 

Den- 
sity. 
g/cm» 

Viscos- 
ity in 
centi- 
poises. 

roo  X 
Kine- 
matic 
viscos- 
ity. 

Gfyc- 
erol. 

Den- 
sity, 
g/cm' 

Viscos- 
ity in 
centi- 
poises. 

ioo  X 
Kine- 
matic 
viscos- 
ity. 

Git 
erol. 

Den- 
sity. 
g/cnV 

Viscos- 
ity in 
centi- 
poises. 

ioo  X 
Kine- 
matic 
viscos- 
ity- 

5 

1.0098 

I.lSl 

1.170 

35 

-0855 

3-II5 

2.870 

65 

1.1662 

I4-5I 

12.44 

10 

1.0217 

1.364 

1-335 

40 

.0989 

3-791 

3-450 

70 

1.1797 

21.49 

l8.22 

15 

1-0337 

1.580 

I-529 

45 

.1124 

4.692 

4.218 

75 

1.1932 

33-71 

28.25 

20 

1.0461 

1.846 

r-765 

50 

.1258 

5.908 

5.248 

80 

I  .  2066 

55-34 

45-86 

25 

1.0590 

2.176 

2-055 

55 

•1393 

7.664 

6.727 

85 

I.  2201 

102.5 

84.01 

30 

1.0720 

2.585 

2.411 

60 

.1528 

10.31 

8-943 

90 

1-2335 

207.6 

168.3 

The  kinematic  viscosity  is  the  ordinary  viscosity  in  cgs  units  (poises)  divided  by  the  density. 
TABLE  154.  —  Viscosity  and  Density  of  Castor  Oil  (Temperature  Variation). 


°c 

B 

x  •/ 

1  Kinematic  1 
'-ity.  ! 

°C 

ft 

I! 

1U 

°C 

i! 

Q  M 

>.£ 

Kinematic  1  1 
viscosity.  1 

°C 

is 

'7s  ,J5 

Kinematic  1 
viscosity.  1 

5 

.9707 

37.6 

38.7 

14 

•9645 

16.61 

17.22 

23 

-9583 

7.6; 

8.00 

32 

.9520 

3-94 

4.14 

6 

.9700 

34.5 

35-5 

15 

.9638 

15-14 

15-71 

24 

•9576 

7.06 

7-37 

33 

•9513 

3-65 

3.84 

7 

.9693 

31-6 

32.6 

16 

•9631 

13.80 

M-33 

25 

•9569 

6.51 

6.80 

34 

.9506 

3-40 

3.58 

8 

.9686 

28.9 

29.8 

17 

.9624 

12.65 

13-14 

26 

•9562 

6.04 

6-32 

35 

•9499 

3.16 

3-33 

9 

.9679 

26.4 

27-3 

18 

.9617 

11.62 

12.09 

27 

•9555 

5-6i 

5.87 

36 

.9492 

2.94 

3.10 

10 

.9672 

24.2 

25.0 

19 

.9610 

10.  71 

11.15 

28 

.9548 

5-21 

5-46 

37 

•  9485 

2.74 

2.89 

ii 

.9665 

22.1 

22.8 

20 

.9603 

9.86 

10.  27 

29 

•9541 

4-8<> 

5.08 

38 

.9478 

2.58 

2.72 

12 

.9659 

20.  I 

20.8 

21 

•9596 

9.06 

9-44 

30 

•9534 

4-51 

4-73 

39 

.9471 

2.44 

2.58 

13 

.9652 

18.2 

18.9 

22 

•9589 

8-34 

8.70 

•9527 

4.21 

4-42 

40 

•9464 

2.31 

2-44 

1 

Tables  153  and  154,  taken  from  Technologic  Paper  112,  Bureau  of  Standards,  1918.    Glycerol 
data  due  to  Archbutt,  Deeley  and  Gerlac}r,  Castor  Oil  to  Kahlbaum  and  Raber.    See  preceding 
table  for  definition  of  kinematic  viscosity.    Archbutt  and  Deeley  give  for  the  density  and  viscosity 
of  castor  oil  at  65.6°  C,  0.9284  and  0.605,  respectively;  at  100°  C,  0.9050  and  0.169. 
SMITHSONIAN  TABLES. 


TABLE  155. 
VISCOSITY    OF    LIQUIDS- 

Viscosities  are  given  in  cgs  units,  dyne-seconds  per  cm2,  or  poises. 


157 


Liquid. 

°C 

Viscosity. 

Refer- 
ence. 

Liquid. 

°C 

Viscosity. 

Refer- 
ence 

Acetaldehyde  

0. 

10. 

0.00275 
0.00252 
0.00231 

i 
i 

i 

*  Dark  cylinder  
*"  Extra  L.  L."  

37-8 

IOO.O 

37  8 

7-324 
0.341 

10 
IO 

Air  
Aniline 

-192.3 

o.  00172 
o.  04467 

2 

3 

Linseed  .925  $ 

IOO.O 

0.451 

10 

Bismuth 

60. 
285 

0.0156 
o.  0161 

3 
4 

-922  
•  914 

50. 

0.176 

9 

?6e 

o  0146 

Olive    9195 

i   x8 

Copal  lac  
Glycerine 

22. 
2    8 

4.80 

4-2    2 

I 

15- 

1-075 

ii 

14  3 

13.87 

6 

"     9065 

3° 

tt         

20.3 
26  5 

8.30 

4.  94 

6 
6 

"    .9000  

40. 
5° 

0.363 

o  258 

ii 

8o.3i%H2O.. 
64.05%H20.. 
49-79%H20.. 

8-5 
8.5 
8.5 

i  .  02  1 

O.222 

o.  092 

6 
6 
6 

tRape  '.'.'.'.'.'.'.'.'.'. 

70. 
15-6 
37-8 

0.124 
i.n8 
0.422 

ii 

10 
IO 

Hydrogen,  liquid  
Menthol,  solid  
liquid  

14.9 
34-9 

0.  0001  I 
2  X   1012 
0.069 

2 

7 
7 
g 

(another)  
(another)  

IOO.O 

15.6 

IOO.O 

0.080 
1.176 
0.085 

IO 

10 
10 

o. 

20. 

o.  01661 
0.01547 
o  01476 

4 
4 

"        "      .915  
"      .906  
t  Sperm 

50.0 
90.0 
15.6 

0.206 
0.078 

9 
0 
IO 

ii 

O8 

37  8 

o  185 

11 

ii 

Oils: 

299. 

0.00975 

4 

Paraffins: 
Pentane 

21  .  O 

o  0026 

12 

Dogfish-liver  .  923  J.  .  . 
"     .918.... 
"     .908.... 

30. 
50. 

0.414 

0.  211 

o  080 

9 
9 

Hexane  
Heptane  
Octane 

23-7 
24.0 
22.  2 

0.0033 
0.0045 
o  0053 

12 
12 
12 

Linseed  .925  
"         922 

30. 

0.331 

9 

Nonane  

22.3 

0.0062 

12 

"        .914  

QO. 

O.O?! 

9 

Undecane  

22.7 

0.0095 

12 

*  Spindle  oil  .  885  .... 

IS.6 

37  8 

0-453 

o  162 

10 

Dodecane  
Tridecane 

23-3 
23.3 

0.0126 
o  OI55 

12 

12 

*  Light  machinery 

IOO.O 

0.033 

10 

Tetradecane  
Pentadecane 

21.9 
22.0 

0.0213 
0.0281 

12 
12 

.  907  t  

is  6 

I   138 

22.  2 

o  0359 

12 

*  Light  machinery  .... 

37  8 

0.342 

IO 

Phenol..                    

18.3 

o.  1274 

13 

9O.O 

o  0126 

13 

*  "  Solar  red"  engine.  . 

15  6 

1  .  915 

IO 

Sulphur  

170. 

320.0 

14 

37  8 

o  496 

IO 

180. 

550.0 

14 

ii       ii          ii 

o  058 

187. 

560  o 

14 

*"  Bayonne"  engine.. 

15.6 
37  8 

2.172 

o  S72 

IO 

200. 
25O. 

500.0 
104.0 

14 
14 

*           «               " 

IOO.O 

0.063 

IO 

300. 

24.0 

14 

*  "  Queen's  red  "  engine 

15  6 

2  995 

IO 

340. 

6.2 

14 

37  8 

380. 

.  5 

14 

*  "  Galena  "  axle  oil  . 

IOO.O 

IS  6 

0.070 
4  366 

10 

420. 

448. 

:S 

14 
14 

*          ii           ii     <• 

?7  g 

t  Tallow 

66. 

.  176 

IO 

*  Heavy  machinery.  .  . 

IS  6 

6  606 

IO 

IOO. 

.078 

10 

37  8 

280. 

.0168 

4 

*  Filtered  cylinder.  .  .  . 

37.8 

2  .406 

IO 

357- 

.0142 

4 

IOO    O 

o  187 

« 

389- 

.0131 

4 

*  Dark  cylinder  

37-8 

IOO.O 

4.224 
0.240 

10 
10 

*  American  mineral  oils;   based  on  water  as  .01028  at  20°  C.     t  Based  on  water  as  per  ist  footnote.    J  Densities. 

References:  (i)  Thorpe  and  Rodger,  1894-7;  (2)  Verschaffelt,  Sc.  Ab.  1917;  (3)  Wijkander,  1879;  (4)  Plus*. 
Z.  An.  Ch.  93,  1915;  (5)  Metz,  C.  R.  1903;  (6)  Schottner,  Wien.  Ber.  77,  1878,  79,  1879;  (7)  Heydweiller,  W.  Ann. 
63,  1897;  (8)  Koch,  W.  Ann.  14,  1881;  (9)  White,  Bui.  Bur.  Fish.  32,  1912;  (10)  Archbutt-Deeley,  Lubrication  and 
Lubricants,  1912;  (n)  Higgins,  Nat.  Phys.  Lab.  n,  1914;  (12)  Bartolli,  Stracciati,  1885-6;  (13)  Scarpa,  1903-4; 
(14)  Rotinganz,  Z.  Ph.  Ch.  62,  1908. 


SMITHSONIAN  TABLES. 


j  t-g  TABLE  166. 

VISCOSITY  OF   LIQUIDS- 

Compiled  from  Landolt  and  Bornstein,  1912.     Based  principally  on  work  of  Thorpe  and 
Rogers,  1894-97.    Viscosity  given  in  centipoises.    One  centipoise  =  o.oi  dyne-second  per  cm2. 


Liquid. 

Viscosity  in  centipoises. 

Formula. 

o°C 

10°  C 

20°  C 

30°  C 

40°  C 

50°  C 

70°  C 

100°  C 

Acids:  Formic  
Acetic  
Propionic 

CH202 
C2H4O2 
C3H602 

C.H802 

C4H802 
CH40 
C2H60 
CsHeO 
C3H80 
C3H80 
C^oO 
C4H100 
C5H120 
C5H120 
C6H6 
C7H8 
C8H10 
C8H10 
CgHio 
C8Hio 
C2H5Br 
C3H7Br 
C3H7Br 
C3H5Br 
C2H4Br 
Br 
C3H7C1 
C3H5C1 
C2H4C1 
CHCla 

CC14 

C4H100 
C4H100 
C6H120 
C6H140 
C2H402 
C3H60 
C3H602 
Cjls02 
CH3I 
C2H6I 
C3H7I 
C3H6I 
C5H12 
CsHi2 
CeHi4 
C6H14 
C7H16 
C7H16 
C8His 
CS2 
C4H10S 

solid 
solid 
1.521 

2.286 
1.887 
0.817 
1.772 

2-145 
3-883 
4-565 
5.186 
8.038 
ii.  129 
8-532 
0.906 
0.772 
0.877 
1.  105 
0.806 
solid 
0.487 
0.651 
0.611 
0.626 
2.438 
i.  267 
0.442 
0.413 
1.132 
0.706 

!-35i 
0.294 

0-314 
0.402 

o-544 
0.436 
0.510 
0.484 
0.582 
0.606 
0.727 

0-944 
0.936 
o.  289 
0.284 
0.401 
0.376 
0.524 
0.481 
o.  706 

0.438 

0.563 
2.248 

2.247 

solid 
.289 
.851 
.568 
.690 
.466 

•70S 
2.918 
3.246 

3-873 
5-548 
7-425 
6.000 
0.763 
0.671 
o.  761 

0.937 
0.702 
0.738 
0.441 

0.582 

0-545 
0.560 
2.039 

I.  120 
0.396 
0-372 
0.966 
0-633 
I.I38 
0.268 
0.285 
0.360 
0.479 
0.391 
0-454 

0-431 
0.512 
0.548 
0.654 

0-833 
0.826 
0.262 
0.256 
0.360 
0-338 
0.465 
0.428 
0.616 
0.405 
0.501 
1-783 

1.784 
I.  222 
I.  IO2 
1-540 
I.3I8 
0.596 
I  .  200 

1.363 
2.  256 
2.370 
2.948 

3.907 
5.092 
4-342 
0.654 
0.590 
0.669 
0.810 
O.62O 
0.648 
0.402 
0.524 
0.489 
0.504 
I.72I 
1.005 

0-359 
0-337 
0.838 

0-571 
0-975 
0-245 
0.260 
0.324 
0.425 

o-355 
0.408 
0.388 

0-455 
0.500 
0.592 
0-744 
0-734 
o.  240 
0.234 
0.326 
0.306 
0.416 
0.384 
0.542 
0.376 
0.450 
1.487 

.460 
.040 
.960 

•304 
.129 

.520 
.003 
.168 

•779 

•757 
2.267 
2.864 
3-594 
3.207 
0.567 
0.525 

0-594 
o.  709 

0-552 
0-574 
0.368 

0-475 
0-443 
0.458 

1-475 
0.911 

0.326 
0.307 
0.736 

o-5i9 
0.848 
0.223 
0.237 
0.294 
0.381 
0-325 
0.369 
o-352 
0.407 
0.460 
0.540 
0.669 
0.660 
o.  220 

o.  296 
0.279 
0-375 
0-347 
0.483 
0-352 
0.407 
1.272 

1.219 
0.905 
0.845 
I.  1  2O 
0.980 
0.456 
0.834 
0.914 
1.405 

I-33I 
1.782 
2.  122 
2.6O7 
2.415 
0.498 
0.471 

0.531 
0.627 
0.497 
0.513 

0-433 
0.403 
0.419 
1.286 
0.830 
0.299 
0.282 
0.652 

0-474 
0.746 

0.268 
0-344 

0.336 
0.320 

0.367 
0.424 

0-495 
0.607 

0-597 

0.271 
0.254 
0.341 
0.315 
0-433 
0.330 
0.369 
I.07I 

1.036 
0.796 
0-752 
0-975 
0.862 

0.403 
o.  702 

0.763 
.130 
.029 
.411 
.611 

•937 
.851 
0.444 
0.426 
0.479 
0.560 
0.451 
0.463 

0-397 
0.368 
0.384 
1.131 
o.  761 

0.584 
0-435 
0.662 

0.245 
0.311 

0.308 
0.293 
0-333 

0.456 

0.552 
0-544 

0.248 
0.233 
0.310 
0.288 
0.391 

0.338 
0.926 

.780 
•631 
.607 
.760 
•683 

.510 

•553 
.760 
.646 
•930 

•359 
•354 
•397 
•458 
•375 
•383 

•338 

•328 
•903 

•479 
•534 

.279 

•391 
.466 
.458 

.262 
•243 

-324 

.287 
.728 

•549 
•465 
•459 
•551 
.501 

-540 
•527 
.610 
.632 

.278 
.310 
•352 
.  296 
.300 

.678 

— 

•371 
•365 

•  252 

Butyric 

i-Butyric  . 

Alcohols:  Methyl  .  . 

Ethyl  *  ... 

Allyl        

Proovl 

•  1UK7»  

i-Propyl.  . 

Butyric 

i-Butyric 

Amyl,  op.  act  
Amyl,  op.  inact. 

Aroma  tics:  Benzene  
Toluene 

Ethylbenzole  
Orthoxylene  . 

Metaxylene 

Paraxylene 

Bromides-  Ethyl   

Propyl 

i-Propyl.  .  .  . 

Allyl  

Ethylene  

Bromine.  .  . 

Chlorides:  Propyl  
Allyl 

Ethylene 

Chloroform  .  .  . 

Carbon-tetra  
Ethers:  Diethyl 

Methyl-propyl  

Ethyl-propyl  .  . 

Dipropyl  
Esters:  Methylformate  .  .  . 
Ethylformate 

Methylacetate  
Ethylacetate  
Iodides:  Methyl  
Ethyl  
Propyl  

Allyl  

Paraffines:  Pentane  
i-Pentane. 

.me  .  . 

i-Hexane  
Heptane  
i-Heptane  
Octane 

Sulphides:  Carbon  di-.  .  .  . 
Kthyl  

Turpentine  f  

SMITHSONIAN  TABLES. 


Bureau  of  Standards,  see  special  table,     f  Glaser. 


TABLE  157. 
VISCOSITY  OF  SOLUTIONS. 


159 


This  table  is  intended  to  show  the  effect  of  change  of  concentration  and  change  of  temperature  on  the  viscosity  of 
solutions  of  salts  in  water.  The  specific  viscosity  X  100  is  given  for  two  or  more  densities  and  for  several  tem- 
peratures in  the  case  of  each  solution,  /u.  stands  for  specific  viscosity,  and  t  for  temperature  Centigrade. 


Salt. 

Percentage 
by  weight 

of  salt  in 
solution. 

Authority* 

BaCl2 

7-60 

_ 

77-9 

10 

44.0 

30 

35-2 

5p 

_ 

_ 

Sprung. 

" 

15.40 

— 

86.4 

" 

56.0 

39-6 

— 

- 

" 

" 

24-34 

- 

100.7 

u 

66.2 

M 

47-7 

M 

- 

- 

" 

Ba(NO3)2 

2.98 

1.027 

62.0 

15 

5" 

25 

42.4 

35 

34-8 

45 

Wagner. 

: 

5-24 

1.051 

68.1 

54-2 

44.1 

36-9 

" 

CaCl2 

I5-I7 

- 

1  10.9 

10 

7i-3 

30 

50-3 

5° 

- 

_ 

Sprung. 

" 

31.60 

— 

272.5 

M 

177.0 

" 

124.0 

" 

- 

— 

" 

" 

39-75 

- 

670.0 

" 

379-o 

" 

245-5 

" 

- 

- 

M 

" 

44.09 

- 

— 

- 

593-1 

" 

363-2 

M 

- 

- 

* 

Ca(NO3)2 

'7-55 

1.171 

93-8 

15 

74-6 

25 

60.0 

35 

49-9 

45 

Wagner. 

" 

30.10 

1.274 

144.1 

" 

112.7 

4* 

90.7 

" 

75-1 

" 

u 

« 

40.13 

1.386 

242.6 

u 

217.1 

M 

156-5 

u 

128.1 

" 

" 

CdCl2 

11.09 

1.109 

77-5 

I5 

60.5 

25 

49.1 

35 

40.7 

45 

« 

" 

16.30 

1.181 

88.9 

" 

70-5 

" 

57-5 

47-2 

" 

M 

24.79 

1.320 

104.0 

" 

804 

" 

64.6 

" 

53-6 

" 

" 

Cd(NO3)2 

7.81 

1.074 

61.9 

15 

50.1 

25 

41.1 

35 

34-o 

45 

u 

u 

15.71 

I-I59 

71.8 

58.7 

M 

48.8 

41-3 

" 

" 

22.36 

1.241 

85.1 

u 

69.0 

" 

57-3 

" 

47-5 

" 

" 

CdS04 

7.14 

i.  068 

78.9 

15 

61.8 

25 

49-9 

35 

4i-3 

45 

« 

" 

14.66 

1-159 

96.2 

" 

72.4 

58.1 

48.8 

" 

" 

22.OI 

1.268 

120.8 

•  u 

91.8 

" 

73-5 

" 

60.  i 

" 

" 

CoCl2 

7-97 

1.081 

83.0 

15 

65.1 

25 

53-6 

35 

44-9 

45 

« 

'   « 

14.86 

22.27 

1.161 
1.264 

1  1  1.  6 
161.6 

85.1 
126.6 

73-7 
101.6 

85^6 

M 

« 

Co(NO3)2 

8.28 

1-073 

74-7 

15 

§•9 

25 

48.7 

35 

39-8 

45 

H 

" 

15.96 

1.144 

87.0 

.2 

55-4 

44-9 

" 

" 

24-53 

1.229 

110.4 

u 

.0 

" 

" 

59-  i 

M 

H 

CoSO4 
« 

7.24 
14.16 
21.17 

i.  086 

I-I59 

1.240 

86.7 
117.8 
193.6 

y 

68.7 

95-5 
146.2 

25 

55-o 
76.0 
113.0 

35 

6il7 
89.9 

45 

M 
H 

CuCl2 

I2.OI 

1.104 

87.2 

y 

67.8 

25 

55.1 

35 

45-6 

45 

« 

11 

21-35 

1.215 

121.5 

95-8 

77-o 

63-2 

44 

u 

u 

33-03 

178.4 

14 

137.2 

M 

107.6 

" 

87.1 

M 

Cu(N03)2 

18.99 

1.177 

97-3 

y 

76.0 

25 

61.5 

35 

51.3 

45 

ft 

" 

26.68 

1.264 

126.2 

98.8 

80.9 

68.6 

tk 

" 

H 

46.71 

'•536 

382.9 

" 

283.8 

" 

215-3 

" 

172.2 

" 

" 

CuSO4 

6-79 

1-055 

79-6 

y 

61.8 

25 

49-8 

35 

41.4 

45 

" 

M 

12.57 

1.115 

98.2 

74.0 

" 

59-7 

" 

52-0 

" 

17.49 

1.163 

124.5 

u 

96.8 

" 

75-9 

61.8 

HC1 

8.14 

1-037 

71.0 

y 

57-9 

25 

48-3 

35 

40.1 

45 

M 

u 

16.12 

1.084 

80.0 

66.5 

56.4 

48.1 

" 

M 

" 

23.04 

1.114 

91.8 

" 

79-9 

M 

65-9 

" 

56-4 

HgCl2 

0.23 

3-55 

1.002 

I-°33 

76.75 

IO 

58-5 
59-2 

20 

46.8 
46.6 

3f 

38-3 
38.3 

40 

U 

SMITHSONIAN  TABLES. 


i6o 


TABLE    157  (continued). 

VISCOSITY    OF    SOLUTIONS, 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density 

- 

t 

* 

Authority. 

HN08 

8-37 

1.067 

66.4 

15 

54-8 

25 

45-4 

35 

37-6 

45 

Wagner. 

" 

12.20 

I.IIO 

69-5 

" 

57-3 

u 

47-9 

" 

40.7 

" 

" 

" 

28.31 

1.178 

80.3 

" 

65.5 

" 

54-9 

" 

46.2 

" 

" 

H2S04 

7.87 

1.065 

77-8 

15 

61.0 

25 

50.0 

35 

41.7 

45 

u 

•• 

I5-50 

1.130 

95.1 

«< 

75-o 

<( 

60.5 

u 

49-8 

« 

" 

23-43 

1.200 

122.7 

u 

95-5 

" 

77-5 

" 

64-3 

M 

" 

KCi 

IO.23 

- 

70.0 

10 

46.1 

30 

33.1 

50 

_ 

_ 

Sprung. 

22.21 

— 

70.0 

" 

48.6 

M 

•36.4 

" 

— 

- 

" 

KBr 

14.02 

_ 

67.6 

IO 

44.8 

3? 

32.1 

5° 

_ 

_ 

M 

.. 

23.16 

— 

66.2 

" 

44-7 

33-2 

M 

_ 

_ 

« 

" 

34.64 

— 

66.6 

M 

47-o 

" 

35-7 

H 

- 

- 

" 

KI 

8.42 

- 

69.5 

IO 

44-o 

3° 

fci-3 

50 

_ 

_ 

H 

I7.OI 

— 

65-3 

u 

42.9 

" 

— 

_ 

H 

" 

33-03 

— 

61.8 

" 

42.9 

" 

32-4 

" 

_ 

_ 

" 

" 

45-98 

— 

67.0 

M 

45-2 

" 

35-3 

" 

_ 

_ 

«< 

" 

54-oo 

- 

68.8 

U 

48.5 

u 

37-6 

" 

- 

- 

" 

KC103 

3-51 

- 

71.7 

IO 

44-7 

30 

3i-5 

50 

_ 

_ 

u 

5-69 

~ 

*• 

45-o 

31-4 

- 

- 

" 

KNO3 

6.32 

_ 

70.8 

10 

44.6 

3° 

31.8 

5° 

_ 

_ 

u 

M 

12.19 

— 

68.7 

" 

44.8 

32-3 

" 

_ 

_ 

U 

" 

17.60 

- 

68.8 

H 

46.0 

" 

33-4 

" 

- 

- 

M 

K2SO4 

5-T7 

- 

77-4 

IO 

48.6 

3p 

34-3 

50 

_ 

_ 

m 

9-77 

— 

81.0 

" 

52.0 

36-9 

u 

- 

- 

* 

K2Cr04 

"•93 

_ 

75-8 

10 

62.5 

3f 

41.0 

4p 

_ 

_ 

„ 

19.61 

— 

85.3 

" 

68.7 

47-9 

_ 

_ 

n 

24.26 

1-233 

97.8 

" 

74-5 

" 

« 

_ 

_ 

Slotte. 

32.78 

109.5 

" 

88.9 

" 

62.6 

It 

- 

- 

Sprung. 

K2Cr2O7 

4.71 
6.97 

1.032 
1.049 

72.6 
73-i 

10 

55-9 
5°-4 

20 

45-3 
45-5 

3? 

37-5 
37-7 

4p 

Slotte. 

LiCl 

776 

- 

96.1 

10 

59-7 

30 

41.2 

5° 

_ 

_ 

Sprung. 

'3-91 

~ 

21.3 

75-9 

" 

52.6 

— 

— 

" 

26.93 

— 

229.4 

" 

142.1 

" 

98.0 

" 

- 

- 

" 

Mg(N08)2 

18.62 
34-19 

1.  102 
I.2OO 

^99.8 

IS 

81.3 
164.4 

25 

66.5 
132.4 

35 

56.2 
109.9 

45 

Wagner. 

39-77 

1.430 

3x7-o 

M 

250.0 

" 

191.4 

" 

158.1 

" 

" 

MgS04 

4-98 

- 

96.2 

10 

59-o 

3f 

40.9 

50 

_ 

_ 

Sprung. 

it 

9-5° 
19.32 

- 

30-9 

1O2.2 

« 

77-7 
166.4 

53-o 
1  06.0 

« 

_ 

_ 

I 

MgCr04 

2^86 

1.089 
1.164 

"•3 

67.1 

10 

84.8 
I25-3 

20 

67.4 
99-0 

3f 

55-o 
79-4 

40 

Slotte. 

27.71 

I.2I7 

232.2 

" 

172.6 

" 

133-9 

" 

06.6 

" 

u 

MnCl2 

8.01 

1.096 
1.196 

92.8 
30-9 

y 

71.1 
104.2 

25 

57-5 
84.0 

35 

48.1 
68.7 

45 

Wagner. 

30-33 

J-337 

56-3 

M 

193.2 

" 

T55-° 

" 

23-7 

M 

H 

40.13 

*-453 

37-3 

393-4 

300.4 

" 

48.5 

" 

M 

SMITHSONIAN  TABLES. 

TABLE  157 
VISCOSITY   OF   SOLUTIONS. 


161 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

M 

t 

fi 

t 

M 

i 

M 

t 

Authority. 

Mn(N03)2 

18.31 

29.60 
49-31 

1.148 
1.506 

96.0 

167-5 
396.8 

\s 

76.4 
126.0 

301.1 

2} 

ii 

64-5 
104.6 
22I.O 

35 

5^.6 
88.6 
188.8 

45 
tt 

Wagner. 

«< 

MnS04 
u 

"•45 
18.80 
22.08 

I.I47 
I.25I 
1.306 

129.4 
228.6 
661.8 

15 

U 

98.6 
172.2 
474.3 

2u5 

78.3 
I37-I 

347-9 

35 

63-4 
107.4 
266.8 

45 

M 

NaCl 

7-95 
I4-31 

- 

82.4 
94.8 

10 

U 

52.0 

60.  1 

30 

31.8 
36-9 

5° 

- 

- 

Sprung. 

" 

23.22 

- 

r&3 

u 

79-4 

" 

47-4 

" 

- 

- 

M 

NaBr 

9-77 
18.58 

- 

L5:66 

IO 

48.7 
53-5 

30 

34-4 

38.2 

So 

- 

- 

" 

« 

27.27 

— 

95-9 

" 

61.7 

" 

43-8 

" 

- 

- 

(( 

Nal 

8.83 

- 

73-i 

10 

46.0 

3f 

324 

5° 

_ 

_ 

H 

M 

17-15 
35-69 

_ 

73-8 
86.0 

« 

47-4 
55-7 

M 

33-7 
40.6 

: 

: 

u 

" 

55-47 

- 

157-2 

M 

96.4 

" 

66.9 

" 

- 

- 

" 

NaClO3 

11.50 

_ 

78.7 

IO 

50.0 

3f 

35-3 

5° 

_ 

_ 

M 

" 

20.59 

— 

88.9 

" 

56.8 

40.4 

— 

- 

" 

« 

33-54 

-      - 

I2I.O 

" 

75-7 

" 

53-° 

" 

- 

- 

«« 

NaNO3 

7-25 

_ 

75-6 

IO 

47-9 

3f 

33-8 

5f 

_ 

_ 

« 

" 

I2-35 

— 

81.2 

" 

51.0 

36.1 

_ 

_ 

(« 

« 

18.20 

- 

87.0 

" 

55-9 

" 

39-3 

" 

- 

- 

" 

u 

3i-55 

— 

121.  2 

« 

76.2 

" 

53-4 

M 

- 

- 

* 

Na2SO4 

4.98 

- 

96.2 

IO 

59-o 

3f 

40.9 

5f 

_ 

_ 

M 

" 

9-50 

— 

130.9 

« 

77-7 

53-o 

— 

— 

(< 

« 

14.03 

— 

187.9 

" 

107.4 

" 

71.1 

M 

— 

_ 

" 

" 

19.32 

- 

302,2 

" 

166.4 

" 

106.0 

" 

- 

- 

" 

Na2CrO4 

5.76 

1.058 

85.8 

10 

66.6 

2O 

53-4 

3° 

43-8 

4? 

Slotte. 

« 
« 

10.62 
14.81 

1.  112 
1.164 

103-3 
127-5 

« 

79-3 
97.1 

« 

63-5 
77-3 

« 

<« 

52-3 
63.0 

« 

M 

NH4C1 

3-67 

_ 

71-5 

IO 

45-° 

3? 

3i-9 

5° 

_ 

_ 

Sprung. 

« 

8.67 

— 

69.1 

« 

45-3 

32.6 

— 

- 

" 

« 

15.68 

— 

67-3 

M 

46.2 

" 

34-o 

" 

— 

- 

" 

" 

23-37 

- 

67-4 

" 

47-7 

M 

36.1 

" 

- 

- 

" 

NH4Br 

J5-97 

_ 

65.2 

IO 

43-2 

3° 

3T-5 

5° 

- 

_ 

« 

11 

25-33 

— 

62.6 

" 

43-3 

32.2 

" 

— 

- 

«< 

" 

36.88 

- 

62.4 

« 

44-6 

" 

34-3 

M 

- 

- 

«« 

NH4N03 

5-97 

- 

69.6 

10 

44-3 

3° 

31.6 

5f 

- 

«« 

" 

12.19 

— 

66.8 

" 

44-3 

3'-9 

— 

- 

" 

" 

27.08 

— 

67.0 

" 

47-7 

" 

349 

M 

- 

- 

H 

.< 

37-22 

49-83 

- 

71.7 
81.1 

« 

51.2 
63-3 

» 

38.8 
48.9 

« 
« 

: 

: 

M 
M 

(NH4)2S04 

8.ro 

- 

107.9 

10 

52-3 

30 

37-o 

5° 

- 

- 

<« 

" 

r5-94 

— 

I  20.  2 

" 

60.4      - 

43-2 

" 

- 

- 

II 

25-51 

: 

148.4 

74-8 

54-i 

«« 

SMITHSONIAN  TABLES. 


162 


TABLE  157  (continued). 

VISCOSITY   OF   SOLUTIONS, 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

M 

t 

* 

t 

/A 

' 

M 

t 

Authority. 

(NH4)2Cr04 

10.52 

1-063 

79-3 

10 

62.4 

20 

_ 

_ 

42-4 

40 

Slotte. 

H 

19-75 
28.04 

1.  120 
I-I73 

88.2 

IOI.I 

« 

70.0 

80.7 

M 

00.8 

3? 

48.4 
56.4 

- 

M 
M 

(NH4)2Cr207 

6.85 

1.039 

72-5 

10 

56.3 

20 

45-8 

30 

38.0 

40 

" 

" 

13.00 

1.078 

72.6 

" 

57-2 

" 

46.8 

u 

39-i 

" 

M 

u 

19-93 

I.I26 

77-6 

It 

58.8 

" 

48.7 

" 

40.9 

" 

« 

NiCl2 

11.45 

I.I09 

90.4 

15 

70.0 

25 

r?.r 

35 

48.2 

45 

Wagner. 

" 

22.69 

1.226 

140.2 

" 

109.7 

" 

87.8 

" 

72-7 

'' 

* 

" 

30.40 

1-337 

229.5 

" 

171.8 

" 

139-2 

" 

111.9 

u 

" 

Ni(N08)2 

16.49 

1.136 

90.7 

15 

70.1 

25 

j§7-4 

35 

48.9 

45 

« 

" 

30.01 

1.278 

T35-6 

M 

105.9 

" 

85.5 

'• 

70.7 

M 

M 

" 

40-95 

1.388 

222.6 

M 

169.7 

M 

128.2 

" 

152.4 

" 

M 

NiS04 

10.62 

1.092 

94-6 

iS 

73-5 

25 

60.  i 

35 

49-8 

45 

M 

" 

18.19 

1.198 

154-9 

119.9 

99-5 

75-7 

M 

n 

25-35 

i-3H 

298-5 

" 

224.9 

" 

173-0 

" 

1524 

" 

U 

Pb(N08)2 

17-93 

1.179 

74.0 

15 

59-' 

25 

48-5 

35 

40-3 

45 

» 

32-22 

1.362 

91.8 

72.5 

M 

59-6 

M 

50.6 

M 

Sr(N03)2 

10.29 

i.  088 

69-3 

15 

56.0 

25 

45-9 

35 

39-  1 

45 

U 

M 

21.19 

1.124 

87-3 

69.2 

57-8 

48.1 

u 

" 

M 

32-61 

i  -3°7 

116.9 

H 

93-3 

M 

76.7 

" 

62.3 

" 

" 

ZnCl2 

'5-33 

1.146 

93-6 

15 

727 

25 

57-8 

35 

48.2 

45 

H 

u 

23-49 

1.229 

111.5 

86.6 

ii 

69.8 

u 

57-5 

U 

ii 

33-78 

1-343 

iS1-? 

117.9 

U 

90.0 

u 

72.6 

M 

" 

Zn(N03)2 

I5.95 

1.115 

80.7 

15 

64-3 

25 

52.6 

35 

43-8 

45 

« 

H 
H 

30.23 

44-5° 

1.229 
1-437 

104.7 
167.9 

it 

85.7 
130.6 

U 

(I 

69.5 
105.4 

57-7 
87-9 

« 

ZnSO4 

7.12 

1.106 

97.1 

IS 

79-3 

25 

62.7 

35 

51.5 

45 

« 

u 

16.64 

1.195 

156.0 

u 

118.6 

94-2 

ii 

73-5 

" 

23.09 

1.281 

232.8 

i?7-4 

135-2 

u 

108.1 

SMITHSONIAN   TABLts. 


TABLE  158. 
SPECIFIC   VISCOSITY.* 


I63 


Dissolved  salt. 

Normal  solution. 

J  normal. 

\  normal. 

£  normal. 

Authority. 

>> 

•5 

1 

££ 

\l 

C/T£ 

>> 

1 

Specific 
viscosity. 

>, 

1 

4)    >> 

4ri 

*U    O 
0)    U 

£•* 

£, 

i 

Q 

u  >> 

•si 
n 

Acids  :  C12O3      .     . 

1.0562 

I.OI2 

1.0283 

1.003 

1.0143 

I.OOO 

1.0074 

0.999 

Reyher. 

HC1  .     .    . 

1.0177 

1.067 

1.0092 

1.034 

1.0045 

1.017 

1.0025 

1.009 

M 

HC1O3   .     . 

1.0485 

1.052 

1.0244 

1.025 

I.OI26 

1.014 

1.0064 

1.  006 

" 

HNO3    .     . 

1.0332 

1.027 

I.OI68 

I.OII 

1.0086 

1.005 

1.0044 

1.003 

" 

H2SO4    .     . 

1.0303 

I.OOXD 

1.0154 

1.043 

1.0074 

I.  O2  2 

1-0035 

1.  008 

Wagner. 

Aluminium  sulphate 

1.0550 

1.406 

1.0278 

I.I78 

1.0138 

I.082 

1.0068 

1.038 

a 

Barium  chloride  .     . 

1.0884 

I.I23 

1.0441 

L057 

I.O226 

I.O26 

I.OII4 

1.013 

u 

"        nitrate     .     . 

—  • 

1.0518 

1.044 

1.0259 

I.  O2  1 

1.0130 

1.  008 

u 

Calcium  chloride      . 

1.0446 

1.156 

I.02I8 

1.076 

1.0105 

1.036 

1.0050 

1.017 

« 

"         nitrate  .     , 

1.0596 

I.II7 

1.0300 

1-053 

1.0151 

1.022 

1.0076 

1.008 

u 

Cadmium  chloride  . 

1.0779 

I-I34 

1.0394 

1.063 

1.0197 

1.031 

1.0098 

I.O2O 

« 

"          nitrate 

1.0954 

I.I65 

1.0479 

1.074 

1.0249 

1.038 

I.OII9 

I.OI8 

« 

"          sulphate  . 

1.0973 

1.348 

1.0487 

I-I57 

1.0244 

1.078 

I.OI20 

I-°33 

« 

Cobalt  chloride   .     . 

1.0571 

I.2O4 

1.0286 

1.097 

1.0144 

1.048 

1.0058 

1.023 

M 

"       nitrate      .     . 

1.0728 

I.I66 

1.0369 

1-075 

1.0184 

1.032 

1.0094 

1.018 

" 

"      sulphate  .     . 

1.0750 

1-354 

1-0383 

1.160 

I.OI93 

1.077 

I.OIIO 

1.040 

" 

Copper  chloride  .     . 

1.0624 

1.205 

I-03I3 

1.098 

1.0158 

1.047 

1.0077 

1.027 

« 

"        nitrate     .     . 

r-0755 

1.179 

1.0372 

1.080 

1.0185 

I.O4O 

1.0092 

1.018 

" 

"        sulphate 

1.0790 

1-358 

1  .0402 

1.160 

1.0205 

I.OSO 

I.OI03 

1.038 

" 

Lead  nitrate    .     .     . 

1.1380 

I.IOI 

0.0699 

1.042 

*-°35* 

I.OI7 

I.OI75 

1.007 

ti 

Lithium  chloride 

1.0243 

1.142 

1.0129 

i.  066 

i  .0062 

I.03I 

I.OO3O 

I.OI2 

" 

"         sulphate 

1-0453 

1.290 

1.0234 

i-i37 

1.0115 

1.065 

1.0057 

1.032 

" 

Magnesium  chloride 

i-i375 

I.2OI 

i.  oi  88 

1.094 

1.0091 

1.044 

1.0043 

I.  O2  1 

M 

"            nitrate  . 

1.0512 

I.I7I 

1.0259 

1.082 

1.0130 

1.040 

1.0066 

1.020 

" 

"           sulphate 

1.0584 

!-367 

1.0297 

1.164 

1.0152 

1.078 

1.0076 

1.032 

« 

Manganese  chloride 

1-0513 

1.209 

1.0259 

1.098 

1.0125 

1.048 

1.0063 

I.O23 

K 

"           nitrate   . 

1.0690 

1.183 

1-0349 

1.087 

1.0174 

1.043 

1.0093 

1.023 

"           sulphate 

1.0728 

1.364 

1-0365 

1.169 

1.0179 

1.076 

1.0087 

1.037 

Nickel  chloride    .     •> 

1.0591 

1.205 

1.0308 

1.097 

1.0144 

1.044 

1.0067 

1.  02  1 

« 

"       nitrate  .     .     . 

I-°755 

1.180 

1.0381 

1.084 

1.0192 

I.O42 

1.0096 

I.OI9 

" 

"       sulphate  .     . 

1.0773 

1.361 

1.0391 

1.161 

1.0198 

1-075 

I.OOI7 

1.032 

" 

Potassium  chloride  . 

1.0466 

0.987 

.0235 

0.987 

1.0117 

0.990 

1.0059 

0-993 

64 

"          chromate 

1.0935 

1.113 

•0475 

I-°53 

1.0241 

I.O22 

I.OI2I 

I.OI2 

|| 

"           nitrate    . 

1.0605 

0-975 

•0305 

0.982 

1.0161 

0.987 

1.0075 

0.992 

« 

"           sulphate 

i  .0664 

1.105 

•0338 

1.049 

1.0170 

I.  O2  1 

1  .0084 

1.008 

Sodium  chloride  .     . 

1.0401 

1.097 

.0208 

1.047 

1.0107 

1.024 

I.OO56 

I.OI3 

Reyher. 

"        bromide  .     . 

1.0786 

1.064 

.0396 

1.030 

1.0190 

I.OI5 

I.OIOO 

1.008 

M 

"        chlorate      . 

1.0710 

1.090 

•0359 

1.042 

1.0180 

I.O22 

1.0092 

1.  01  2 

"        nitrate    .     . 
Silver  nitrate  .     .     . 

1-0554 
1.1386 

1.065 
1.058 

.0281 
.0692 

1.026 
i.  020 

1.0141 
1.0348 

I.OI2 
1.  006 

1.0071 

1.0173 

I.OO7 
I.OOO 

Wagner. 

Strontium  chloride  . 

i  .0676 

1.141 

•°336 

1.067 

1.0171 

1.034 

1.0084 

1.014 

u 

nitrate    . 

1.0822 

1.115 

.0419 

1.049 

1.0208 

1.024 

1.0104 

I.OII 

« 

Zinc  chloride  .     .     . 

1.0590 

1.189 

.0302 

1.096 

1.0152 

1-053 

1.0077 

1.024 

"     nitrate     .     .     . 

1.0758 

1.164 

.0404 

i.  086 

1.0191 

1.039 

1  .0096 

1.019 

"    sulphate.     .     . 

1.0792 

1.367 

1.0402 

i-i73 

1.0198 

1.082 

1.0094 

1.036 

*  In  the  case  of  solutions  of  salts  it  has  been  found  (vide  Arrhennius,  Zeits.  fur  Phys.  Chem.  vol.  i,  p.  285)  that 
the  specific  viscosity  can,  in  many  cases,  be  nearly  expressed  by  the  equation  /u.  =:MI">  where  fxt  is  the  spec 
for  a  normal  solution  referred  to  the  solvent  at  the  same  temperature,  and  n  the  number  of  gramme  molecules 
solution  under  consideration.     The  same  rule  may  of  course  be  applied  to  solutions  stated  in  percentages 
gramme  molecules.    The  table  here  given  has  been  compiled  from  the  results  of  Reyher  (Zeits.  fur  Phys.  Lhem.  vol.  2, 
p.  749)  and  of  Wagner  (Zeits.  fur  Phys.  Chem.  vol.  5,  p.  3')  and  illustrates  this  rule.    The  numbers  are  all  i 

SMITHSONIAN  TABLES. 


164 


TABLE  159. 

VISCOSITY   OF   GASES   AND   VAPORS- 
The  values  of  /A  given  in  the  table  are  io6  times  the  coefficients  of  viscosity  in  C.  G.  S.  units. 


Substance. 

Temp. 

M 

Refer- 
ence. 

Substance. 

Temp. 

Refer- 
ence. 

18.0 
-21.4 
0.0 

15-0 
99.1 
182.4 
302.0 
66.8 
78.4 

97-4 
82.8 
116.9 
108.4 
82.9 

0.0 
20.  0 
0.0 
14-7 
17.9 

99-7 
183-7 
o. 
19.0 

100.  O 

16.9 

-20.7 

0. 

15-0 
99.1 
182.4 
302.0 

0.0 
20.0 

o.o 
20.  o 
o.o 

17-4 
61.2 

o.o 

78. 

163.9 

173-3 
180.7 
220.3 

255-9 
299-3 
135- 
142. 

142. 
162. 

143- 
144. 

160. 

96. 

108. 
210.4 

220.8 

224.1 

273-3 
322.1 
70. 

79- 
118. 
92.4 
129.4 
142. 

145-7 
186.1 

222.1 
268.2 
163.0 
184.0 
128.7 
147.0 

95-9 
102.9 
189.0 
68.9 

I 
2 
2 
2 
2 
2 
2 

3 
3 

3 
3 
3 
3 
3 
4 
4 
5 
5 
5 
5 
5 

10 

6 
6 

i 

2 
10 
2 
2 
2 
2 
10 

4 
4 
4 

i 
i 

3 

i 

Ether  

16.1 
36-5 

0. 

72-3 
o.o 

0.0 

15-3 

66.6 
184.6 
—  20.  6 
o.o 
15- 
99-2 
182.4 
302.0 

i5-o 
270.0 
300.0 
330-o 
360.0 
390.0 

20.0 
0.0 
15-0 
302.0 

44-0 

-2i-5 
o. 
10.9 

53-5 
o. 

0. 

o. 

15-4 

53-5 
o.o 
16.7 

IOO.O 

15. 

73-2 
79-3 
93-5 
216.0 
96.1 
189.1 
196.9 
234.8 
269.9 
81.9 
86.7 
88.9 

105-9 

121.5 
139.2 
246. 
489-  1 
532-  1 
582.  t 
627.  f 
671-t 

120.  I 
98.8 
105.2 
213.9 
232. 
156-3 

166. 
170.7 
189.4 
179. 
138- 
189. 
195-7 
215-9 
90.4 
96.7 
132.0 

222. 

i 
I 
4 
3 

2 

5 
5 
5 
5 

2 
IO 
2 
2 
2 
2 
II 

8 
8 
8 
8 
8 
4 

2 
2 
2 

3 

7 

10 

7 
7 

IO 
10 
IO 

7 
7 

i 
i 

9 
ii 

\  r  * 

Ethyl  chloride.  .  .  . 
Ethyl  iodide  

Ethylene  

Helium  

a 

Alcohol,  Methyl.  .  .  . 
Alcohol  Ethyl  

n 

n 
Hydrogen  

u 
ll 

it 

Krypton  

Alcohol,  Propyl, 
norm        

Alcohol,  Isopropyl.  . 
Alcohol,  Butyl,  norm  . 
Alcohol,  Isobutyl.  .  . 
Alcohol,  Tert.  butyl. 
•\mmonia 

Mercury  

•Yreon 

u 

u 

i 

i 

( 

Methane  

Benzene  

Methyl  chloride  .  .  . 

u             u 

u                  it 

Methyl  iodide.  .  .  . 
Nitrogen  

i 

i 

Carbon  bisulphide  .  . 
Carbon  dioxide  

< 
< 

Carbon  monoxide.  .  . 

«              « 

Chlorine 

u 

Nitric  oxide  
Nitrous  oxide.  .  .  . 
Oxygen  

a 

n 

Chloroform  
it 

Water  Vapor  

a.          a 

n 

Xenon  

Ether 

i  Puluj,  Wien.  Ber.  69  (2),  1874.                        9  Meyer-Schumann,  Wied.  Ann.  13,  1881. 
2  Breitenbach,  Ann.  Phys.  5,  1901.                    io  Jeans,  assumed  mean,  1916. 
3  Steudel,  Wied.  Ann.  16,  1882.                          n  Rankine,  1910. 
4  Graham,  Philos.  Trans.  Lond.  1846,  III.       12  Vogel  (Eucken,  Phys.  Z.  14,  1913).    For 
5  Schultze,  Ann.  Phys.  (4),  5,  6,  1901.                           summaries  see:  Fisher,  Phys.  Rev.  24, 
6  Schumann,  Wied.  Ann.  23,  1884.                                 1904;     Chapman,    Phil.   Tr.   A.  211, 
7  Obermayer,  Wien.  Ber.  71  (2a),  1875.                        1911;    Gilchrist,  Phys.  Rev.  i,  1913. 
8  Koch,  Wied.  Ann.  14,  1881,  19,  1883.                         Schmidt,  Ann.  d.  Phys.  30,  1909. 

*  Gilchrist's  value  of  the  viscosity  of  air  may  be  taken  as  the  most  accurate  at  present  avail- 
able. His  value  at  20.2°  C  is  1.812  x  io~4.  The  temperature  variation  given  by  Holman  (Phil. 
Mag.  1886)  gives  p  =  1715.50  x  io~7(i  +  .oo275/  -  .00000034/2).  See  Phys.  Rev.  i,  1913. 
MilHkan  (Ann.  Phys.  41,  759,  1913)  gives  for  the  most  accurate  value  f*t  =  0.00018240  - 
0.000000493(23-0  when  (23>*>i2)  whence  ju20  =  0.0001809  ±  0.1%.  For  //0  he  gives 
0.0001711. 

fThe  values  here  given  were  calculated  from  Koch's  table  (Wied.  Ann.  19,  p.  869,  1883) 
by  the  formula  /z  =  489  [i  4-  746(/  —  270)]. 

SMITHSONIAN  TABLES. 


TABLE  160. 

VISCOSITY  OF  GASES- 
Variation  of  Viscosity  with  Pressure  and  Temperature. 


165 


According  to  the  kinetic  theory  of  gases  the  coefficient  of  viscosity  ju  =  i(pc/),  p  being  the 
density,  c  the  average  velocity  of  the  molecules,  /  the  average  path.  Since  /  varies  inversely 
as  the  number  of  molecules  per  unit  volume,  pi  is  a  constant  and  JJL  should  be  independent  of  the 
density  and  pressure  of  a  gas  (Maxwell's  law).  This  has  been  found  true  for  ordinary  pressures; 
below  -fa  atmosphere  it  may  fail,  and  for  certain  gases  it  has  been  proved  untrue  for  high  pres- 
sures, e.g.,  CO2  at  33°  and  above  50  atm.  See  Jeans,  "  Dynamical  Theory  of  Gases." 

c  depends  only  on  the  temperature  and  the  molecular  weight;  viscosity  should,  therefore, 
increase  with  the  pressures  for  gases,  c  varies  as  the  Vr,  but  fj,  has  been  found  to  increase  much 
more  rapidly.  Meyer's  formula,  juj  =  jUo(i  +  at),  where  a  is  a  constant  and  /A>  the  viscosity  at 
o°  C,  is  a  convenient  approximate  relation.  Sutherland's  formula  (Phil.  Mag.  31,  1893). 


is  the  most  accurate  formula  in  use,  taking  in  account  the  effect  of  molecular  forces.  It  holds 
for  temperatures  above  the  critical  and  for  pressures  following  approximately  Boyle's  law.  It 
may  be  thrown  into  the  form  T  =  KT^/fj,  —  C  which  is  linear  in  terms  of  T  and  T^/JJL,  with  a 
slope  equal  to  K  and  the  ordinate  intercept  equal  to  —  C.  See  Fisher,  Phys.  Rev.  24,  1907, 
from  which  most  of  the  following  table  is  taken.  Onnes  (see  Jeans)  shows  that  this  formula  does 
not  represent  Helium  at  low  temperatures  with  anything  like  the  accuracy  of  the  simpler  formula 


The  following  table  contains  the  constants  for  the  above  three  formulae,  T  being  always  the 
absolute  temperature,  Centigrade  scale. 


Gas. 

C 

K 

Xio' 

a 

«* 

Gas. 

C 

K 

X  io7 

a 

11- 

Air  

124 

150 

_ 

.754 

Hydrogen  

72 

66 



.69 

Argon  

172 

206 

— 

.819 

Krypton  

1  88 

— 

— 

— 

Carbon  mo- 

Neon   

2<2 







noxide  ... 

102 

J35 

.00269 

•74 

Nitrogen  

1  10 

143 

.00269 

•74 

Carbon  dioxide 

240 

158 

.00348 

.98 

Nitrous  oxide, 

Chloroform.  .  . 

454 

159 

— 

— 

N2O  

313 

172 

•00345 

•93 

Ethylene. 

226 

1  06 

OO^^O 



Oxygen  

1^1 

176 



•79 

Helium  

80 

148 

.683 

Xenon  

252 

— 

Helium  

.647 

*The  authorities  for  n  are:  Air,  Rayleigh;  Ar,  Mean,  Rayleigh,  Schultze;  CO,  CO2,  X_>, 
N2O,  von  Obermayer;  Helium,  Mean,  Rayleigh,  Schultze;  2d  value,  low  temperature  work  of 
Onnes;  H2,  O2,  Mean,  Rayleigh,  von  Obermayer. 

SMITHSONIAN  TABLES. 


1  66  TABLE  161. 

DIFFUSION  OF  AN  AQUEOUS  SOLUTION   INTO  PURE  WATER. 

If  k  is  the  coefficient  of  diffusion,  dS  the  amount  of  the  substance  which  passes  in  the  time  dtt 
at  the  place  x,  through  q  sq.  cm.  of  a  diffusion  cylinder  under  the  influence  of  a  drop  of  concen- 
tration del  dx,  then 


gives  the  gram-molecules  per  liter. 


-. 

dx 

k  depends  on  the  temperature  and  the  concentration. 
The  unit  of  time  is  a  day. 


Substance. 

c 

,o 

k 

tf  « 

Substance. 

• 

. 

k 

Ii 

Bromine  . 

O.I 

12. 

0.8 

i 

Calcium  chloride 

0.864 

8.5 

0.70 

4 

Chlorine  . 

•• 

12. 

1.22 

«« 

t<             if 

1.22 

9- 

0.72 

44 

Copper  sulphate 

II 

17- 

o-39 

2 

"             '4  .        . 

O.O6O 

9- 

0.64 

44 

Glycerine 

M 

IO.I4 

o-357 

3 

44             44   . 

0.047 

9- 

0.68 

44 

Hydrochloric  acid    . 

" 

19.2 

2.21 

Copper  sulphate 

17- 

0.23 

2 

Iodine 

II 

12. 

(0.5) 

i 

44            " 

o-95 

17- 

0.26 

it 

Nitric  acid 

ft 

19-S 

2.07 

2 

u            ii 

0.30 

17- 

o-33 

'4 

Potassium  chloride  . 

" 

17-S 

1.38 

2 

44            " 

0.005 

17. 

o-47 

" 

hydroxide  • 

ft 

'3-5 

1.72 

2 

Glycerine 

2/8 

10.14 

0-354 

3 

Silver  nitrate    . 

fl 

12. 

0.985 

2 

44         .        . 

6/8 

10.14 

0-345 

" 

Sodium  chloride 

" 

15.0 

o-94 

2 

44         ... 

10/8 

10.14 

0.329 

it 

Urea 

" 

14-8 

0.97 

3 

44         ... 

14/8 

10.14 

0.300 

" 

Acetic  acid 

O.2 

0.77 

4 

Hydrochloric  acid    . 

4.52 

n-5 

2-93 

4 

Barium  chloride 

" 

8. 

0.66 

4 

u              u 

3.16 

ii. 

2.67 

ii 

Glycerine 

" 

IO.I 

3-55 

3 

it               t< 

0-945 

n. 

2.12 

4' 

Sodium  actetate 

it 

12. 

0.67 

5 

it               it 

0.387 

n. 

2.02 

44 

44      chloride 

u 

15.0 

o-94 

2 

«t              it 

O.2CO 

ii. 

1.84 

" 

Urea 

it 

14-8 

0.969 

3 

Magnesium  sulphate 

2.18 

5-5 

O.28 

4 

Acetic  acid 

1.0 

12. 

0.74 

6 

ti               if 

0.541 

5-5 

0.32 

it 

Ammonia 

it 

I5-23 

J-54 

7 

it               «t 

3-23 

10. 

0.27 

it 

Formic  acid 

" 

12. 

o-97 

7 

it               ii 

O.4O2 

10. 

0-34 

«• 

Glycerine 
Hydrochloric  acid    . 

" 

IO.I4 
12. 

0-339 
2.09 

I 

Potassium  hydroxide 

0-75 
0-49 

12. 
12. 

.72 
.70 

6 

Magnesium  sulphate 

" 

7- 

0.30 

4 

it                it 

0-375 

12. 

.70 

•• 

Potassium  bromide  . 

*' 

10. 

I-I3 

8 

44           nitrate    . 

3-9 

I7.6 

0.89 

2 

44       hydroxide  . 
Sodium  chloride 

t. 

12. 
15.0 

1.72 
0.94 

6 

2 

44    : 

1.4 

o-3 

I7.6 
I7.6 

.IO 
.26 

ii 

a           u 

u 

'4-3 

0.964 

3 

u       ii 

O.O2 

I7.6 

.28 

" 

"        hydroxide  . 

it 

12. 

i.i  i 

2 

sulphate 

o-95 

19.6 

0.79 

" 

iodide 

it 

10. 

0.80 

8 

if                tt 

0.28 

19.6 

0.86 

it 

Sugar*     . 

" 

12. 

0.254 

6 

ft                ii 

0.05 

19.6 

o-97 

" 

Sulphuric  acid 

" 

12. 

1.  12 

6 

if                n 

O.O2 

19.6 

I.OI 

" 

Zinc  sulphate  . 

tt 

14-8 

0.236 

Q 

Silver  nitrate    . 

3-9 

12. 

o-535 

" 

Acetic  acid 

2.0 

12. 

0.69 

5 

"           44 

0.9 

12. 

0.88 

" 

Calcium  chloride 

it 

IO. 

0.68 

8 

u           ti 

O.O2 

12. 

I-°35 

" 

Cadmium  sulphate  . 
Hydrochloric  acid    . 

u 

19.04 
12. 

0.246 

2.21 

I 

Sodium  chloride 

2/8 

4/8 

14-33 
14-33 

1.013 

3 

Sodium  iodide 

ti 

10. 

O.9O 

8 

41             " 

6/8 

J4-33 

0.980 

2 

Sulphuric  acid 

" 

12. 

1.16 

6 

it             u 

10/8 

J4-33 

0.948 

" 

Zinc  acetate 

41 

18.05 

0.210 

9 

"             "     . 

14/8 

!4-33 

0.917 

14 

"         "            . 

44 

0.04 

0.120 

9 

Sulphuric  acid 

9-85 

18. 

2-36 

2 

Acetic  acid 

3-° 

12. 

0.68 

"              « 

4-85 

18. 

1.90 

" 

Potassium  carbonate 

10. 

0.60 

8 

it              ii 

2.85 

18. 

i.  60 

ii 

"         Jiydroxide 

it 

12. 

1.89 

6 

II                            ft 

0.85 

1  8. 

i-34 

" 

Acetic  acid 

4-0     12. 

0.66 

6 

<4                            " 

°-35 

18. 

1.32 

«« 

Potassium  chloride.- 

14 

10. 

1.27 

8 

If                            II 

0.005 

18. 

1.30 

" 

i   Euler,  Wied.  Ann.  63,  1897.                                 5  Kawalki,  Wied.  Ann.  52,  1894;  59,  1896. 

2  Thovert,  C.  R.  133,  1901  ;   134,  1902.                  6  Arrhenius,  Zeitschr.  Phys.  Chem.  10,  1892. 
3  Heimbrodt,  Diss.  Leipzig,  1903.                          7  Abegg,  Zeitschr.  Phys.  Chem.  n,  1893. 
4  Scheffer,  Chem.  Ber.  15,   1882;    16,   1883;      8  Schuhmeister,  Wien.  Ber.  79  (2  ,  1879. 

Zeitschr.  Phys.  Chem.  2,  1888.                         9  Seitz,  Wied.  Ann.  64,  1898. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  162. 
DIFFUSION   OF   VAPORS. 


167 


Coefficients  of  diffusion  of  vapors  in  C.  G.  S.  units.     The  coefficients  are  for  the  temperatures  given  in  the  table  and 
a  pressure  of  76  centimeters  of  mercury.* 


Vapor. 

Temp.  C. 

o 

7ft  for  vapor 
diffusing  into 
hydrogen. 

kt  for  vapor 
diffusing  into 
air. 

kt  for  vapor 
diffusing  into 
carbon  dioxide. 

Acids  :  Formic         .... 
a 

O.O 
65.4 
84-9 

0.5I3I 
0.7873 
0.8830 

O.I3I5 
0.2035 
0.2244 

0.0879 

0.1343 
0.1519 

Acetic           .... 

O.O 

0.4040 

0.1061 

0.0713 

u 

65.5 

O.62II 

0.1578 

0.1048 

Isovaleric     .... 

98.5 

O.O 

0.7481 
0.2II8 

0.1965 

0-0555 

O.I32I 
0.0375 

. 

98.0 

0-3934 

0.1031 

0.0696 

Alcohols  :  Methyl    .... 

O.O 

0.5001 

0-1325 

O.o88o 

i< 

25.6 

0.6015 

0.1620 

0.1046 

i4 

49.6 

0.6738 

0.1809 

0.1234 

Ethyl        ..'.'. 

O.O 

0.3806 

0.0994 

0.0693 

. 

40.4 

0.5030 

0.1372 

0.0898 

. 

66.9 

0.5430. 

0-1475 

O.IO26 

Propyl      .... 

0.0 

0-3I53 

0.0803 

0.0577 

• 

66.9 

0.4832 

0.1237 

0.0901 

.         .         . 

83-5 

0-5434 

°-I379 

0.0976 

Butyl       .... 

0.0 

0.2716 

0.068  1 

0.0476 

, 

99.0 

'    0.5045 

0.1265 

0.0884 

Amyl       .... 

O.O 

0.2351 

0.0589 

0.0422 

« 

99.1 

0.4362 

0.1094 

0.0784 

Hexyl      .... 

0.0 

0.1998 

0.0499 

0-0351 

99.0 

0.3712 

0.0927 

0.0651 

O.O 

O  2Q4.O 

O  O7  ?I 

O  O?27 

19.9 

\j.^^\j 
0.3409 

U.U/^l 

0.0877 

\_».W^.£/ 

0.0609 



45-0 

0-3993 

O.IOII 

0.0715 

Carbon  disulphide    .... 

O.O 

0.3690 

0.0883 

0.0629 

. 

19.9 

0-4255 

O.IOI5 

0.0726 

it              « 

32.8 

0.4626 

O.II2O 

0.0789 

Esters  :  Methyl  acetate    . 

0.0 

0.3277 

0.0840 

0.0557 

i(             « 

20.3 

0.3928 

O.IOI3 

0.0679 

Ethyl          «          .'         ! 

O.O 

46.1 

0-2373 
0.3729 

0.0630 
0.0970 

0.0450 
0.0666 

Methyl  butyrate  . 

0.0 

0.2422 

0.0640 

0.0438 

«             « 

Q2.I 

0.4308 

O.II39 

0.0809 

Ethyl                    !         ! 

O.O 

0.2238 

0.0573 

0.0406 

«               « 

96.5 

0.4112 

0.1064 

0.0756 

"      valerate 

O.O 

0.2050 

0.0505 

0.0366 

•  . 

97.6 

0.3784 

0.0932 

0.0676 

Ether         

O.O  - 

0.2060 

0.0775 

OXKC2 

H 

19.9 

v*^      ;/ 
0.3410 

0.0893 

J-3 

0.0636 

Water       

0.0 

0.6870 

0.1980 

0.1310 

"           

49-5 

I.OOOO 

0.2827 

o.iSir 

. 

92.4 

1.1794 

Q-3451 

0.2384 

*  Taken  from  Winkelmamrs  papers  (Wied.  Ann.  vols.  22,  23,  and  26).  The  coefficients  for  o°  were  calculated 
by  Winkelmann  on  the  assumption  that  the  rate  of  diffusion  is  proportional  to  the  absolute  temperature.  According 
to  the  investigations  of  Loschmidt  and  of  Obenneyer  the  coefficient  of  diffusion  of  a  gas,  or  vapor,  at  o°  C.  and  a 
pressure  of  76  centimetres  of  mercury  may  be  calculated  from  the  observed  coefficient  at  another  temperature  and 

pressure  by  the  formula  kQ  =  kT  \-A)    — »  where   T  is  temperature  absolute  and  /  the  pressure  of  the  gas.     The 

exponent  n  is  found  to  be  about  1.75  for  the  permanent  gases  and  about  2  for  condensible  gases.     The  following 
are  examples:   Air— CO2,   »=  1.968;    CO2  — N,O,   «=a.psj  CO,— H,   «=i.742;   CO  — O,  «  — 1.785.:  H 

nii's  results,  as  given  in  the  above  table,  se 


«z=i,755?  O — N,  «=i.792.     Winkelma 
diffusing  into  air,  hydrogen  or  carbon  dioxide. 

SMITHSONIAN  TABLES. 


seem  to  give  about  2  for  vapors 


T68  TABLES   163-164. 

DIFFUSION    OF    GASES,  VAPORS,  AND    METALS. 

TABLE  168.  —  Coefficients  of  Diffusion  for  Various  Oases  and  Vapors.* 


Gas  or  Vapor  diffusing.                     Gas  or  Vapor  diffused  into. 

Temp. 

°c. 

Coefficient 
of  Diffusion. 

Authority. 

Air 

o 
o 

0 
0 

o 
o 
o 
o 
o 
o 
o 

0 
0 

o 

0 
0 

o 
o 

0 

o 
o 
o 

0 

o 
o 
o 
o 
o 

0 
0 

o 
8 
18 
18 

0.661 

0.1775 
0.1423 
0.1360 
0.1405 
O.I3H 

0-5437 
0.1465 
0.0983 
O.I  802 

0.0995 
0.1314 

o.ior 
0.6422 
0.1802 
0.1872 
0.0827 

0.3054 
0.6340 

0.53^4 
0.6488 

°-4593 
0.4863 
0.6254 

0-5347 
0.6788 
0.1787 

°-l3S7 
0.7217 
o.  1  7  1  o 
0.4828 
0.2390 
0.2475 
0.8710 

Schulze. 
Obermayer. 
Loschmidt. 
Waitz. 
Loschmidt. 
Obermayer. 

Loschmidt. 

Stefan. 
Obermayer. 

Loschmidt. 

Obermayer. 

Stefan. 
ii 

Obermayer. 
i 

ti 

Loschmidt. 
Obermayer. 
Loschmidt. 
Guglilemo. 

Carbon  dioxide     .... 

<t            u 

Air      

ft 

.1            •< 

M 

M 

!  '.  '.  . 
u 

Carbon  disulphide    .     .     . 
Carbon  monoxide      .     .     . 

«              « 
Ether 

Carbon  monoxide      .     . 

Methane        •          ... 

Nitrous  oxide    .... 
Oxygen     
Air 

Carbon  dioxide      .     .     . 
Ethylene            .... 

Air  

<( 

Hydrogen          .... 
Air                 

Carbon  dioxide      .     .     . 
"  .    monoxide      .     . 
Ethane     
Ethylene  

« 

M 

u 

„ 

Methane        

tt 

Nitrous  oxide    .... 

If 

if 

Oxygen 

Carbon  dioxide      .     . 
Hydrogen     

tt 

Nitrogen       

Sulphur  dioxide    .... 
Water          

u 

it 

Hydrogen                    . 

*  Compiled  for  the  most  part  from  a  similar  table  in  Landolt  &  Bernstein's  Phys.  Chem.  Tab. 


TABLE  164,-  Diffusion  of  Metals  into  Metals. 


dv     _    d'^v     where  x  is  the  distance  in  direction  of  diffusion  ;  v,  the  degree  of  concentration  of 
&    ~  '    dxi  '    the  diffusing  metal  ;  /,  the  time  ;  k,  the  diffusion  constant  =  the  quantity  of  metal 
in  grams  diffusing  through  a  sq.  cm.    in  a  day  when  unit  difference  of  concentra- 
tion (gr.  per  cu.  cm.)  is  maintained  between  two  sides  of  a  layer  one  cm.  thick. 


Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  C. 

k. 

Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  c. 

k. 

Gold    .     . 

Lead     . 

555 

3-*9 

Platinum  . 

Lead     . 

492 

1.69 

" 

492 

3.00 

Lead    .     . 

Tin  .     . 

555 

3.18 

' 

251 

0.03 

Rhodium  . 

Lead      . 

55° 

3-°4 

' 

200 

0.008 

Tin       .     . 

Mercury 

i5 

1.22* 

' 

" 

l65 

0.004 

Lead    .     . 

; 

15 

1.0* 

' 

IOO 

0.00002 

Zinc 

I  C 

I  0* 

« 

Bismuth 
Tin    .     . 

555 
555 

4.52 
4-65 

Sodium     . 
Potassium 

15 

15 

0.45* 

0.40* 

Silver  .     . 

555 

4.14 

Gold     .     . 

15 

0.72* 

From  Roberts-Austen,  Philosophical  Transactions,  i 
*  These  values  are  from  Guthrie. 


p.  383,  1896. 


SMITHSONIAN  TABLES. 


TABLE   165. 

SOLUBILITY  OF  INORGANIC  SALTS    IN  WATER;   VARIATION  WITH 
THE    TEMPERATURE. 

The  numbers  give  the  number  of  grams  of  the  anhydrous  salt  soluble  in  rooo  grams  of  water  at 

the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10° 

20°            30° 

40° 

50° 

60° 

?o° 

80° 

90°        100° 

AgNO3  

1150 

3*3 

3° 
26 
ii 
3i6 
50 
595 
405 
1614 

93 
1671 
818 
149 

744 
156 
43 
540 
1050 
285 

M 

5° 
225 
1279 

i33 
970 

7 
74 
127 

528 
260 
408 
297 
119 
1183 
706 
795 

7i 
204 

356 
820 

3r7 
1630 
69 

25 
i59o 
73° 

1600 
335 

45 
15 
333 
70 
650 
45° 
1747 
149 

I731 

819 

208 
66 

312 

50 
609 

85 
277 
1361 
209 
1030 

9 
92 
127 
535 
3°9 
422 

333 
159 

730 

8tl 

126 
263 

357 
890 
502 
1700 
82 

A39 
1690 

805 

2150 
362 

66 

22 

357 
92 

745 

1865 
230 
1787 
1250 

685 
918 
264 

74 
650 

343 
7i 
629 

*3! 

332 

1442 

3'6 
1  1  20 
ii 
in 

128 

545 
356 
439 

372 

210 

754 
903 

214 

& 

990 
900 
1800 
96 

93 

1790 
880 

2700 
404 
84 
9i 

h 

116 

IOIO 

565 
T973 
339 
1841 

255 

3j: 

1140 

373 

101 

650 

390 

1523 
458 

H 
T3Q 
129 

409 

453 
414 
270 
2418 
780 

39 
409 

$ 

1970 
in 
241 
1900 
962 

3350 

457 

124 

40 
408 
142 

"53 
650 
2080 

i899 
1598 
295 

402 

f 
760 
1170 
401 

H5 
670 
292 

453 
1600 

639 
1360 
18 
148 
130 

4-jo- 
458 

2970 
810 
1058 

(laq) 
363 
1235 
960 

2  2OO 
127 

639 
2O5O 
1049 

4000 
52' 

159 

436 
171 

935 
2185 
644 
1949 

336 

820 

3!5J 

486 

"3 

1210 

429 
197 
690 

lolo 

855 

1400 

22 
I65 
133 

504 

5°4 

3540? 
844 
1160 
105 

475 
367 

1050 
2480 
145 

2280 
1140 

4700 

59o 

248 

211 
62 
464 

,$ 

940 
2290 
838 
1999 
1791 
390 

55° 
139 
860 
1270 

455 
260 
710 

5°5 
600 
1760 
1099 
1460 
26 
182 
138 
610 

550 

552 

4300? 
880 
1170 

200 

464 

371 
1470 
II5O 
2830 
164 

2570 
1246 

5500 
662 

270 

494 
236 
1417 
95° 
2395 
1070 
2050 

457 

560 
J73 

'$ 

325 
730 

1840 
1380 
1510 

J 

144 

513°? 
916 

244 

4~58 
375 

3230 
949 
1360 

6500 
73i 

352 
95 
524 
270 
1470 
960 
2500 
1340 
2103 
2078 

535 
1040 

5258 
506 

243 
955 
1400 

5io 
396 
751 
730 

1920 
1690 
1590 
38 
214 

£ 

642 
656 

5800 

953 
1185 

3M 

% 

175° 
1240 
3860 

2950 
1480 

7600 

808 

556 

306 
1527 

2601 
1630 

2149 

6~27 
1050 

430 
371 

1470 
538 
475 

77i 

2OIO 
2040 
l68o 

J 

689 
713 

7400 
992 

4~o8 

452 

3«5 

1610 

9100 
891 
1540 

J8 

342 
1590 
1030 
2705 
1970 
2203 

735 
1060 

5357 

540 
1050 
1560 
566 
560 
791 

1020 

2O9O 
2460 
1780 

52 
24I 

'75 
730 

7*38 
773 

8710 

1033 
1205 

523 

452 
39i 
2040 
1260 
4330 

988 
3020 
'755 

A12(S04)3  .... 
A12K2(S04)4  .  .  . 
A12(NH4)2(S04)4  . 
B2O3  

BaCl2  
Ba(N03)2  .... 
CaCl2 

CoCl2 

CsCl  

CsNO3 

CsoSO.i 

Cu(N03)2  .... 
CuSO4  .  .  . 

FeCl2  
Fe2Cl6  

FeSO4  .  ... 

HgCl2 

KBr 

K2CO3  
KC1 

KC103  
K2CrO4  
K2Cr2O7  .... 
KHCO3 

KI 

KNO3  

KOH  .  .  . 

K2PtCl6 

KoSO-t 

LiOH  

MgCl2     
MgSO4    .     .      (7aq) 
.     .      (6aq) 
NH4C1    

NH4HCO3.  .  .  . 
NH4NO8  .... 
(NH4)2S04.  .  .  . 
NaBr  .  . 

Na2B4O7      .... 
Na2CO3  .     .     (ioaq) 
"         •     •      (?aq) 
NaCl  
NaClO3  
Na2CrO4      .... 
Na2Cr2O7    .... 
NaHC03     .... 
Na.2HPO4    .... 
Nal 

NaN03  

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  165  &*•••»**) -167. 

SOLUBILITY    OF    SALTS    AND    CASES    IN    WATER. 

TABLE  165  (concluded)  -  Solubility  ol  Inorganic  Salts  In  Water  ;  Variation  with  the  Temperature. 
The  numbers  give  the  number  of  grams  of  the  anhydrous  salt  soluble  in   1000  grams  of  water  at 

the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10°            20° 

30° 

40° 

5°° 

60° 

70° 

80° 

00° 

100° 

NaOH 
NjuPoO- 

420 

32 
141 

5° 
196 

525 

272 

36^ 

770 

'95 
364 
442 

395 

7 

2 

39 
27 
442 
948 

5'5 

39 

90 

305 
610 
600 

6 

444 
844 
330 
426 

483 
549 

10 

2 
62 

37 

1090 
62 
287 
194 

447 
700 
640 

8 

523 
911 

$ 

539 

10 

708 
14 

*i 

_49 

1190 

99 
400 

847 
680 
425 

12 

607 

976 
813 

535 
600 

12 
876 
20 

5 

143 
62 

1290 
U5 

495 
[482 

1026 
720 

£ 

1035 
1167 

14 
913 

30 
40 
6 
209 
76 

2069 
700 

145° 
174 

468 

'697 
760 

502 
20 

787 
1093 

1556 
63I 

744 
I? 
926 

5i 

1 

304 
92 

7~68 

1740 

220 

455 
2067 
810 
548 
24 
880 
"55 

2OOO 
674 

831 
21 
940 

16 

IO 

462 
109 
104 

255 

445 

% 

977 
1214 
2510 

7H 
896 

25 
956 

ii 

<£ 

127 

72 

8~90 

3T3° 
300 

437 
2488 

632 

1076 
1272 
3090 
750 
924 
3° 
972 

16 

IIIO 

146 
69 

860 

429 

2542 

688 

1174 
i33i 
375° 
787 
962 

34 
990 

20 

2OOO 

I63 
58 

920 

330 
427 
2660 

7~76 
48 

1270 

1389 
4520 
818 
1019 
40 

IOII 

4140 
47 
7~85 

Na2S08    
Na2SO4    .     .     (ioaq) 
.     .       (7aq) 
Na2S203  
NiCL.  

NiSO4  

PbBr2  
Pb(N03)2  .... 
RbCl  

RbNO3  

Rb2SO4 

SrCl2 

Snlo  

Sr(NO«),       .... 
Th(S04)2      .     .(9aq) 
.     ,(4aq) 
T1C1     
T1XO3     

T1.2SO4 

Yb.2(S04)3  .... 
Zn(N03)2  .... 
ZnSO4  

TABLE  166. -Solubility  ol  a  Few  Organic  Salts  in  Water;  Variation  with  the  Temperature. 


Salt. 

0° 

10° 

20° 

30° 

40° 

S°° 

60° 

7o° 

80° 

90° 

100° 

H2(C02)2      .... 
H2(CH2.C02)2      .     . 

36 

28 

53 
45 

IO2 
69 

'59 
106 

228 
162 

32I 
244 

445 

635 

5IT 

978 
708 

1200 

1209 

Tartaric  acid     .     .     . 

1150 

1260 

1390 

1560 

1760 

195° 

2180 

2440 

2730 

3070 

3430 

Racemic    "       ... 

92 

140 

206 

291 

433 

595 

783 

999 

1250 

'530 

1850 

K(HCO2)     .... 

2900 

- 

335° 

— 

3810 

4550 

— 

575° 

— 

7900 

KH(C4H40«)   .     .     . 

3 

4 

6 

9 

13 

18 

24 

32 

45 

57 

69 

TABLE    167,-  Solubility  ol  Gases  in  Water ;  Variation  with  the  Temperature. 

The  table  gives  the  weight  in  grams  of  the  gas  which  will  be  absorbed  in  1000  grams  of  water 
when  the  partial  pressure  of  the  gas  plus  the  vapor  pressure  of  the  liquid  at  the  given  tempera- 
ture equals  760  mm. 


Gas. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

0, 

HI 

N2 
Br2 

.0705 

.00192 

.0293 
431- 

•055' 
.00174 
.0230 
248. 

•0443 
.00160 
.0189 
148. 

.0368 
.00147 
.0161 
94- 

.0311 
.00138 
.0139 
62. 

.0263 
.00129 
.0121 
40. 

.0221 
.00118 
.0105 
28. 

.0181 

.00102 
.0089 

1  8. 

•0135 
.00079 
.0069 
II. 

C12 
C02 

3-35 

9-97 
2.32 

7.29 
1.69 

5-72 
1.26 

4-59 
0.97 

3-93 
0.76 

3-30 
0.58 

2-79 

2.23 

H2S 

7.10 

5-30 

3-98 

_ 

_ 

_ 

_ 

_ 

_ 

Ml, 

987.     689r 

535- 

422. 

_ 

_ 

_ 

_ 

_ 

228.     162.     113. 

78. 

54- 

~ 

~ 

— 

— 

Compiled  from  Landolt-Bdrnstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  168. 
CHANCE   OF  SOLUBILITY   PRODUCED   BY   UNIFORM   PRESSURE. 


Pressure 
in 
atmos- 
pheres. 

CdS048/3H20  at  25° 

ZnSO4.7H2O  at  25° 

Mannite  at  24.05° 

NaCl  at  24.05° 

.   •  o 
a  &° 

3 

Percentage  change. 

JfJ 

j^  8 

§  MM 
O 

Percentage  change. 

Cone,  of  satd.  soln. 
cs.  monnite  per 
100  gs.  H20. 

Percentage  change. 

i 

Percentage  change. 

I 

76.80 

— 

57-95 

— 

20.66 

— 

35-90 

—        . 

500 

78.01 

+  !-57 

57.87 

—  0.14 

21.14 

+  2.32 

36-55 

+  1.81 

IOOO 

78.84 

+  2.68 

57-65 

—  0.52 

21.40 

+  3-57 

37.02 

+  3-12 

1500 

— 

— 

— 

— 

21.64 

+  4.72 

37.36 

+  4-07 

*  E.  Cohen  and  L.  R.  Sinnige,  Z.  physik.  Client.  67,  p.  432,   1909;  69,  p.  102,  1909.     E.  Cohen,  K.  Inouye  and 
C.  Euwen,  ibid.  75,  p.  257,  1911.     These  authors  give  a  critical  resume  of  earlier  work  along  this  line. 


SMITHSONIAN   TABLES. 


172 


TABLE  169. 
ABSORPTION  OF  CASES  BY  LIQUIDS, 


ABSORPTION  COEFFICIENTS,  af>  FOR  GASES  IN  WATER. 

Temperature 

Centigrade. 

t 

Carbon 
dioxide. 
CO, 

Carbon 
monoxide. 
CO 

Hydrogen. 
H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N,0 

Oxygen. 

0 

1.797 

0-0354 

0.02  1  10 

0.02399 

0.0738 

1.048 

0.04925 

5 

10 

I.4IJO 
1.185 

•03  !  5 
.0282 

.02022 
.01944 

•02134 
.01918 

.0646 

.0571 

0.8778 
0-7377 

•04335 
.03852 

'5 

I.OO2 

.0254 

.01875 

.01742 

•0515 

0.6294 

•03456 

20 

O.OXd 

.0232 

.01809 

•01599 

.0471 

0-5443 

•03137 

25 

0.772 

.0214 

•01745 

.01481 

.0432 

.02874 

3° 

.0200 

.01690 

.01370 

.0400 

— 

.02646 

40 

0.506 

.0177 

.01644 

•OII95 

•0351 

- 

.02316 

5° 

.0161 

.Ol6o8 

.01074 

•°3  1  5 

— 

.02080 

100 

0.244 

.0141 

.Ol6oO 

.OIOII 

.0263 

— 

.01690 

Temperature 
Centigrade. 

t 

Air. 

Ammonia. 
NH3 

Chlorine. 
Cl 

Ethylene. 
C2H4 

Methane. 
CH4 

Hydrogen 
sulphide. 
H2S 

Sulphur 
dioxide. 
S02 

0 

0.02471 

1174.6 

3-036 

0.2563 

0.05473 

4-371 

79-79 

5 

.02179 

971-5 

2.808 

•2I53 

.04889 

3-965 

67.48 

10 

•01953 

840.2 

2.585 

•1837 

.04367 

3.586 

56-65 

15 

.01795 

7J6.0 

2.388 

.1615 

•03903 

3-233 

47.28 

20 

.01704 

683.1 

2.156 

.1488 

•03499 

2.905 

39-37 

25 

610.8 

1.950 

~ 

.02542 

2.604 

32-79 

ABSORPTION  COEFFICIENTS,  at,  FOR  GASES  IN  ALCOHOL,  G>H5OH. 

T* 

Centigrade. 
t 

Carbon 
dioxide. 
C02 

Ethylene.  Methane.    Hydrogen. 
C2H4          CH4               H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N2O 

Hydrogen    Sulphur 
sulphide,      dioxide. 
H2S            S02 

0 

4.329 

3-595      0.5226      0.0692 

0.1263 

0.3161 

4.190 

17.89        328.6 

5 

3.891 

3.323          .5086          .0685 

.1241 

.2998 

3-838 

14.78        251.7 

IO 

'5 

20 
25 

3-5H 
3-199 
2.946 
2,756 

3.086        .4953        -0679 
2.882        .4828        .0673 
2-713        -4710        .0667 

2.578      .4598      .0662 

.1228 
.1214 
.I2O4 
.1196 

.2861 
.2748 
•2659 
-2595 

3-525 
3-215 
3-015 
2.819 

II.99        190.3 

9-54       144-5 
7.41       114.3 
5.62        99.8 

iis  table  contains  the  volumes  of  different  gases,  supposed  measured  at  o°  C.  and  76  centimeters'  pressure,  which 
it  volume  of  the  liquid  named  will  absorb  at  atmospheric  pressure  and  the  temperature  stated  in  the  first  column. 
The  numbers  tabulated  are  commonly  called  the  absorption  coefficients  for  the  gases  in  water,  or  in  alcohol,  at  the 
temperature  t  and  under  one  atmosphere  of  pressure.  The  table  has  been  compiled  from  data  published  by  Bohr  & 
Bock,  Bunsen,  Carius,  Dittmar,  Hamberg,  Henrick,  Pagliano  &  Kmo,  Raoult,  Schbnfeld,  Setschenow,  and  Winkler. 
The  numbers  are  in  many  cases  averages  from  several  of  these  authorities. 

OTE.  —  The  effect  of  increase  of  pressure  is  generally  to  increase  the  absorption  coefficient.     The  following  is 
approximately  the  magnitude  of  the  effect  in  the  case  of  ammonia  in  alcohol  at  a  temperature  of  23°  C. : 

(  P    ~  45  cms.         50  cms.         55  cms.         60  cms.         65  cms. 

'  033  =:  69  74  7g  g4  gg 

According  to  Setschenow  the  effect  of  varying  the  pressure  from  45  to  85  centimeters  in  the  case  of  carbonic  acid  in 
water  is  very  small. 

SMITHSONIAN  TABLES. 


TABLES    17O-172. 
CAPILLARITY. -SURFACE    TENSION  OF  LIQUIDS/ 


173 


TABLE  170.  -Water  and  Alcohol  In  Contact  with  Air. 


TABLE  172.  -Solutions  of  Salts  In 
Water,  t 


Surface  tension 
in   dynes   per 
centimeter. 

Surface  tension 
in   dynes  per 
centimeter. 

Surface 
tension 
in  dynes 

Salt  in 
solution. 

Density. 

Temp. 

Tension 
n  dynes 
per  cm. 

Temp. 

Temp. 

c/. 

Temp. 

timeter. 

Water. 

Ethyl 
alcohol. 

Water. 

affl. 

Water. 

BaCl2 
CaClo 

1.2820 
1.0497 

15-16 
15-16 

8l.8 

77-5 

0° 

5 
10 

75-6 
74-9 
74-2 

23-5 
23.I 
22.6 

40° 

45 
5° 

70.0 

2O.O 

19-5 
19.1 

80° 

85 
90 

64-3 
63-6 
62.9 

HC1 

1-2773 
1.1190 
1.0887 

19 
19 

2O 
20 

95-° 
90.2 

73-6 
74-5 

15 
20 

25 
30 
35 

73-5 

72.1 
71.4 

70.7 

22.2 
21.7 

21-3 

20.8 

20.4 

& 

65 

70 

75 

67.8 
67.1 
66.4 
65-7 
65.0 

18.6 
18.2 
17-8 

'7-3 
16.9 

95 

100 

62.2 
61.5 

KC1 

MgCl2 

1.0242 
1.1699 
I.IOII 
1.0463 
L2338 
1.1694 

2O 
15-16 
15-16 
15-16 
15-16 
15-16 

i  ^  16 

m 

so.  i 
78.2 
90.1 
85.2 

78  o 

NaCl 

1.1932 

20 

a 

I.I074 

20 

80.5 

« 

1.0360 

20 

77.6 

NH4C1 

1.0758 

16 

84.3 

TABLE  171. 

-Miscellaneous  Liquids  in  Contact  with  Air. 

„ 

1-0535 
I.028I 

16 
16 

81.7 
78.8 

SrCl2 

T   11  T  A 

i  c—  1  6 

8  c  ft 

Liquid. 

Surface 

Authority. 

I.I2O4 

15-16 

79-4 

Temp. 
C  ° 

tension 
in  dynes 

K2C03 

1.0567 

'•3575 

15-16 
15-16 

77-8 
90.9 

per  cen 

a 

1.1576 

15-16 

81.8 

timeter. 

"Mo   CT} 

i  .0400 

15-16 

77-5 

1.1329 

14-15 

79-3 

Aceton    .... 
Acetic  acid  . 
Amyl  alcohol  .     . 
Benzole  .... 

1  6.8 
17.0 
I5.0 
15.0 

23-3 
30.2 
24.8 
28.8 

Ramsay-Shields. 
Average  of  various. 

KNO3 

M 

1.0605 
1.0283 
1.1263 
1.0466 

14-15 
14-15 
14 
14 

77.8 
77-2 
78.9 
77-6 

Butyric  acid      .     . 

iq.o 

28.7 

M 

NaNO3 

1.3022 

12 

83-5 

Carbon  disulphide      20.0 
Chloroform      .     .      20.0 
Ether  20.0 

3°-  5 
28.3 
18.4 

Quincke. 
Average  of  various. 

CuSO4 

1.1311 

I-I775 
1.0276 

12 
15-16 
15-16 

80.0 
78.6 
77-o    ; 

Glycerine 

.     .     .      17.0 

63.14 

Hall. 

H2SO4 

1.8278 

15 

63.0  ? 

Hexane  . 

.      .      .          0.0 

21.2 

Schiff. 

1-4453 

15 

79-7 

M 

'    68.0 

14.2 

it 

1.2636 

15 

79-7 

Mercury  .... 
Methyl  alcohol     . 
Olive  oil  .... 

1  8.0 
15.0 

2O.O 

520.0 
24.7 
34.7 

Average  of  various. 

K2S04 
MgS04 

1.0744 
1.0360 
1.2744 

15-16 
15-16 
15-16 

78.0 

77-4 
83.2 

Petroleum   . 
Propyl  alcohol 

2O.O 
5.8 

25-9 
25-9 

Magie. 
Schiff. 

Mn2SO4 

i.  0680 
1.1119 

15-16 
15-16 

77.8 
79.1 

M 

M 

97.1 

18.0 

M 

" 

1.0329 

15-16 

77-3 

Toluol     .... 

i  q.o 

29.1 

« 

ZnS04 

1-3981 

15-16 

83-3 

n 

18  9 

M 

M 

1.2830 

15-16 

80.7 

Turpentine  . 

2I.O 

2s:5 

Average  of  various. 

H 

1.1039 

15-16 

77-8 

*  This  determination  of  the  capillary  constants  of  liquids  has  been  the  subject  of  many  careful  experiments,  but  the 
results  of  the  different  experimenters,  and  even  of  the  same  observer  when  the  method  of  measurement  is  changed, 
do  not  agree  well  together.  The  values  here  quoted  can  only  be  taken  as  approximations  to  the  actual  values  for  th 
liquids  in  a  state  of  purity  in  contact  with  pure  air.  In  the  case  of  water  the  values  given  by  Lord  Rayleigh  from  the 
wave  length  of  ripples  (Phil.  Mag.  1890)  and  by  Hall  from  direct  measurement  of  the  tension  of  a  flat  film  (Phil.  Mag. 
1893)  have  been  preferred,  and  the  temperature  correction  has  been  taken  as  0.141  dyne  per  degree  centigrade.  The 
values  for  alcohol  were  derived  from  the  experiments  of  Hall  above  referred  to  and  the  experiments  on  the  effect  of 
temperature  made  by  Timberg  (Wied.  Ann.  vol.  30). 

The  authority  for  a  few  of  the  other  values  given  is  quoted,  but  they  are  for  the  most  part  average  values  derived 
from  a  large  number  of  results  published  by  different  experimenters. 

f  From  Volkmann  (Wied.  Ann.  vol.  17,  p.  353). 

For  more  recent  data  see  especially  Harkins,  J.  Am.  Ch.  Soc.,  39,  p.  55,  1917  (336  liquids),  and  42, 
p    702,  2543,  1920. 
SMITHSONIAN  TABLFS 


J74 


TABLES  173-176. 

TENSION    OF    LIQUIDS. 

TABLE   173. -Surface  Tension  of 


r 

Liquid. 

Specific 
gravity. 

Surface  tension  in  dynes  per  cen- 
timeter of  liquid  in  contact  with  — 

Air. 

Water. 

Mercury. 

Water    .                 

I.O 

•?ia 

1.4878 
0.7906 
0.9136 
0.8867 

•7977 

1.  10 

1.1248 

75-o 
5  '3-0 
3°-5 

(31-8) 
(24.1) 

34-6 
28.8 
29.7 

(72.9) 
69.9 

o.o 

392.0 
41.7 
26.8 

18.6 

"•5 

(28.9) 

(392) 
0 

(387) 
(415) 
364 
317 
241 
271 

(392) 
429 

Mercury          ........ 

Bisulphide  of  carbon     

Kthyl  alcohol         
Olive  oil         
Turpentine     ........ 

Petroleum       ........ 

Hyposulphite  of  soda  solution      .... 

TABLE  174.  -  Surface  Tension  of  Liquids  at  Solidifying  Point,  t 


Substance. 

Tempera- 
ture of 
solidifi- 
cation. 
Cent.0 

Surface 
tension  in 
dynes  per 
centimeter. 

Substance. 

Tempera- 
ture of 
solidifi- 
cation. 

Cent.0 

Surface 
tension  in 
dynes  per 
centimeter. 

Platinum 

2OOO 

I69I 

Antimony 

432 

249 

Gold      .... 

I2OO 

1003 

Borax    .... 

IOOO 

216 

Zinc       .... 

360 

877 

Carbonate  of  soda 

IOOO 

2IO 

Tin         .... 

230 

Chloride  of  sodium 

_ 

116 

Mercury 

—40 

588 

Water    .... 

0 

87-9J 

Lead     .... 

330 

457 

Selenium 

217 

71.8 

Silver    .... 

IOOO 

427 

Sulphur 

III 

42.1 

Bismuth 

26< 

1390 

Phosphorus  . 

43 

42.0 

Potassium 

58 

37  T 

Wax      .... 

68 

34.1 

Sodium 

90 

iss 

TABLE  175.  — Tension  of  Soap  Films. 


Elaborate  measurements  of  the  thickness  of  soap  films  have  been  made  by  Reinold  and 
Rucker.y  They  find  that  a  film  of  oleate  of  soda  solution  containing  i  of  soap  to  70  of 
water,  and  having  3  per  cent  of  KNO3  added  to  increase  electrical  conductivity,  breaks  at 
a  thickness  varying  between  7.2  and  14.5  micro-millimeters,  the  average  being  12.1  micro- 
millimeters.  The  film  becomes  black  and  apparently  of  nearly  uniform  thickness  round 
the  point  where  fracture  begins.  Outside  the  black  patch  there  is  the  usual  display  of 
colors,  and  the  thickness  at  these  parts  may  be  estimated  from  the  colors  of  thin  plates 
and  the  refractive  index  of  the  solution. 

When  the  percentage  of  KNO3  is  diminished,  the  thickness  of  the  black  patch  increases. 
For  example,  KN():J  =3  i  0.5  o.o 

Thickness  =  12.4  13.5  14.5  22.1  micro-mm. 

A  similar  variation  was  found  in  the  other  soaps. 

It  was  also  found  that  diminishing  the  proportion  of  soap  in  the  solution,  there  being 
no  KNQs  dissolved,  increased  the  thickness  of  the  film. 

i   part  soap  to  30  of  water  gave  thickness  21.6  micro-mm. 

I  part  soap  to  40  of  water  gave  thickness  22.1  micro-mm. 

i  part  soap  to  60  of  water  gave  thickness  27.7  micro-mm. 

i  part  soap  to  80  of  water  gave  thickness  29.3  micro-mm. 


Qa,.,^c»  ,«u.i-.  ,1  .....  m«K   vui.  zo,  inn5;  wnn  me  exception  ot   those  in  brackets,  which  were  not  corrected  by 
bout  Jo^C™ '  3re  somewhat  too  high,  for  the  reason  stated  by  Worthington.     The  temperature  was 

t  Quincke,  "  Pogg.  Ann."  vol.  13?,  p.  661. 

It  will  be  observed  that  the  value  here  given  on  the  authority  of  Quincke  is  much  higher  than  his  subsequent 
measurements,  as  quoted  above,  give. 

"  Proc.  Roy.  Soc."  1877,  and  "  Phil.  Trans.  Roy.  Soc."  1881,  1883,  and  1893. 

NOTE.  —  Quincke  points  out  that  substances  may  be  divided  into  groups  in  each  of  which  the  ratio  of  the  surface 
tension  to  the  dens.ty  ,.  nearly  constant.  Thus,  ,f  this  ratio  for  mercury  be  taken  as  unit,  the  ratio  for  the  bromides 
and  iodides  is  about  a  half  :  that  of  the  nitrates,  chlorides,  sugars,  and  fats,  as  well  as  the  metals,  lead,  bismuth,  and 
antimony,  about  i :  that  of  water,  the  carbonates,  sulphates,  and  probably  phosphates,  and  the  metals  platinum,  gold, 
silver,  cadmium,  tin,  and  copper,  2 ;  that  of  zinc,  iron,  and  palladium,  3;  and  that  of  sodium,  6. 
SMITHSONIAN  TABLES. 


VAPOR  PRESSURE. 
TABLE  176.  —  Vapor  Pressure  of  Elements. 


175 


Hydrogen. 

Oxygen. 

Nitrogen. 

Argon. 

Xenon. 

Krypton. 

H  scale. 

mm 

H  scale. 

mm 

T 

mm 

°K 

mm 

°K 

mm 

°K 

mm 

20.4I°K 

20.22 

19-93 
19.41 
18.82 
I8.I5 
17.36 
16.37 
14-93 

800 
76o 
700 
600 
500 
400 
300 
2OO 
IOO 

9o.6o°K 
90.  10 

89.33 
87.91 
86.29 

84-39 
82.09 
79.07 

.  800 
760 
700 
600 
500 

400 

300 

200 

77-33°K 
76-83 
76-65 
75-44 
74-03 
72-39 
70.42 
67.80 
63-65 

76o. 

7I4.5 
700. 
600. 
500. 
400. 
300. 
2OO. 
IOO. 

155-6, 
139.0 
137-8 
136.8 
123.1 
87.8 
86.5 
85-5 
83-8 
82.6 
8l.7 
77-3 

J.O2OO. 
2325I- 
21334- 

20700. 

[0313. 
821.2 
704.5 
633-4 
524-3 
465.0 

410.  1 

215.0 

287.7 

273-3 
255-6 
254.0 
252.6 

248.7 
244.2 

239-7 
237-4 
23L4 
183.2 

44112 
3I50I 
21967 
21512 
19984 

I8I53 
15868 

I397I 
13505 
IH34 
2O20 

210.5 
206.4 
204.  I 
201.5 
2OI.O 
197.9 
170.9 
II2.7 

88.6 
84.2 

41245 
37006 

34693 
31621 

30837 
28808 
11970 
387 
17-4 
9- 

Travers,   Sen- 
ter,    jaque- 
rod,  1902-3. 

Travers,  Jaque- 
rod,  1902-5. 

Fischer,  Alt, 
1902. 

Ramsay,  Travers,  Zs 

.  phys.  Ch.  38, 

rooi. 

Chlorine. 

Bromine. 

Iodine. 

Copper. 

Silver. 

°C 

Pressure. 

°C 

mm 

°C 

mm 

°C 

Atme. 

°C 

Atme. 

+  146. 
+100. 
+50. 
+  20. 
O. 

—  20. 
-33-6 
-40. 
-50- 
-60. 
-70. 
-80. 

-85- 
-88. 

93  .  50  atm. 
41  .  70  atm. 
14.  70  atm. 
6.62  atm. 
3.66  atm. 
i  .  84  atm. 
760.     mm 
560.     mm 
350.    mm 
210.     mm 
118.     mm 
62.5  mm 
45-     mm 
37-5  mm 

+58.75 
56.3 
51-95 
46.8 

40.45 
33-05 
23-45 
16.95 

8.20 

-5-05 
-7.0 

-8.4 

—  12.  O 

-16.65 

76o 
700 
600 
500 
400 
300 
2OO 
150 
IOO 

50 

45 
40 
30 

20 

+55 
5o 
45 
40 
35 
30 
25 
15 
o 

3.084 
2.154 
1.498 
1.025 
0.699 
0.469 

0.305 
0.131 
0.030 

2310 
2180 
1980 

1.0 
0.338 
O.I3I5 

1955 
1780 
1660 

I.O 

0.346 
0.1355 

Lead 

Bismuth. 

°C 

Atme. 

°C 

Atme. 

2100 
1870 

1525 
1420 
1320 

II.  7 
6-3 

I.O 

o.35o 
0.138 

2060 
1950 
1740 
1420 
1310 
1  200 

16.5 
n.  7 

6-3 

I.O 

0.338 
0.134 

Baxter,    Hick- 
ey,  Holmes, 
J.   Am.    Ch 
Soc.  1907. 

.  Zinc. 

Tin. 

Knietsch,  W.  Ann.   1890. 
Cu  to  Sn,  Greenwood,  Pr. 
Roy.    Soc.    83A,   1910; 
Zs.  ph.  Ch.  76,  1911. 

Ramsay,  Young 
J.     Ch.     Soc. 
1886. 

°C 

Atme. 

°C 

Atme. 

1510 
1280 
1230 
II2O 

53-o 

21-5 

ii.  7 
6.3 

2270 

2100 
1970 

I.O 
0-345 
0.133 

TABLE  177.  —  Vapor  Pressure  and  Rate  of  Evaporization 


°K 

Mo 
mm 

W 

mm 

Evaporation  rate. 

g/cm2/sec. 

Platinum. 

Mo 

W 

°K 

mm 

g/cm2/sec. 

1800 
2OOO 
2200 
2400 
2600 
2800 
3000 
3200 
3500 

o.o8643 
0.06789 
o  .  04396 
0.021027 
0.0160 
0.1679 

3890°      \ 

760  mm  / 

0.011645 
o  .  09849 
0.07492 
0.05151 
0.04286 
0.03362 
0-02333 
0.0572 

0.010863 
O.O7IOO 

o  .  06480 

O.04I20 
0.03179 
0.02l8l 

o.  012114 
0.010144 
0.09798 
0.07236 
0.06429 
0.05523 
0.04467 
0.03769 

1000 
I20O 
I4OO 
I60O 
I800 
2000 
4l80 

0.017324 

O.Oi2lH 

o.  09188 
o  .  07484 

0.05350 

0.03107 
760  mm 

0.019832 
O.Ou26o 
0.011401 
o  .  09966 
0.07667 
0.05195 

Langmuir,    MacKay,   Phys. 
Rev.  2,  1913;    4,  19*4- 
Order  of  vacuum,  o.  ooi-mm. 

p  =  K.T~^e~^o/RT  dynes/cm2.     Egerton,  Phil.  Mag.  33,  p.  33,  1917. 
Zn,  X0  =  3.28  x  io4;  K  =  1.17  x  io14       Cd,  X0=  2.77  X  io4;  K  =  5.27  X  io13 
Hg,  X0  =  i.  60  x  io4;       =3.72  X  io13  (Plnudsen) 
SMITHSONIAN  TABLES. 

1 76 


TABLE  178. 
VAPOR    PRESSURES, 


The  vapor  pressures  here  tabulated  have  been  taken,  with  one  exception,  from  Regnault's  results 
The  vapor  pressure  of  Pictefs  fluid  is  given  on  his  own  authority.  The  pressures  are  in  centimeters  of 
mercury. 


Tem- 
pera- 
ture 
Cent. 

Acetone. 
C8H60 

Benzol. 
C6H6 

Carbon 
bisul- 
phide. 
CS, 

Carbon 
tetra- 
chloride. 

ecu 

Chloro- 
form. 
CHC18 

Ethyl 
alcohol. 
C2H60 

Ethyl 
ether. 
C4H100 

Ethyl 
bromide. 
C2H5Br 

Methyl 
alcohol. 
CH40 

Turpen- 
tine. 
C10H6 

—25° 

_ 

_ 

4.41 

.41 

_ 

—  20 

_ 

.c8 

4-73 

"98 

- 

•33 

6.89 

5.92 

•63 

- 

—  15 

- 

.88 

6.16 

i-35 

- 

•g 

8-93 

7.81 

•93 

— 

—  10 

— 

1.29 

7-94 

1.85 

— 

•65 

11.47 

10.15 

1.35 

— 

—5 

- 

1.83 

10.13 

2.48 

- 

.91 

I4.6l 

13.06 

1.92 

— 

0 

_ 

2-53 

12.79 

3-29 

5-97 

1.27 

18.44 

16.56 

2.68 

.21 

5 

_ 

3-42 

1  6.00 

4-32 

1.76 

23.09 

20.72 

3-69 

— 

10 

_ 

4.52 

19.85 

5.60 

10.05 

2.42 

28.68 

25-74 

5-oi 

.29 

15 

_ 

5  89 

24.41 

7.17 

_ 

3-3° 

35.36 

31.69 

6.71 

— 

20 

17.96 

7:56 

29.80 

9.10 

16.05 

4-45 

43.28 

38.70 

8.87 

•44 

25 

22.63 

9-59 

36.11 

n-43 

20.02 

5-94 

52.59 

46.91 

1  1.  60 

- 

3° 

28.10 

12.02 

43-46 

14.23 

24-75 

7-85 

6348 

56.45 

15.00 

.69 

35 

34-52 

14-93 

51-97 

17-55 

30-35 

10.29 

76.12 

67.49 

19.20 

- 

40 

42.OI 

18.36 

61-75 

21.48 

36.93 

'3-37 

90.70 

80.19 

24-35 

i.  08 

45 

50-75 

22.41 

72.95 

26.08 

44.60 

17.22 

107.42 

94-73 

30.61 

— 

50 

62.29 

27.14 

85-71 

3M4 

53-50 

21.99 

126.48 

111.28 

38.17 

1.70 

55 

72.59 

32.64 

100.16 

37-63 

63-77 

27.86 

148.11 

130-03 

47.22 

— 

So 

86.05 

39-oi 

116.45 

44-74 

7  c  CA 
K 

35-02 

172.50 

151.19 

57-99 

2.65 

65 

70 

101.43 
118.94 

46-34 
54-74 

1  34-7  5 
1  55-2  1 

52-87 
62.11 

104.21 

43-69 
54-n 

199.89 
230.49 

174-95 
201.51 

70.73 
85-71 

4.06 

75 

138.76 

64.32 

177.99 

72-57 

121.42 

66-55 

264.54 

231.07 

103.21 

- 

80 

161.10 

75-!9 

203.25 

84-33 

140.76 

81.29 

302.28 

263.86 

123.85 

6.13 

85 
9° 

186.18 
214.17 

87.46 
101.27 

231.17 
261.91 

97-51 
112.23 

162.41 

186.52 

98.64 
118.93 

343-95 
389-83 

300.06 
339-89 

147.09 
174.17 

9.06 

95 

245.28 

116.75 

296.63 

128.69 

213.28 

142.51 

440.18 

205.17 

— 

100 

279-73 

134.01 

332-51 

146.71 

242.85 

169.75 

495-33 

431.23 

240.51 

13.11 

105 
no 

317.70 
359-40 

153.18 
174-44 

372.72 
416.41 

166.72 

188.74 

275-40 

311.10 

201.04 
236-76 

555-62 
621.46 

483.12 
539-40 

280.63 
325-96 

18.60 

"5 

405.00 

197.82 

463-74 

212.91 

350.10 

277-34 

693-33 

600.24 

376.98 

- 

1  20 

454.69 

223.54 

514-88 

239-37 

392.57 

323-17 

771.92 

665.80 

434.18 

25-70 

125 

508.62 

231.71 

569-97 

268.24 

438.66 

374-69 

_ 

736.22 

498.05 

- 

130 
'35 

566.97 
629.87 

282.43 
3^-85 

629.16 
692-59 

299.69 
333-86 

542.25 

432-30 
496.42 

— 

811.65 
892.19 

569-13 
647-93 

34-90 

140 

697.44 

352-07 

760.40 

370.90 

600.02 

567-46 

— 

977.96 

733-71 

46.40 

391.21 

832.69 

411.00 

661.92 

645.80 

— 

830.89 

— 

150 

'55 

- 

433-37 
478.65 

909.59 

454.31 
501.02 

728.06 

798.53 

731-84 
825.92 

- 

936-13 

60.50 
68.60 

160 

- 

527-14 

— 

55I-3I 

873.42 

— 

— 

— 

77-5° 

165 
170 

- 

568.30 
634.07 

- 

605.38 
663.44 

952.78 

- 

- 

- 

- 

- 

SMITHSONIAN  TABLES. 


TABLE    178  (continued). 

VAPOR    PRESSURES. 


177 


Tem- 
pera- 
ture, 
Centi- 
grade. 

Ammonia. 
NH3 

Carbon 
dioxide. 
C02 

Ethyl 
chloride. 
CjH8Cl 

Ethyl 
iodide. 
C2H5I 

Methyl 
chloride. 
CH3C1 

Methylic 
ether. 
C2H60 

Nitrous 
oxide. 
NjO 

Pictet's 
fluid. 

44C022by 
weight 

Sulphur 
dioxide. 

so, 

Hydrogen 
sulphide. 

—30° 

86.61 

- 

11.02 

- 

57-90 

57-65 

- 

58.52 

28.75 

- 

—25 

110.43 

1300.70 

14.50 

- 

7J.78 

71.61 

1569.49 

67.64 

37.38 

374-93 

—  20 

139.21 

1514.24 

18.75 

— 

88.32 

88.20 

1758.66 

74.48 

47.95 

443.85 

—'5 

—  10 

I73-65 
214.46 

I758-25 
2034.02 

23.96 
30.21 

_ 

107.92 
130.96 

107.77 
130.66 

1968.43 
2200.80 

89.68 
101.84 

60.79 
76.25 

5*9-65 
608.46 

—5 

264.42 

2344.13 

37.67 

- 

157.87 

J57-25 

2457.92 

121.60 

94.69 

706.60 

0 

318.33 

2690.66 

46.52 

4.19 

189.10 

187.90 

2742.10 

139.08 

116.51 

820.63 

5 

383-03 

3075.38 

56-93 

5-41 

225.11 

222.90 

3055-86 

167.20 

142.11 

949.08 

10 

457-40 

3499-86 

69.11 

6.92 

266.38 

262.90 

3401.91 

193.80 

J7I-95 

1089.63 

15 

543.34 

3964-69 

83.26 

8.76 

313.41 

307-98 

3783.I7 

226.48 

206.49 

1244.79 

20 

638.78 

4471.66 

99.62 

II.OO 

366.69 

358.60 

4202.79 

258.40 

246.20 

1415.15 

25 

30 

747.70 
870.10 

5020.73 
5611.90 

118.42 
139.90 

13.69 
16.91 

426.74 
494.05 

415.10 
477.8o 

4664.14 

5  i  70.85 

297.92 

291.60 
343-18 

1601.24 
1803.53 

35 

1007.02 

6244.73 

164.32 

20.71 

569.11 

— 

6335-9« 

383.80 

401.48 

2002.43 

40 

11  59-  53 

6918.44 

191.96 

25.I7 

- 

434.72 

467.02 

2258.25 

45 

1328.73 

7631.46 

223.07 

30.38 

— 

— 

— 

478.80 

540.35 

249543 

50 

1515-83 

- 

257-94 

36.40 

- 

- 

_ 

521.36 

622.00 

2781.48 

& 

1721.98 
1948.21 

: 

266.84 
340.05 

43-32 
51.22 

: 

: 

*™ 

712.50 
812.38 

3069-07 
3374-02 

65 

2196.51 

- 

387.85 

- 

- 

- 

- 

922.14 

3696.15 

70 

2467.55 

— 

440.50 

— 

— 

— 

- 

- 

- 

4035.32 

75 

2763.00 

_ 

498.27 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

80 

3084.31 

- 

561.41 

- 

- 

- 

- 

- 

- 

- 

85 

3433-09 

— 

630.16 

— 

— 

— 

— 

— 

- 

— 

90 

3810.92 

— 

704.75 

— 

— 

— 

— 

— 

— 

— 

95 

4219.57 

— 

785.39 

— 

— 

- 

- 

- 

— 

— 

100 

4660.82 

- 

872.28 

- 

•  - 

- 

- 

- 

- 

- 

SMITHSONIAN  TABLES. 


i78 


TABLES   179-18O. 
VAPOR    PRESSURE, 


TABLE  179.  —Vapor  Pressure  of  Ethyl  Alcohol.* 


i 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

10 
20 

30 

40 

£ 

70 

12.24 
23-78 
44.00 
78.06 

I33-70 
220.00 

350-30 
541.20 

13.18 

$6 

82.50 

140.75 
230.80 
366.40 
564.35 

27.94 

49-47 
87.17 

148.10 
242.50 
383-10 
588.35 

15.16 
28.67 

52-44 
92.07 

155.80 
253-80 
400.40 
613.20 

16.21 
30.50 

97-21 

163.80 
265.90 

638'95 

3244 
58.86 
102.60 

172.20 
278.60 
437.00 
665.55 

18.46 

34-49 
62.33 
108.24 

181.00 
291.85 

456.35 
693.10 

19.68 
36-67 
65.97 
114.15 

190.10 
305-65 
476.45 

721.55 

20.98 

38.97 
69.80 
120.35 

199.65 
3*9-95 

751.00 

22.34 
41.40 

209.60 

334.85 
518.85 

781.45 

From  the  formula  log/  =  a  -j-  ba*  +  cf?  Ramsay  and  Young  obtain  the  following  numbers.f 

0 

! 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

IOO 

200 

12.24 
1692.3. 
22182. 

23-73 

43-97 
3223.0 

32196- 

78.11 
4318.7 
38389- 

13342 
5686.6 

219.82 
7368.7 

350.21 
9409.9 

540.91 
11858. 

811.81 
14764. 

1186.5 
18185. 

TABLE   180.  — Vapor  Pressure  of  Methyl  Alcohol,  t 


o 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

E 

H 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

10 

gr 

31.6 

57.o 

33-6 
60.3 

35-6 
63.8 

37-8 
67-5 

40.2 
71.4 

42.6 

75-5 

45-2 
79-8 

47-9 
84-3 

50.8 
89.0 

20 

94-o 

99-2 

104.7 

1  10.4 

116.5 

122.7 

129.3 

136.2 

143-4 

151.0 

30 

40 

'& 

158.9 
259-4 
409-4 
624.3 

167.1 
271.9 

427.7 
650.0 

175-7 
285.0 
446.6 
676.5 

184.7 
298-5 
466.3 
703.8 

194.1 
312.6 
486.6 
732.0 

203.9 
327.3 
5077 
761.1 

214.1 

342.5 

529-5 
791.1 

224.7 

358.3 
552-0 
822.0 

235-8 
374-7 
575-3 

247-4 
391-7 

599-4 

*  This  table  has  been  compiled  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc.  vol.  47,  and  Phil. 
Trans.  Roy.  Soc.,  1886). 

t   In  this  formula  «:=  5.0720301  ;    log  b—  2.6406131 ;  log  c  =  0.6050854 ;   log  a  =  0.003377538;  log  0=  1.99682424 
<c  is  negative). 

t  Taken  from  a  paper  by  Dittmar  and  Fawsitt  (Trans.  Roy.  Soc.  Edin.  vol.  33). 
SMITHSONIAN   TABLES. 


TABLE    181. 
VAPOR   PRESSURE.* 

Carbon  Bisulphide,  Chlorobenzene,  Bromobenzene,  and  Aniline. 


179 


Temp. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9°    . 

(a)   CARBON  BISULPHIDE. 

0° 

127.90 

133-85 

140.05 

146.45 

153-10 

160.00 

167.15 

174.60 

182.25 

190.20 

10 

20 

30 
40 

198.45 
298.05 
434.60 
617.50 

207.00 
309.90 
450-65 
638.70 

215.80 
322.10 

467-15 
660.50 

224.95 
334-70 
484.15 
682.90 

234.40 
347-70 
501.65 
705.90 

244.15 
361.10 

5I9-65 
729.50 

254-25 
374.95 
538.15 

753-75 

264.65 
389.20 

557-15 
778.60 

275.40 
403.90 

576.75 
804.10 

286.55 
419.00 
596.85 
830.25 

(b)    CHLOROBENZENE. 

20° 

8.65 

9.14 

9.66 

IO.2I 

10.79 

11.40 

12.04 

12.71 

13.42 

14.17 

3° 

14-95 

15-77 

16.63 

17-53 

18.47 

'9-45 

20.48 

21.56 

22.69 

23.87 

40 

25.10 

26.38 

27.72 

29.12 

30.58 

32.10 

33-69 

35-35 

37.08 

38.88 

50 

40-75 

42.69 

44.72 

46.84 

49-05 

5T-35 

53-74 

56.22 

58-79 

61.45 

60 

64.20 

67.06 

70.03 

73-n 

76.30 

79.60 

83.02 

86.56 

90.22 

94.00 

70 
80 

97.90 
144.80 

101.95 
150.30 

106.10 
156-05 

110.41 
161.95 

114.85 
168.00 

"9-45 
J74-25 

124.20 
181.70 

129.10 
187.30 

'34-15 
194.10 

139.40 
201.15 

90 

208.35 

215.80 

223.45 

231.30 

239-35 

247.70 

256.20 

265.00 

274.00 

283.25 

100 

292.75 

302.50 

312.50 

322.80 

333-35 

344.15 

355-25 

366.65 

378.30 

390.25 

no 

402.55 

415.10 

427.95 

44i.i5 

454-65 

468.50 

482.65 

497.20 

5I2-o5 

527.25 

120 

542.80 

55f.7o 

575-05 

59!-7o 

608.75 

626.15 

643-95 

662.15 

680.75 

699-65 

130 

718.95 

738-65 

758.80 

" 

*• 

~ 

— 

~ 

— 

(c)   BROMOBENZENE. 

40° 

'      - 

- 

- 

- 

- 

12.40 

13.06 

13-75 

14.47 

15.22 

50 

16.00 

16.82 

17.68 

18.58 

19-S2 

20.50 

21.52 

22.59 

23-71 

24.88 

60 

26.10 

27.36 

28.68 

30.06 

3i-5o 

33-oo 

34.56 

36.18 

37-86 

39.60 

70 

41.40 

43.28 

45-24 

47.28 

49.40 

51.60 

53-88 

56-25 

58.71 

61.26 

80 

63.90 

66.64 

69.48 

7242 

7546 

78.60 

81.84 

85.20 

88.68 

92.28 

90 

96.00 

99.84 

103.80 

107.88 

112.08 

116.40 

120.86 

125.46 

130.20 

135-08 

100 

140.10 

145.26 

150.57 

156-03 

161.64 

167.40 

I73-32 

179.41 

18^.67 

192.10 

no 

198.70 

205.48 

212.44 

219.58 

226.90 

234-40 

242.10 

250.00 

258.10 

266.40 

1  20 
130 

274.90 
372-65 

283.65 
383-75 

292.60 
395-!o 

301-75 
406.70 

3"-i5 
418.60 

320.80 
430-75 

330-70 
443-20 

340.80 
455-90 

35i.i5 
468.90 

361.80 
482.20 

140 

495.80 

509.70 

523-90 

538-40 

553-20 

568.35 

583-85 

599-65 

615-75 

632.25 

150 

649.05 

666.25 

683.80 

701.65 

7I9-95 

738.55 

757-55 

776.95 

796.70 

816.90 

(d)  ANILINE. 

80° 

1  8.80 

19.78 

20.79 

21.83 

22.90 

24.00 

2^.14 

26.32 

27-54 

28.80 

90 

30.10 

3M4 

32.83 

34-27 

35-76 

37-3° 

38.90 

40.56 

42.28 

44.06 

100 

45-90 

47.80 

49-78 

51.84 

53-98 

56.20 

58.50 

60.88 

63-34 

65.88 

no 

68.50 

71.22 

74-04 

76.96 

79.98 

83.10 

86.32 

89.66 

93.12 

96.70 

1  20 

100.40 

104.22 

108.17 

112.25 

116.46 

120.80 

I2C.28 

129.91 

134.69 

139.62 

130 

144.70 

149.94 

1  55-34 

160.90 

166.62 

172.50 

178.56 

184.80 

191.22 

I97.82 

140 

204.60 

211.58 

2?8.76 

226.14 

233-72 

241.50 

249.50 

257.72 

266.16 

274.82 

150 

283.70 

292.80 

302.15 

3IT-75 

321.60 

33I-70 

342.05 

352-65 

363-5° 

374.60 

160 

386.00 

397.65 

409.60 

421.80 

434-30 

447.10 

460.20 

473.60 

487-25 

501.25 

170 

5  J  5-6o 

530.20 

545.20     560.45 

576.10 

592-05 

608.35 

625.05 

642.05 

659-45 

1  80 

677-15 

695-30 

7I3-75     732-65 

75^90 

771-5° 

*  These  tables  of  vapor  pressures  are  quoted  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc. 
vol.  47).     The  tables  are  intended  to  give  a  series  suitable  for  hot-jacket  purposes. 

SMITHSONIAN  TABLES. 


i8o 


TABLE  181    (continued). 
VAPOR   PRESSURE. 

Methyl  Salicylate,  Bromonaphthalene.  and  Mercury. 


Temp. 

0° 

1° 

2° 

3° 

4° 

6° 

6° 

7° 

8° 

9° 

(e)  METHYL  SALICYLATE. 

70° 

80 

2.40 
4.60 

2.58 

4.87 

2.77 
5-15 

2.97 
5-44 

5-74 

3-40 
6.05 

3.62 
6.37 

6.70 

4.09 

7-05 

4-34 

7.42 

90 

7.8o 

8.20 

8.62 

9.06 

9-52 

9-95 

10.44 

10.95 

11.48 

12.03 

100 

12.60 

13.20 

13.82 

14.47 

I5.IS 

15-85 

16.58 

17-34 

18.13 

18.95 

I  IO 
120 

19.80 
30.25 

20.68 
3r-52 

21.60 
32-84 

22-55 
34-21 

23-53 
35-63 

24-55 
37-10 

25.61 
38.67 

26.71 
40.24 

27-85 
41.84 

29.03 
43-54 

130 
140 

45-30 
66.55 

47.12 
69.08 

49.01 
71.69 

50-96 
74.38 

52-97 
77^5 

55-05 
80.00 

57.20 
82.94 

59-43 
85-97 

61-73 
89.09 

64.10 
92.30 

150 

160 

170 

95.60 

134.25 

1^4.70 

99.00 
138.72 
190.48 

102.50 

M3-3I 
196.41 

106.10 
148.03 
202.49 

109.80 
152.88 
208.72 

113.60 

157-85 
215.10 

H7-51 
162.95 
221.65 

121.53 
168.19 
228.30 

125.66 
I73-56 
235-I5 

129.90 
1  79.06 

242.15 

180 

249-35 

256.70 

264.20 

271.90 

279-75 

287.80 

296.00 

304.48 

3I3-05 

321.85 

190 

330.85 

340.05 

349-45 

359-05 

368.85 

378-90 

389-  i  5 

399-6o 

410.30 

421.20 

200 

432.35 

443-75 

455-35 

467-25 

479-35 

491.70 

504-35 

5I7-25 

530'40 

543-8o 

210 

557-50 

571-45 

585-70 

600.25 

615-05 

630.15 

645-55 

661.25 

677.25 

693.60 

220 

710.10 

727-05 

744.35 

761.90 

779.85 

798.10 

(f)  BROMONAPHTHALENE. 

110 

3-6o 

3-74 

3-89 

4-05 

4.22 

4-40 

4-59 

4-79 

5-0° 

5-22 

120 

5-45 

5-70 

5.96 

6.23 

6.51 

6.80 

7.10 

7.42 

7.76 

8.12 

I30 

8.50 

8.89 

9-29 

9.71 

10.15 

1  0.60 

11.07 

11.56 

12.07 

12.60 

140 

'3-iS 

I3-72 

14-31 

14.92 

15-55 

16.20 

16.87 

17-56 

18.28 

19.03 

150 

19.80 

20.59 

21.41 

22.25 

23.11 

24.00 

24.92 

25.86 

26.83 

'  27.83 

160 

28.85 

29.90 

30.98 

32.09 

33-23 

34-40 

35-6o 

36-83 

38.10 

39.41 

170 

•  40-75 

42.12 

43-53 

44-99 

46.50 

48.05 

49.64 

51.28 

52-96 

54.68 

180 

56-45 

58-27 

60.14 

62.04 

64.06 

66.10 

68.19 

70.34 

72.55 

74.82 

190 

77-15 

79-54 

81.99 

84.51 

87.10 

89.75 

9247 

95-26 

98.12 

101.05 

200 

104.05 

107.12 

110.27 

Ir3-50 

116.81 

1  20.20 

123.67 

127.22 

130.86 

r34-59 

,     210 

220 

138.40 
181.75 

142.30 
186.65 

146.29 
191.65 

150-38 
196-75 

J54-57 
202.00 

158.85 
207.35 

163-25 
212.80 

167.70 
218.40 

172.30 
224.15 

176-95 
230.00 

230 

235-95 

242.05 

248.30 

254-65 

261.20 

267.85 

274-65 

281.60 

288.70 

295-95 

240 

303.35 

310.90 

318.65 

326.50 

334-55 

342.75 

351-10 

359-65 

368.40 

377-3° 

250 

260 
270 

386.35 
487-35 
608.75 

395-60 

498.55 
622.10 

405.05 
509.90 
635-70 

414.65 
649.50 

42445 
533-35 
663-55 

434-45 
545-35 
677-85 

444.65 
557-6o 
692.40 

455-0° 
570-05 
707.15 

465.60 
582.70 
722.15 

476.35 
595-60 

737-45 

(g)  MERCURY. 

270 

280 
290 

123.92 

157-35 
198.04 

1  26.97 
161.07 
202.53 

130.08 
164.86 
207.10 

133-26 
211.76 

136-50 
172.67 
216.50 

139.81 
176.79 
221.33 

143.18 
180.88 
226.25 

146.61 
185-05 
231-25 

150.12 
189.30 
236-34 

I53.70 
I93-63 
24I-53 

300 

246.81 

252.18 

257-6^5 

263.21 

268.87 

274.63 

280.48 

286.43 

292.49 

298.66 

3'° 
320 

304.93 
373-67 

311.30 
381.18 

388.81 

324.37 
396.56 

404.43 

412.44 

344.81 
420.58 

428:83 

359-00 

437.22 

366.28 
445-75 

330 
340 

454.41 
548.64 

463.20 
558.87 

472.12 
569.25 

4X1.19 
57978 

490.40 
590-48 

499-74 
601.33 

509.22 
612.34 

518^85 
623.51 

528.63 
634-85 

646.36 

350 

658.03 

669.86 

681.86 

694.04 

706.40 

718.94 

73^65 

744-54 

757-6i 

770-87 

36o 

784-  3  i 

SMITHSONIAN  TABLES 


TABLE  182.  jgf 

VAPOR  PRESSURE  OF  SOLUTIONS  OF  SALTS  IN  WATER.* 

The  first  column  gives  the  chemical  formula  of  the  salt.  The  headings  of  the  other  columns  give  the  number  of 
gram-molecules  of  the  salt  in  a  liter  of  water.  The  numbers  in  these  columns  give  the  lowering  of  the  vapor 
pressure  produced  by  the  salt  at  the  temperature  of  boiling  water  under  76  centimeters  barometric  pressure. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

A12(S04)3    . 
AlCls  .... 

12.8 

22.5 

36.5 

61.0 

179.0 

318.0 

BaS2O6 

6.6 

15-4 

34-4 

Ba(OH)2     . 

12.3 

22.5 

39.0 

Ba(N03)2    . 

13-5 

27.0 

Ba(ClO3)2    . 

15.8 

33-3 

70.5 

1  08.2 

BaCl2  .... 

16.4 

36-7 

77.6 

BaBro  .         .       '  . 

16.8 

38-8 

91.4 

150.0 

204.7 

CaS208 

9-9 

23.0 

56.0 

1  06.0 

Ca(NO3)2    . 

16.4 

34-8 

74.6 

J39-3 

161.7 

205.4 

• 

CaCl2  .... 

17.0 

39-8 

95-3 

166.6 

241.5 

319.5 

CaBr2  .... 

17.7 

44-2 

105.8 

191.0 

283-3 

368.5 

CdS04 

4.1 

8.9 

18.1 

CdI2    .... 
CdBr2. 

7.6 
8.6 

$ 

HI 

52-7 
55-7 

80.0 

CdCl2. 

9.6 

18.8 

36-7 

57-0 

77-3 

99-o 

Cd(N03)2    . 

15-9 

36.1 

78.0 

122.2 

Cd(C103)2  .        .        .  < 

J7-5 

CoSO4 

5-5 

10.7 

22.9 

45-5 

CoCl2. 

15.0 

34-8 

83.0 

136.0 

186.4 

Co(N03)2    . 

'7-3 

39-2 

89.0 

152.0 

218.7 

282.0 

332-0 

FeSO4 

5-8 

10.7 

24.0 

42.4 

H8B08 

6.0 

12.3 

2C.I 

38.0 

51.0 

H3P04 

6.6 

14.0 

28.6 

45-2 

62.0 

81.5 

103.0 

146.9 

189.5 

H3AsO4 

7-3 

15.0 

30.2 

46.4 

64.9 

H2S04 

12.9 

26.5 

62.8 

104.0 

148.0 

198.4 

247.0 

343-2 

KH2PO4      . 

10.2 

JQ.C 

33-3 

47.8 

60.5 

73-1 

85.2 

KN03. 

10.3 

21.  1 

40.1 

57.6 

74-5 

88.2 

102.  1 

126.3 

148.0 

KC1O3 

10.6 

21.6 

42.8 

62.1 

80.0 

KBr03 

10.9 

22.4 

45-° 

KIISO4 

10.9 

21-9 

43-3 

65.3 

85.5 

107.8 

129.2 

170.0 

KNO2 

ii.  i 

22.8 

44-8 

67.0 

90.0 

110.5 

130.7 

167.0 

198.8 

KC104 

1  1.5 

22-3 

KC1     .... 

KHCO2       . 

12.2 
II.6 

24.4 
23.6 

48.8 
59-o 

74.1 
77-6 

100.9 

104.2 

128.5 
132.0 

I|2.2 

1  60.0 

210.0 

255.0 

KI 

12-5 

25-3 

52.2 

82.6 

1  1  2.2 

141-5 

I7I.8 

225-5 

278.5 

K2C2O4 

13-9 

28.3 

59.8 

94-2 

I3I.O 

K2W04       . 

33-o 

75-0 

123.8 

175-4 

226.4 

K2C03 

144 

31.0 

68.3 

105-5 

I52.O 

209.0 

258.5 

35°-0 

KOH  .... 

I5.0 

29-5 

64.0 

99-2 

140.0 

181.8 

223.0 

309.5 

387.8 

K2CrO4        . 

16.2 

29-5 

60.0 

LiNOs 

12.2 

25-9 

55-7 

88.9 

122.2 

I55-1 

188.0 

2534 

309.2 

LiCl     .... 

12.  1 

25-5 

95-0 

132.5 

175-5 

219.5 

311-  5 

393-5 

LiBr     .... 

12.2 

26.2 

60.0 

97.0 

I4O.O 

186.3 

241.5 

341-5 

438.0 

Li2S04 

I3-3 

28.1 

56.8 

89.0 

LiHSO4       . 

12.8 

27.0 

57-0 

93-o 

130.0 

1  68.0 

Lil 

Li2SiFl6       . 

I3.6 
15-4 

28.6 
34-0 

70.0 

105.2 
106.0 

'54-5 

206.0 

264.0 

357-o 

445-0 

LiOH  .... 

T5-9 

37-4 

78.1 

Li2CrO4 

16.4 

32.6 

74-o 

I2O.O 

171.0 

*  Compiled  from  a  table  by  Tammann,  "  Mem.  Ac.  St.  Petersb.''  35,  No.  9,  1887.     See  also  Referate,  "  Zeit.  f. 
Phys."  ch.  2,  42,  1886. 

SMITHSONIAN  TABLES. 


TABLE  182  (continued). 
VAPOR    PRESSURE    OF   SOLUTIONS   OF   SALTS    IN    WATER. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

Ms^SO4 

6.5 

12.0 

24-5 

47-5 

MgClo. 

1  6.8 

39-o 

100.5 

183-3 

277.0 

377-o 

Mg(NOs)2  • 

17.6 

42.0 

IOI.O 

174.8 

MgBr2 

17.9 

44-o 

115.8 

205.3 

298.5 

MgH2(S04)2        . 

18.3 

46.0 

116.0 

MnSO4 

6.0 

10.5 

2I.O 

MnCl2. 
NaH2PO4    . 
NaHSO4     . 

15.0 
10.5 
10.9 

34-0 

2O.O 
22.1 

76.0 

36.5 

47-3 

122.3 

167.0 
66.8 

100.2 

209.0 
82.0 
126.1 

96.5 
148.5 

126.7 
189.7 

157.1 
23oi 

XaX08 

10.6 

22-5 

46.2 

6b.i 

90-3 

111.5 

W-7 

167.8 

198.8 

NaClOg        .         /      . 

10.5 

23.0 

48.4 

73-5 

98.5 

I23-3 

147-5 

196.5 

223-5 

(XaPO8)«     . 

11.6 

NaOH          ... 

n.8 

22.8 

48.2 

77-3 

107-5 

I39-I 

1/2.5 

243-3 

314-0 

NaNOa 

1  1.6 

24.4 

50.0 

98.2 

122.5 

146.5 

189.0 

226.2 

Na2HPO4    . 

12.  1 

23-5 

43-o 

60.0 

78.7 

99.8 

122.  1 

XaHCOt     . 

12.9 

24.1 

48.2 

77-6 

IO2.2 

127.8 

I52.O 

198.0 

239-4 

Xa2SO4 

12.6 

25.0 

48.9 

74-2 

XaCl    .... 

12.3 

25.2 

52.1 

80.0 

III.O 

143.0 

176.5 

NaBrO3       . 

12.  1 

25.0 

54-i 

81.3 

108.8 

136.0 

NaBr   .... 

12.6 

25-9 

57-0 

89.2 

124.2 

159-5 

J97-5 

268.0 

Nal      . 

I2.I 

25.6 

60.2 

99-5 

136.7 

177-5 

22I.O 

301.5 

370.0 

Na4P2O? 

13.2 

22.0 

Na2CO8        . 

14-3 

27-3 

53-5 

80.2 

III.O 

Na2C2O4      . 

14-5 

3O.O 

65.8 

105.8 

146.0 

Xa2WO4      . 

14.8 

33-6 

71.6 

"5-7 

162.6 

Xa3P04        . 

I6.S 

3°.O 

52-5 

(NaP03)3    .         .         . 

I7.I 

36.5 

XH4X03     . 

12.8 

22.0 

42.1 

62.7 

82.9 

103.8 

I2I.O 

152.2 

180.0 

(NH4)2SiFl6 
NH4C1 

12.0 

25.0 

23-7 

44-5 

69-3 

94-2 

118.5 

138.2 

179.0 

213.8 

XH4HSO4  . 

ir-5 

22.O 

46.8 

71.0 

94-5 

118. 

139.0 

181.2 

218.0 

(XH4)2S04. 

II.O 

24.O 

46-5 

69-5 

93-o 

117.0 

I4I.8 

XH4Br 
NH4I  .... 

11.9 

12.9 

23-9 
25.1 

48.8 
49.8 

74.1 
78.5 

99-4 
104.5 

121.5 
I32-3 

145-5 
156.0 

190.2 

200.0 

228.5 
243-5 

NiSO4 

5-o 

IO.2 

21.5 

NiCl2  .... 

16.1 

37-o 

86.7 

147.0 

212.8 

Xi(N03)2    . 

16.1 

37-3 

156.2 

235-0 

Pb(N08)2    . 

12.3 

23-5 

45-o 

63.0 

SrfSO,),      .        .        . 

7.2 

20.3 

47.0 

03)2     .         .         . 

15.8 

31.0 

64.0 

97-4 

I3I-4 

SrCl2  .... 

1  6.8 

38.8 

91.4 

156.8 

223.3 

281.5 

Sri  Jr.,  .... 

17.8 

42.0 

IOI.I 

179.0 

267.0 

ZnS04 

4.9 

10.4 

21.5 

42.1 

66.2 

ZnCl  

9.2 

18.7 

46.2 

75-o 

107.0 

I53'° 

195.0 

/n<XO:J)2      .          .          .. 

16.6 

39-o 

93-5 

157.5 

223-8 

SMITHSONIAN   TABLES, 


TABLES  m-185.  ^3 

PRESSURE  OF  SATURATED  AQUEOUS  VAPOR. 

The  following  tables  for  the  pressure  of  saturated  aqueous  vapor  are  taken  princi- 
pally from  the  Fourth  Revised  Edition  (1918)  of  the  Smithsonian  Meteorological  Tables. 

TABLE  183.  — At  Low  Temperatures,  -  69°  to  0°  C  over  Ice. 


Temp. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

-60 

0.008 

0.007 

O.OO6 

0.005 

0.004 

0.004 

0.003 

0.003 

0.003 

O.OO2 

-50 

O.O2Q 

0.026 

0.023 

O.O2O 

0.017 

0.015 

0.013 

0.012 

O.OIO 

0.009 

-40 

0.096 

0.086 

0.076 

0.068 

O.o6o 

0.054 

0.048 

0.042 

0.037 

0-033 

-30 

0.288 

0.259 

0.233 

o.  209 

O.lSS 

0.169 

0.151 

0.135 

O.  121 

0.108 

-2O 

0.783 

0.712 

0.646 

0.585 

0.530 

0.480 

0-434 

0.392 

0-354 

0.319 

—  10 

1.964 

1.798 

1.644 

1-503 

1-373 

1.252 

1.  142 

1.041 

0-947 

0.861 

-    0 

4.580 

4.  2  2O 

3.887 

3-578 

3.291 

3-025 

2.778 

2.550 

2.340 

2.144 

TABLE  184.  —  At  Low  Temperatures,  -  16°  to  0°  C  over  Water. 


Temp. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

-10° 

2.144 

1.979 

1.826 

1.684 

I-55I 

1.429 

I-3I5 

— 

— 

— 

-   0° 

4-579 

4-255 

3-952 

3.669 

3-404 

3.158 

2.928 

2.712 

2.509 

2.321 

TABLE  185.  —  For  Temperatures  0°  to  374°  C  over  Water. 


Temp. 

.O 

.1 

.2 

•3 

•4 

•  5 

.6 

•  7 

.8 

-9 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

0° 

4.580 

4-614 

4.647 

4.681 

4-715 

4-750 

4.784 

4.819 

4.854 

4.889 

I 

4.924 

4.960 

4.996 

5-032 

5.068 

5-105 

5.I42 

5-J79 

5.  216 

5-254 

2 

5.291 

5-329 

5.368 

5.406 

5-445 

5.484 

5-523 

5.562 

5-6o2 

5-642 

3 

5.682 

5-723 

5-763 

5-804 

5.846 

5-887 

5-929 

5-971 

6.013 

6.056 

4 

6.098 

6.  141 

6.185 

6.228 

6.  272 

6.316 

6.361 

6.406 

6.450 

6.496 

5 

6.541 

6.587 

6-633 

6.680 

6.726 

6-773 

6.820 

6.868 

6.916 

6.964 

6 

7.012 

7.061 

7.IIO 

7-159 

7.209 

7-259 

7-309 

7.360 

7.410 

7.462 

7 

7.5I3 

7-565 

7-617 

7.669 

7.722 

7-775 

7.828 

7.882 

7.936 

7.991 

8 

8.045 

8.100 

8.156 

8.  211 

8.267 

8-324 

8.380 

8-437 

8.494 

8-552 

9 

8.610 

8.669 

8.727 

8.786 

8.846 

8.906 

8.966 

9.026 

9.087 

9.148 

10 

9.21 

9.27 

9-33 

9-40 

9.46 

9-52 

9-59 

9-65 

9-72 

9.78 

ii 

9-85 

9.91 

9.98 

IO.O4 

IO.  II 

10.18 

10.25 

10.31 

10.38 

10-45 

12 

10.52 

10.59 

10.66 

10.73 

10.  So 

10.87 

10.94 

1  1.  02 

II.O9 

ii.  16 

13 

ii.  24 

11.31 

11.38 

11.46 

ii-53 

ii.  61 

11.68 

ii.  76 

11.84 

11.92 

14 

11.99 

12.07 

12.15 

12.23 

12.31 

12.39 

12.47 

12-55 

12.63 

12.71 

15 

12.79 

12.88 

12.96 

13.04 

13-13 

13.21 

I3-30 

13-38 

13-47 

13-56 

16 

13-64 

13-73 

13.82 

I3-9I 

14.00 

14.08 

14.17 

14.  26 

I4.36 

14-45 

17 

14-54 

14.63 

14-73 

14.82 

14.91 

15.01 

15.10 

15.20 

I5.29 

15-39 

18 

15-49 

15-58 

15-68 

15.78 

15-88 

15.98 

16.08 

16.18 

16.28 

16.39 

19 

16.49 

16.59 

16.  70 

16.80 

16.91 

17.01 

17.12 

17.22 

17-33 

17-44 

20 

I7-SS 

17.66 

17.77 

17.88 

17.99 

18.10 

18.21 

18.32 

18.44 

18.55 

21 

18.66 

18.78 

18.90 

19.01 

19-  !3 

19-25 

19.36 

19.48 

19.60 

19.72 

22 

19.84 

19.96 

20.09 

2O.  21 

20.33 

20.46 

20.58 

20.71 

20.83 

20.96 

23 

21.09 

21.  22 

21.34 

21-47 

21  .60 

21.73 

21.87 

22.00 

22.13 

22.  26 

24 

22.40 

22-53 

22.67 

22.80 

22.94 

23-08 

23.22 

23-36 

23.50 

23-64 

25 

23.78 

23.92 

24.06 

24.21 

24-35 

24.50 

24.64 

24.79 

24-94 

25.09 

SMITHSONIAN  TABLES. 


184 


TABLE  185  (continued). 

PRESSURE  OF   SATURATED  AQUEOUS  VAPOR. 
TABLE  185.  —  For  Temperatures  0°  to  374°  C  over  Water. 


Tempera- 
ture. 

.0 

.1 

.  2 

•3 

•  4 

•  5 

.6 

-7 

.8 

•  9 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

mm 

25° 

23-78 

23.92 

24.06 

24.21 

24-35 

24-50 

24.64 

24.79 

24.94 

25.09 

26 

25-24 

25-38 

25-54 

25.69 

25-84 

25-99 

26.  14 

26.30 

26.46 

26.61 

27 

26.77 

26.92 

27.08 

27.24 

27.40 

27-56 

27.72 

27-89 

28.05 

28.22 

28 

28.38 

28.55 

28.71 

28.88 

29.05 

29.22 

29-39 

29-56 

29-73 

29.90 

29 

30.08 

30.25 

30-43 

30.60 

30.78 

30.96 

3I-I4 

31-32 

31-50 

31.68 

30 

31-86 

32.04 

32.23 

32.41 

32.60 

32.79 

32-97 

33-i6 

33-35 

33-54 

31 

33-74 

33-93 

34-12 

34-32 

34.51 

34-71 

34-91 

35-10 

35-30 

35-50 

32 

35.70 

35-91 

36.11 

36.32 

36.52 

36.73 

36.94 

37-14 

37-35 

37-56 

33 

37.78 

37-99 

38.20 

38.42 

38.63 

38.85 

39.06 

39-28 

39-50 

39-72 

34 

39-95 

40.17 

40-39 

40.62 

40.85 

41.07 

41-30 

41-53 

41.76 

41.99 

35 

42.23 

42.46 

42.70 

42-93 

43-17 

43-41 

43-65 

43-89 

44-13 

44-37 

36 

44.62 

44-86 

45-H 

45.36 

45.61 

45-86 

46.  n 

46-36 

46.62 

46.87 

37 

47-13 

47.38 

47.64 

47.90 

48.16 

48.43 

48.69 

48.95 

49-22 

49-49 

38 

49.76 

50.02 

50.30 

50.57 

50.84 

51-12 

51-39 

51-67 

5L95 

52.23 

39 

52.51 

52-79 

S3-o8 

53.36 

53-65 

53-94 

54-23 

54-52 

54.81 

55-10 

40 

55-40 

55.69 

55-99 

56.29 

56.59 

56-89 

57-19 

57-50 

57.80 

58.11 

58.42 

58.73 

59-04 

59-35 

59-66 

59.98 

60.30 

60.62 

60.94 

61.26 

42 

61.58 

61.90 

62.  23 

62.56 

62.89 

63-22 

63.55 

63.88 

64.  22 

64-55 

43 

64.89 

65-23 

65-57 

65.91 

66.26 

66.60 

66.95 

67-30 

67.64 

68.00 

44 

68.35 

68.70 

69.06 

69.42 

69.78 

70.14 

70.50 

70.87 

71.23 

71.60 

45 

71-97 

72.34 

72.71 

73-09 

73.46 

73.84 

74-22 

74.60 

74.98 

75.36 

46 

75-75 

76.14 

76.53 

76.92 

77-31 

77.70 

78.10 

78.50 

78.90 

79-30 

47 

79.70 

80.  i  i 

80.51 

80.92 

81.33 

81.74 

82.16 

82.57 

82.99 

83.41 

48 

83-83 

84.25 

84.68 

85.10 

85.53 

85-96 

86.39 

86.83 

87.26 

87.70 

49 

88.14 

88.58 

89.02 

89.47 

89.92 

90.36 

90.82 

91.27 

91.72 

92.18 

o. 

i. 

2. 

3- 

4- 

5- 

6. 

7- 

8. 

9- 

So 

92.6 

97-3 

102.  2 

107.3 

112.7 

118.2 

124.0 

130.0 

136.3 

142.8 

60 

149-6 

156.6 

164.0 

171.6 

179-5 

187.8 

196.3 

205.2 

214.4 

224.0 

70 

233-9 

244-2 

254-9 

266.0 

277-4 

289.3 

301.6 

314-4 

327-6 

341  •  2 

80 

00 

355-4 
526.0 

370.0 
546.3 

385.2 
567.2 

400.8 
588.8 

417.0 
611.  i 

433-7 
634-1 

45i-o 
657-8 

468.8 
682.2 

487-3 
707.4 

506.3 

733-3 

100 

760.0 

787.5 

815.9 

845.0 

875-1 

906.0 

937-8 

970.5 

IO04.  2 

1038.8 

no 

1074 

mi 

"49 

1187 

1227 

1268 

1310 

1353 

1397 

1442 

1  20 

1489 

1536 

1585 

1636 

1687 

1740 

1794 

1850 

1907 

1965 

130 

2025 

2086 

2149 

2214 

2280 

2347 

2416 

2487 

2559 

2633 

140 

2709 

2786 

2866 

2947 

3030 

3"5 

3201 

3290 

3381 

3473 

J50 
too 

3568 
4632 

3665 
4751 

3763 
4873 

3864 
4997 

3967 
5123 

4072 
5252 

4180 
5383 

4290 

4402 
5654 

5794 

170 

5936 

6080 

6228 

6378 

6532 

6688 

6847 

7009 

7174 

7342 

i  So 

75i3 

7688 

7865 

8046 

8230 

8417 

8608 

8802 

8999 

9200 

100 

9404 

9612 

9823 

10040 

10260 

10480 

10700 

10940 

III7O 

11410 

200 

11650 

11890 

12140 

12400 

12650 

12920 

13180 

13450 

13730 

14010 

2IO 

14290 

14580 

14870 

15160 

15470 

15770 

16080 

16400 

16720 

17040 

220 

17370 

17710 

18050 

18390 

18740 

19100 

19450 

19820 

20190 

20560 

230 

20950 

21330 

21720 

22120 

22520 

22930 

23350 

23770 

24190 

24620 

240 

25060 

25500 

25950 

26410 

26870 

27340 

27810 

28290 

28780 

29270 

250 

29770 

30280 

30790 

3I3IO 

31830 

32360 

32900 

33450 

34000 

34560 

260 

35130 

357oo 

36280 

36870 

37470 

38070 

38680 

39300 

39920 

40560 

270 

41200 

41840 

42500 

43160 

43840 

44520 

45200 

45900 

46600 

47320 

280 
290 

48040 
55710 

48760 
56530 

49500 
5736o 

50250 
58190 

51000 
59040 

51770 
59890 

52540 
60750 

53320 
61620 

54"0 
62510 

54910 
63400 

300 

64300 

65210 

66130 

67060 

68000 

68960 

69920 

70890 

71870 

72860 

73870 

74880 

75910 

76940 

77990 

79050 

80120 

81200 

82290 

83390 

320 

84500 

85630 

86760 

87910 

89070 

90250 

9H30 

92630 

93840 

95060 

330 

96200 

97530 

9879° 

100060 

101350 

102640 

103950 

105280 

106600 

108000 

340 

109300 

110700 

II2IOO 

"35oo 

114000 

116300 

117800 

119200 

120700 

122200 

350 

123700 

125200 

126800 

i  28300 

i  29900 

131400 

133000 

134600 

136300 

137900 

360 

139600 

141200 

142900 

144600 

146300 

148100 

149800 

i  5  i  600 

153400 

155200 

370 

157000 

158800 

160700 

162600 

164400 

SMITHSONIAN  TABLES. 


TABLES  186-188. 
TABLE  186.  —  Weight  in  Grams  of  a  Cubic  Meter  of  Saturated  Aqueous  Vapor. 


185 


Temp. 

0° 

8° 

9° 

—  20° 
—  10 

—  o 
+  o° 

+  10 

+  20 

+30 

0.894 
2.158 
4.847 

4.847 
9.401 
17-300 
30.371 

0.816 
1.983 
4.482 

S-IQ2 
10.015 
18.338 
32.052 

0.743 
1.820 
4.144 

5-559 
10.664 
19-430 
33-812 

0.677 
1.671 
3-828 

5-947 
11.348 
20.578 
35-656 

0.615 
I-53I 
3-534 

6.360 
12.070 
21.783 
37.583 

0.559 
1-403 
3-  261 

6.797 
12.832 
23.049 
39-599 

0.508 
1.284 
3.006 

7.261 
13.635 
24.378 
41  .  706 

0.461 
I    174 
2.770 

7-751 
14.482 
25-771 
43-908 

0.418 
1-073 
2-551 

8.271 
15-373 
27-234 
46.208 

0.378 
0.980 
2-347 

8.821 
16.311 
28.765 
48.609 

For  higher  temperatures,  see  Table  259. 

TABLE  187.  —  Weight  in  Grains  of  a  Cubic  Foot  of  Saturated  Aqueous  Vapor. 


Temp. 
°F. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

—  20° 

0.167 

0.158 

o.  150 

o.  141 

0.134 

0.126 

0.119 

0.  112 

0.106 

O.IOO 

—  10 

0.286 

0.272 

0.258 

0.244 

o.  232 

O.22O 

0.208 

0.197 

0.187 

o.  176 

—  o 

0.479 

0.455 

0.433 

0.411 

0.391 

0-371 

0-353 

0-335 

0.318 

0.302 

+  o° 

0.479 

0.503 

0.529 

0.556 

0.584 

0.6l3 

0.644 

0.676 

0.709 

0.744 

+  10 

0.780 

0.818 

0.858 

0.900 

0-943 

0.988 

1-035 

1.084 

1.  135 

1.189 

+  20 

1.244 

1.301 

1.362 

1.425 

1.490 

1.558 

1.629 

1-703 

1.779 

1.859 

+  30 

1.942 

2.028 

2.118 

2.  200 

2.286 

2-375 

2.466 

2.  560 

2.658 

2-759 

+  40 

2.863 

2.970 

3.082 

3.196 

3-315 

3-436 

3-563 

3  •  693 

3-828 

3-965 

+  50 

4.108 

4-255 

4.407 

4.564 

4-725 

4.891 

5.062 

5.238 

5.420 

5-607 

+  60 

5.800 

5-999 

6.203 

6.413 

6.630 

6.852 

7.082 

7-317 

7.560 

7.809 

+  70 

8.066 

8.329 

8.600 

8.879 

9.165 

9.460 

9.761 

10.072 

10.392 

10.720 

+  80 

11.056 

11.401 

11.756 

12.  121 

12.494 

12.878 

13-272 

13.676 

14.090 

14.515 

+  90 

14-951 

I5-400 

15-858 

16.328 

16.810 

17-305 

17.812 

18.330 

18.863 

19.407 

100° 

no 

19.966 

26.343 

20.538 
27.066 

21.123 
27.807 

21.723 
28.563 

22.337 
29-338 

22.966 
30.130 

23.611 
30.940 

24.271 

31.768 

24.946 
32.616 

25.636 
33-482 

Tables  are  abridged  from  Smithsonian  Meteorological  Tables,  fourth  revised  edition. 

TABLE  188.  —  Pressure  of  Aqueous  Vapor  in  the  Atmosphere. 

For  various  altitudes  (barometric  readings). 

The  first  column  gives  the  depression  of  the  wet-bulb  temperature  t\  below  the  air  temperature  t.  The  value  cor- 
responding to  the  barometric  height  at  the  altitude  of  observation  is  to  be  subtracted  from  the  vapor  pressure  corre- 
sponding to  the  wet-bulb  temperature  taken  from  Table  185.  The  temperature  corresponding  to  this  vapor  pressure 
taken  from  Table  185  is  the  dew  point.  The  wet  bulb  should  be  ventilated  about  3  meters  per  second.  For  sea-level 
use  Table  189.  Example:  /  =  35°,  h  =  30°,  barometer  74  cm.  Then  31.83  —  2.46  =  29.37  mm  =  aqueous  vapor 
pressure;  the  dew  point  is  28.6°  C. 

Abridged  from  Smithsonian  Meteorological  Tables,  1007. 


/  -h 
°C 

Barometric  pressure  in  centimeters. 

74 

72 

70 

68 

66 

64 

62 

60 

58 

56 

54 

52 

50 

48 

j0 

mm 
0.50 

mm 
0.48 

mm 
0.47 

mm 
0.46 

mm 
0.44 

mm 
0-43 

mm 
0.42 

mm 

0.40 

mm 
0.39 

mm 
0.38 

mm 
0.36 

mm 
0-35 

mm 
0.34 

mm 
0.32 

2 

0.98 

o.  96 

0.93 

0.90 

0.88 

0.85 

0.82 

0.80 

0-77 

0-75 

0.72 

0.69 

0.67 

0.64 

3 

1.47 

1-43 

1-39 

1-35 

1.32 

1.28 

1.24 

1.20 

1.  15 

I.  12 

i.  08 

i  .04 

I.  00 

0.96 

4 

1.97 

1.91 

1.86 

1.81 

1-75 

1.70 

1.65 

I.  60 

1-54 

i  49 

1.44 

1.38 

1-33 

1.28 

5 

2.46 

2-39 

2.32 

2.26 

2.19 

2.13 

2.06 

i  99 

1-93 

1.86 

i.  80 

1-73 

1.66 

i.  60 

6 

2.95 

2.87 

2-79 

2.71 

2.63 

2-55 

2-47 

2-39 

2.32 

2.24 

2.16 

2.08 

2.00 

1.92 

7 

3-45 

3-36 

3.26 

3-17 

3.o8 

2.99 

2.89 

2.8o 

2.71 

2.61 

2.52 

2-43 

2-33 

2.24 

8 

3-95 

3-84 

3-73 

3-63 

3-53 

3-42 

3-3i 

3-20 

3-  10 

2-99- 

2.88 

2.78 

2.67 

2.56 

9 

4-44 

4-32 

4.21 

4.09 

3-97 

3-85 

3-73 

3-6i 

3-49 

3-37 

3-25 

3-13 

3-00 

2.88 

10 

4-94 

4-81 

4.68 

4-54 

4.41 

4.28 

4.14 

4.01 

3-88 

3-74 

3-6i 

3.48 

3-34 

3-31 

II 

5-44 

5-30 

5-15 

5-00 

4.86 

4-71 

4-56 

4.42 

4.27 

4.12 

3-97 

3-83 

3-68 

3-53 

12 

5-94 

5-78 

5-62 

5.46 

5-30 

5-14 

4-98 

4.82 

4-66 

4-50 

4-34 

4.18 

4.02 

3-85 

13 

6-45 

6.27 

6.  10 

5-92 

5-75 

5-57 

5-40 

5-23 

5.05 

4.88 

4.70 

4-53 

4-36 

4.18 

14 

6-95 

6.76 

6.58 

6-39 

6.20 

6.01 

5-83 

5-64 

5-45 

5-26 

5-07 

4.88 

4.70 

4-Si 

15 

7.46 

7.26 

7.06 

6.85 

6.65 

6-45 

6-25 

6.05 

S.8s 

5.64 

5-44 

5-24 

5.04 

4-84 

16 

7.96 

7-75 

7-54 

7-32 

7.11 

6.89 

6.68 

6.46 

6.24 

6.03 

5-8i 

5.6o 

5-38 

5-17 

17 

8.47 

8.24 

8.02 

7-79 

7.56 

7-33 

7.10 

6.87 

6.64 

6.41 

6.18 

5-95 

5-72 

5.50 

SMITHSONIAN  TABLES. 


i86 


TABLE  189. 
PRESSURE  OF  AQUEOUS  VAPOR    IN   THE  ATMOSPHERE. 


This  table  gives  the  vapor  pressure  corresponding  to  various  values  of  the  difference  /  —  h  between  the  readings  of 
dry  and  wet  bulb  thermometers  and  the  temperature  li  of  the  wet  bulb  thermometer.  The  difference  t  —  t\  is  given 
by  two-degree  steps  in  the  top  line,  and  /i  by  degrees  in  the  first  column.  Temperatures  in  Centigrade  degrees,  vapor 
pressures  in  millimeters  of  mercury  are  used  throughout  the  table.  The  table  was  calculated  for  barometric  pressure 
B  equal  to  76  centimeters.  A  correction  is  given  for  each  centimeter  at  the  top  of  the  columns.  Ventilating  velocity 
of  wet  thermometer  about  3  meters  per  second. 


/I 

/  -/i 

=  o° 

2° 

4° 

6° 

8° 

10° 

12° 

14° 

16° 

18° 

20° 

Differ- 
ence 

for 

Corrections 
for  B  per  cm 

.013 

.026 

.040 

-053 

.066 

•079 

.092 

.106 

.119 

.132 

0.1°  in 
/  -h 

—  10 

.96 

0.97 

_ 

_ 

Example. 

0.050 

-  9 

.14 

I-I5 

.16 

— 

— 

0.050 

-  8 

•34 

1-35 

•35 

— 

— 

/  =  17.  2;  /i  =  10.0;  B  =  74.5  cm 

0.050 

—  7 

•55 

I-56 

.66 





t  -h  =  7.2 

0.050 

-  6 

•78 

•79 

— 

— 

From  table:  6.17  —  12  X  0.050  =  5.57 

0.050 

For  B,  1.5  X  .048                         =     .07 

-  5 

3-02 

2.03 

•  03 

0.03 

— 

Hence  p                                          =  5  .  64 

0.050 

—  4 

3.29 

2.29 

•  29 

0.29 

— 

0.050 

—  3 

3.58 

2.58 

.58 

0.58 

MM 

0.050 

—    2 

3.89 

2.89 

.89 

0.88 



— 



— 

— 

— 



0.050 

—  I 

4.22 

3-22 

.22 

I.  21 

0.21 

— 



— 

— 

— 



0.050 

o 

4.58 

3.58 

•  57 

1-57 

•  57 

— 



— 

— 

— 



0.050 

I 

4.92 

3-92 

.92 

1.91 

.91 

— 



— 

— 

— 



0.050 

2 

5.29 

4-29 

3-28 

2.27 

.27 

0.26 

MM 

— 

— 

— 

MM 

0.050 

3 

5-68 

4.68 

3-67 

2.66 

.66 

o.  65 



— 

—  • 

— 

. 

0.050 

4 

6.10 

5-09 

4.08 

3-07 

•  07 

i.  06 

0.05 

— 

— 

— 



0.050 

5 

6.54 

5-53 

4-52 

3-51 

•  51 

1.50 

0.49 

— 

— 

— 



0.050 

6 

7.01 

6.00 

4.99 

3.98 

•97 

1.96 

0-95 

— 

— 

— 



0.050 

7 

7-Si 

6.50 

5-49 

4.48 

3-47 

2.46 

1-45 

•  43 

— 

— 



0.050 

8 

8.04 

7-03 

6.  02 

S-oi 

4.00 

2.98 

1.97 

.96 

— 

— 

, 

0.050 

9 

8.61 

7.60 

6.58 

5-57 

4-56 

3-54 

2-53 

•52 

0.50 

— 



0.050 

10 

9.21 

8.20 

7.18 

6.17 

5-iS 

4.14 

3-12 

.11 

1.09 

0.08 



0.050 

ii 

9-85 

8.83 

7.8! 

6.80 

5-78 

4-77 

3-75 

.73 

1.72 

0.70 

—  — 

0.051 

12 

10.52 

9.50 

8.49 

7-47 

6.45 

5-44 

4.42 

3-40 

2.38 

1-37 

0.35 

0.051 

13 

11.24 

10.22 

9.20 

8.18 

7.16 

6.14 

5-13 

4.11 

3-09 

2.07 

1-05 

0.051 

14 

11.99 

10.97 

9-95 

8.93 

7.91 

6.90 

5-88 

4.86 

3.84 

2.82 

i.  80 

0.051 

15 
16 

12.79 
13.64 

11.77 
12.62 

10.75 
1  1.  60 

9-73 
10.58 

8.71 
9-96 

7-69 
8-53 

6.67 
7-Si 

5-65 
6.49 

4-63 
5-47 

3.6i 
4-45 

2.59 
.  3-43 

0.051 
0.051 

17 

U-54 

I3.52 

12.49 

11.47 

10.45 

9.42 

8.40 

7.38 

6.36 

5-33 

4-31 

0.051 

18 
19 

15-49 
16.49 

14.46 
15.46 

13-44 
14.44 

12.42 
13-41 

II-39 
12.39 

10.37 
11.36 

9-34 
10.34 

8.32 
9-31 

7-30 
8.29 

6.27 
7.26 

5-25 
6.24 

0.051 
0.051 

20 
21 

17-55 
18.66 

16.52 
17.64 

15.50 
16.61 

14.47 
15-58 

13-44 
14.56 

12.42 
13-53 

"•39 
12.50 

10.36 

11.47 

9-34 

10.45 

8.31 
9-42 

7.29 
8.39 

0.051 
0.051 

22 

19.84 

18.82 

17.79 

16.76 

15-73 

14.70 

13-67 

12.64 

11.62 

10.59 

10.57 

0.051 

23 

21.09 

20.06 

19-03 

18.00 

16.97 

15-94 

14.91 

13-88 

12.85 

11.82 

10.79 

0.051 

24 

22.40 

21.37 

20.34 

19-31 

18.27 

17.24 

16.21 

15.18 

14.15 

13-12 

12.09 

0.051 

25 

23-78 

22.75 

21.71 

20.68 

19.65 

18.62 

17.59 

16.56 

15-52 

14.49 

13.46 

0.052 

26 

25-24 

24.20 

23-17 

22.14 

21.10 

20.07 

19.04 

18.00 

16.97 

15-94 

14.90 

0.052 

27 

26.77 

25-73 

24.70 

23.66 

22.63 

21.60 

20.56 

I9-53 

18.49 

17.46 

16.42 

0.052 

28 

28.38 

27-34 

26.31 

25.27 

24.24 

23.20 

22.17 

21.13 

20.10 

19.06 

18.02 

0.052 

29 

30.08 

.29-04 

28.00 

26.97 

25-93 

24.89 

23.86 

22.82 

21.78 

20.75 

19.71 

0.052 

30 

31-86 

30.82 

29.78 

28.75 

27.71 

26.67 

25-63 

24.60 

23.56 

22.52 

21.48 

0.052 

31 
32 
33 

33-74 
35-70 
37.78 

32-70 
34-66 
36.73 

31.66 
33-62 
35-69 

30.62 
32.58 
34.65 

29.58 
31-54 
33-6l 

28.54 
30.50 
32.57 

27-50 
29.46 
31-53 

26.46 
28.42 
30.49 

25.42 
27.38 
29.44 

24.38 
26.34 
28.40 

23-34 
25-30 
27.36 

0.052 
0.052 
0.052 

34 

39-95 

38.00 

37-86 

36.82 

35.78 

34-73 

33-69 

32.65 

3I.6l 

30.57 

29.52 

0.052 

35 

42-23 

41.18 

40.14 

39-10 

38.05 

37-01 

35-97 

34.92 

33-88 

32.83 

31-79 

0.052 

36 

44.62 

43-57 

42.53 

41.48 

40.44 

39-40 

38.35 

37-31 

36.26 

35-22 

34-17 

0.052 

39 

47-13 
49.76 
52.51 

46.08 
48-71 
51.46 

45-04 
47-66 
50.41 

43-99 
46.61 
49-37 

42.94 

45-57 
48-32 

41.90 
44-52 
47.27 

40.85 
43-47 
46.22 

39.8i 
42.43 
45-17 

38.76 
41.38 
44.12 

37.71 
40.33 

43.08 

36.67 
39-29 
42.03 

0.052 
0.052 
0.052 

40 

55-40 

54-35 

53-30 

52.25 

51.20 

50.15 

49.10 

48.05 

47-00 

45.95 

44.00 

0.052 

SMITHSONIAN  TABLES. 


TABLE  190. 
RELATIVE  HUMIDITY. 


i87 


Vertical  argument  is  the  observed  vapor  pressure  which  may  be  computed  from  the  wet  and  dry- 
bulb  readings  through  Table  188  or  189.  The  horizontal  argument  is  the  ebserved  air  temperature 
(dry-bulb  reading).  Based  upon  Table  43,  p.  142,  Smithsonian  Meteorological  Tables,  3d  Revised 
Edition,  1907. 


Vapor 

Air  Temperatures, 

dry  bulb, 

0  Centigrade. 

mm. 

0°     —1° 

-2° 

—3° 

-4° 

—5°      —6° 

—7° 

-8o     -£ 

»o     -10°   -llo   _12o 

—13° 

-14 

>  _15o  _aoo 

0.25 

6       6 

6 

7 

8 

8       9 

IO 

II        12 

13   14  15 

17 

18 

2O       32 

050 

II         12 

n 

14 

iS 

17      18 

2O 

21        23 

25    28  .  30 

34 

37 

40       64 

0.75 

17      18 

21 

23 

25     27 

3° 

32     35 

38    42    46 

5° 

55 

00       96 

1.00 
1.25 
1.50 
1.75 

22        24 
27        30 

33     36 
38      42 

26 
32 

39 

45 

28 

35 
42 
49 

3° 

53 

33     36 

42     45 
50     54 
58     63 

40 

49 

§ 

42     47 

54     58 
64     70 

75     82 

51      56     61 
64    70    76 
76    84    92 

Eg     98 

6? 

84 

IOO 

74 
92 

80 
too 

2.00 

44     48 

S2 

56 

61 

66     72 

79 

86     93 

mm, 

0° 

-1° 

-2°     -»° 

2.25 

49      53 

S8 

63 

69 

75     81 

$9 

96       - 

2.50 
2.75 

55     59 
60     65 

65 

7i 

70 

77 

76 
84 

83     90 

91        ioo 

99 

3.50 
3.75 

77 
82 

83 
89 

90       98 

97       - 

3.00 

66     71 

78 

84 

92 

ioo         - 

- 

- 

4.00 

88 

95 

3.25 

71      77 

84 

91 

99 

_        _ 

— 

—       - 

4.25 

93 

IOO 

—       - 

3.50 

77      83 

9° 

98 

~          ~~ 

~ 

~~       ~ 

4.50 

99 

~ 

" 

Vapor 

Air  Temperatures, 

dry  bulb,  °  Centigrade. 

mm. 

0°      1°      2° 

3° 

40 

8o 

60        70        go 

9° 

10=    11= 

12°    13=    14°    18° 

16° 

17° 

Igo     190     20° 

0.5 

ii     10     9 

Q 

8 

8 

7      7      6 

6 

5      5 

5444 

4 

3 

333 

1.0 

22      2O      19 

18 

16 

15 

14      13      !3 

12 

II      IO 

10     9     8      8 

7 

7 

7      6     6 

1.5 

33    3i    28 

27 

2S 

23 

22     2O     19 

18 

16    15 

14    13    13    12 

ii 

IO 

10     9     9 

2.0 

44    4i    38 

35 

33 

29     27      25 

23 

22     2O 

19    18    17    16 

15 

14 

13      12      12 

2.5 

55    5i    47 

44 

38 

36    33    3i 

29 

27      26 

24      22      21      2O 

18 

17 

16    15    14 

3.0 

66    61    57 

S3 

49 

46 

43    40    38 

35 

33    3i 

29  27  25  24 

22 

21 

20    18    17 

3.5 
4.0 
4.5 
5.0 

77    71    66 
88    81    76 
99    92    85 
-     -    95 

62 
88 

74 
83 

61 

77 

50    47    44 
57    54    50 
65    60    56 
72    67    63 

47 

H 

38  36 

44    4i 
49    46 

55    5i 

34    3i    29    28 
38    36    34    32 
43    40    38    36 

48    45    42    39 

20 

3° 
33 
37 

24 
28 

31 

35 

23     21      2O 
26     2£     23 
29     28     26 

33    3i    29 

5.5 

_     _     _ 

97 

qi 

8s 

79    74    69 

64 

60    56 

53    49    46    43 

41 

38 

36    34    32 

6.0 

_     _     _ 

qq 

Q2 

86    80    75 

70 

66    6  1 

58    54    51    47 

44 

42 

39    37   34 

e*   e 

93    87    81 

76 

71     6? 

62    58    55    51 

48 

41: 

42    40    37 

7.0 
7.5 

-     -     - 

- 

_ 

ioo    94    85 
-   ,00    94 

82 
88 

77    72 
82    77 

67    63    59    55 
72    67    63    59 

52 

55 

49 

52 

46    43    40 
49    46    43 

8.0 

_ 

_ 

_ 

_ 

—       —    ioo 

94 

88    82 

77    72    67    63 

S9 

56 

52    49    46 

p  K 

OQ 

Q-7         87 

82     76     72     67 

63 

<;?    ?2    AQ 

Q  O 

yy 

98    g-> 

86    81    76    71 

67 

6^ 

cq     re     c.2 

Q  «? 

O7 

qT    85    80    75 

7O 

66 

62    c8    s  s 

inn 

06    qo    84.    7q 

74 

6n 

76 

y    67    6^ 

J.J..U 

So 

ST 

78    74    6q 

jL2.ll 

q6 

QO 

J.O.U 

O7 

91    86    So 

JL4.U 

•1  K  f\ 

Q7     Q"7     86 

98    g" 

JLo.U 
17.0 

q8 

SMITHSONIAN   TABLES. 


1 88 


TABLE   190     (continued). 
RELATIVE   HUMIDITY, 


Vapor 
Pressure 


Air  Temperatures,  dry  bulb,  °  Centigrade. 


80°     21°    82°    23°    24°    26°     26°    27°    28°     29°        30°     31°    32°    33°     34°    35°     36°    37°     383    39°     40C 


1 

2 

3 

4 

5 
6 

.  7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 


6  5 

12  II 

17  16 

23  22 

29  27 

34  3J 

40  38 

46  43 

52  49 


69  65 

75    ?o 
So    76 


55544443 
10  10  9  8  8  8  7  7 
15  14  14  13  12  ii  ii  10 
20  19  18  17  16  15  14  13 


33333322222 

66655554444 
10  9988776665 
13  12  ii  ii  10  10  9  9  8  8  7 


25  24 

31  29 

36  34 

41  38 

46  43 

5i  48 

56  53 

61  58 

66  62 

71  67 


23  21  20 

27  26  24 

32  30  28 

36  34  32 

41  38  36 

45  43  40 

50  47  44 

54  5i  48 

63  60  56 


19  18  17 

23  21  20 

26  25  24 

30  29  27 

34  32  30 

38  36  34 

42  39  37 

45  43  40 

49  46  44 

53  50  47 


16  15  14  13  13  12  ii  ii 

19  18  17  16  15  14  14  13 

22  21  20  19  l8  17  l6  15 

25  24  23  21  20  19  l8  17 

29  27  25  24  23  22  20  19 


86  8i  76  72  68  64  60  57 

92  87  82  77  72  68  64  60 

98  92  87  81  77  72  68  64 

-  97  92  86  81  77  72  68 

-  -  97  91  86  81  76  72 

-  -  -  96  90  85  80  76 

-  95  89  84  79 

-  --  -  -  ioo  94  88  83 
-----  98  92  87 
------  96  91 

-  ioo  94 
-------98 


53  50 

57  54 

61  57 

64  60 

68  64 

71  67 

75  7i 

78  74 

82  77 

85  81 

89  84 

93  87 

96  91 

ioo  94 


32  30  28  27 

35  33  31  29 

38  36  34  32 

4i  39  37  35 

44  42  40  37 

48  45  42  40 

51  48  45  43 

54  5r  48  45 

57  54  51  48 

60  57  54  51 

63  60  57  53 

67  63  59  56 

70  66  62  59 

73  69  65  62 

76  72  68  64 


25  24  23  21 

28  26  25  24 

30  29  27  26 

33  31  29  28 

35  33  32  30 

38  36  34  32 

4i  38  36  34 

43  41  38  36 

46  43  41  39 

48  45  43  4i 

51  48  45  43 

53  5°  48  45 

56  53  50  47 

58  55  S2  49 

61  57  54  51 


79  75  71  67  63  60  56  54 

83  78  74  70  66  62  59  56 

86  81  76  72  68  65  61  58 

89  84  79  75  71  67  63  60 

92  87  82  78  73  69  65  62 


10  10  9 

12  12  II 

14  13  J3 

16  15  15 

18  17  16 

20  19  18 

22  21  20 

24  23  22 

26  25  24 

28  27  26 

3°  29  27 

32  31  29 

34  33  31 

37  35  33 

39  36  35 

4i  38  36 

43  40  38 

45  42  40 

47  44  42 

49  46  44 

51  48  46 

53  50  47 

55  52  49 

57  54  5i 

59  56  53 


30  ---------  95  90  85  80  76  72  68  64  61  58  55 

31  ----------  98  93  88  83  78  74  70  66  63  60  56 

32  ----------  -  96  91  86  81  77  72  69  65  62 

33  -----_--__  -  99  93  88  84  79  75  71  67  63 

34  __---__-__  -  -  Q6  91  86  81  77  73  69  65  62 

35  ------  99  94  89  84  79  75  7*  67  64 

36  __________  -  -  -  96  91  86  81  77  73  69  66 

37  ---_----__  -  -  -  99  94  89  84  79  75  71  67 

38  ---_----__  -  -  -  -  96  91  86  81  77  73  69 

39  --------__  ____  99  93  88  83  79  75 

40  -___--____  _____969o868i7773 

41  _________  _____  98  93  88  83  79  75 

42  _________  _  _  _  _  _  I00  95  90  85  81  77 

43  -------___  ______  97  92  87  83  78 

---------  ______  99  94  89  84  80 

45  --_--__-__  _______  96  91  86  82 

46  -______•______  99  93  88  84 

47  _---______  ________  95  90  86 

48  ----------  ________  97  93  87 

__________  ________  99  94  89 

50  __----____  _________  96  91 

51  ---_____     __________  98  93 

52  -  „  95 

54 
55 


MITHSONIAN     TABLES. 


TABLES  190  (concluded),  jgj. 

TABLE  190  (concluded).— Relative  Humidity. 

(Data  from  20°  to  60°  C.  based  upon  Table  185). 


189 


Vapor 

Air  Temperatures, 

dry  bulb, 

0  Centigrade. 

Pressure. 

mm. 

40° 

41°     42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

60° 

51° 

52° 

53° 

54° 

66° 

56° 

67° 

58° 

59°    60° 

5 
10 

9 
18 

9     8 
17    16 

8 
15 

7 
15 

7 
14 

7 

6 
T3 

6 
12 

6 
II 

5 
ii 

5 

10 

5 
10 

5 
9 

4 
9 

I 

'3 

4 
8 

4 
7 

4     3 
7      7 

15 

27 

26    24 

23 

22 

21 

20 

18 

17 

16 

15 

15 

14 

*3 

12 

12 

ii 

10     10 

20 

36 

34    33 

31 

29 

28 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

15 

14    13 

25 

45 

43    4i 

39 

37 

35 

33 

31 

3° 

28 

27 

26 

24 

23 

22 

21 

20 

19 

1  8 

18    17 

30 
35 
40 

is4 

72 

51    49 
60    57 
68    65 

46 
g 

44 
5?- 

42 
49 
56 

40 
46 
53 

38 
44 
50 

36 
42 

48 

34 

40 

45 

43 

41 

29 
34 
39 

28 
33 
37 

27 

25 
3° 

34 

32 

23 

27 

31 

22 
26 
29 

21      20 
25     23 
28     27 

45 

8l 

77    73 

69 

66 

63 

59 

57 

54 

51 

49 

46 

44 

42 

40 

38 

36 

35 

33 

32   3° 

50 

90 

86    81 

77 

73 

70 

66 

63 

60 

57 

54 

51 

49 

47 

44 

42 

40 

38 

37 

35    33 

55 

99 

94    89 

85 

81 

76 

73 

69 

66 

62 

59 

57 

54 

5I 

49 

46 

44 

42 

40 

39    37 

60 

- 

-    98 

93 

88 

83 

Z9 

75 

72 

68 

65 

62 

60 

56 

53 

51 

48 

46 

44 

42    40 

65 

WJf\ 

— 

—     — 

IOO 

95 

90 

86 

82 

oo 

78 

o  . 

74 

Q_ 

67 

so 

61 

Ar 

55 

52 

50 

48 

46    43 

I\J 
75 

- 

-     - 

- 

- 

97 

92 
99 

oo 

94 

54 

90 

oO 

85 

76 

76 
81 

72 
77 

DO 

74 

65 

70 

67 

64 

£ 

58 

51 

55 

49    47 
53    50 

80 

- 

-     - 

- 

- 

- 

_ 

IOO 

96 

91 

86 

82 

78 

75 

7i 

68 

64 

62 

59 

56    54 

85 
90 

~ 

_     _ 

~ 

: 

— 

— 

: 

97 

92 
97 

87 
93 

84 
88 

79 
84 

11 

72 
76 

69 

73 

65 
69 

62 
66 

60    57 
63    60 

95 

- 

mm. 

67° 

58° 

59= 

60° 

_ 

_ 

_ 

98 

94 

89 

84 

80 

77 

73 

70 

67    64 

100 

- 

125 

96 

92 

88 

84 

- 

- 

- 

- 

98 

93 

89 

.85 

81 

77 

73 

70    67 

105 

- 

130 

IOO 

95 

91 

87 

_ 

_ 

_ 

_ 

_ 

_ 

98 

93 

89 

85 

81 

77 

74    70 

110 

— 

135 

— 

99 

95 

9° 

- 

- 

- 

- 

— 

— 

98 

93 

89 

85 

81 

77    74 

115 

- 

140 

- 

98 

94 

— 

— 

— 

- 

— 

— 

— 

97 

93 

88 

84 

81    77 

120 

_ 

145 

97 

92 

88 

84    80 

97 

125 

150 

96 

92 

88    84 

IOO 

TABLE  191.  — Relative  Humidity. 

This  table  gives  the  relative  humidity  direct  from  the  difference  between  the  reading  of  the  dry  (t°  C.)  and  the  wet 
(t!  °  C.)  thermometer.  It  is  computed  for  a  barometer  reading  of  76  cm.  The  wet  thermometer  should  be  ventilated 
about  3  meters  per  second.  From  manuscript  tables  computed  at  the  U.S.  Weather  Bureau. 


Depression  of  wet-bulb  thermometer,  t0-^0. 

t° 

0.2° 

0.4° 

0.6° 

0.8° 

1.0° 

1.2°  1.4°  1.6°  1.8°   2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.6° 

5.0°  6.6° 

-15 

90 

9i 

72 

62 

53 

44    35    25    16    7 

_ 

_ 

_ 

_ 

_ 

_    _ 

-12 

92 

85 

77 

69 

62 

54   47    39    32    25 

7 

— 

— 

- 

- 

-    — 

-9 

94 

88 

81 

75 

70 

62   56    50    44    39 

23 

9 

- 

- 

— 

-    — 

-6 
-3 

95 
96 

89 

85 
87 

80 
82 

74 
?8 

69    64    59    54    49 
74   69    66   61    57 

36 
46 

25 
36 

13 
26 

2 
17 

7 

~    ~ 

0 

96 

92 

89 

8S 

81 

78    74    71    67    64 

55 

46 

38 

29 

21 

13    6 

+3 

97 

94 

87 

84 

81    78    75    72    69 

62 

54 

46 

40 

32 

25   18 

0.5° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0G  3.5°  4.0°  4.5°   60° 

6.0° 

7.0° 

8.0° 

9.0° 

10.° 

11.°  12.° 

+3 

92 

84 

76 

69 

62 

54   46   40   32   25 

12 

_ 

_ 

_ 

_ 

_ 

+6 

94 

80 

73 

66 

60    54    47    41    35 

23 

1  1 

- 

- 

- 

- 

+9 

94 

88 

82 

76 

70 

65    59    53    48    42 

32 

22 

12 

3 

- 

-    - 

+  12 

94 

89 

84 

78 

73 

68   63   58   53   48 

38 

30 

21 

12 

4 

- 

+  15 

95 

90 

8S 

80 

?6 

71   66   62   58   53 

44 

36 

28 

20 

13 

4    - 

+  18 

95 

90 

86 

82 

78 

73    69   65    61    57 

49 

42 

35 

27 

20 

13    6 

+21 

96 

91 

87 

83 

79 

75    71    67   64    60 

53 

46 

39 

32 

26 

»9    13 

+  24 

96 

92 

88 

85 

81 

77    74    7°   66   63 

56 

49 

43 

37 

3T 

26     21 

+27 

96 

93 

90 

86 

82 

79    76    72   68   65 

59 

S3 

47 

4i 

36 

31     26 

+30 

0.6 

93 

90 

86 

82 

79    76    73    70   67 

61 

55 

44 

39 

35    3« 

+33 

96 

93 

90 

86 

83 

80   77    74    7i    68 

63 

57 

S2 

47 

42 

37    33 

+36 
+39 

97 
97 

93 
94 

90 

87 
88 

84 
85 

81    78    75    72    70 
82    79    76    74    71 

64 
66 

57 
61 

54 
56 

5° 
52 

45 
47 

4i    36 
43    39 

SMITHSONIAN   TABLES. 


TABLES  192-193. 
CORRECTION   FOR  TEMPERATURE  OF   EMERGENT   MERCURIAL 

THERMOMETER  THREAD- 

When  the  temperature  of  a  portion  of  a  thermometer  stem  with  its  mercury  thread  differs 
much  from  that  of  the  bulb,  a  correction  is  necessary  to  the  observed  temperature  unless  the 
instrument  has  been  calibrated  for  the  experimental  conditions.  This  stem  correction  is  pro- 
portional to  nft(T  -  /),  where  n  is  the  number  of  degrees  in  the  exposed  stem,  ft  the  apparent 
coefficient  of  expansion  of  mercury  in  the  glass,  T  the  measured  temperature,  and  /  the  mean 
temperature  of  the  exposed  stem.  For  temperatures  up  to  100°  C,  the  value  of  0  is  for  Jena 
i6i"  or  Greiner  and  Friedrich  resistance  glass,  0.000159,  for  Jena  59"',  0.000164,  and  when  of 
unknown  composition  it  is  best  to  use  a  value  of  about  0.000155.  The  formula  requires  a  knowl- 
edge of  the  temperature  of  the  emergent  stem.  This  may  be  approximated  in  one  of  three  ways: 

(1)  by  a  "fadenthermometer"  (see  Buckingham,  Bulletin  Bureau  of  Standards,  8,  p.  239,  1912); 

(2)  by  exploring  the  temperature  distribution  of  the  stem  and  calculating  its  mean  tempera- 
ture;  and  (3)  by  suspending  along  the  side  of,  or  attaching  to  the  stem,  a  single  thermometer. 
Table  192  is  taken  from  the  Smithsonian  Meteorological  Tables,  Tables  193-195  from  Rimbach, 
Z.  f.  Instrumentenkunde,  10,  p.  153,  1890,  and  apply  to  thermometers  of  Jena  or  resistance 
glass. 

TABLE  192.  —  Stem  Correction  for  Centigrade  Thermometers. 
Values  of  o.oooissn(T  —  f). 


(T-t). 

n 

10° 

20° 

30° 

40° 

S°° 

60° 

70° 

80° 

10°  C 

O.O2 

0.03 

0.05 

O.O6 

0.08 

0.09 

O.  II 

O.  12 

20 

0.03 

0.06 

0.09 

O.  12 

o.  16 

o.  19 

O.  22 

0.25 

30 

0.05 

0.09 

0.14 

o.  19 

0.23 

0.28 

0-33 

0-37 

40 

0.06 

O.  12 

o.  19 

0.25 

0.31 

0.37 

0-43 

0.50 

50 

0.08 

o.  16 

0.23 

0.31 

0-39 

0.46 

0-54 

O.62 

60 

O.O9 

o.  19 

0.28 

0-37 

0.46 

0.56 

0.65 

0.74 

70 

O.  II 

0.22 

0-33 

0-43 

0-54 

0.65 

o.  76 

0.87 

80 

O.  12 

0.25 

0-37 

0.50 

0.62 

0.74 

0.87 

0.99 

90 

O.I4 

0.28 

0.42 

0.56 

o.  70 

0.84 

0.98 

I.  12 

IOO 

o.  16 

0.31 

0.46 

O.62 

0.78 

o-93 

I.  08 

1.24 

TABLE  193.  — Stem  Correction  for  Thermometer  of  Jena  Glass  (0°  to  360°  C). 

Degree  length  0.9  to  i.i  mm;   /  =  the  observed  temperature;   t'  =  that  of  the  surrounding  air 
i  dm.  away;  n  =  the  length  of  the  exposed  thread. 


Correction  to  be  added  to  the  reading  /. 

n 

/-  /' 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220  ° 

10 

O.OI 

O.OI 

0.03 

0.04 

0.07 

O.  IO 

0.13 

0.17 

o.  19 

O.  21 

2O 

0.08 

O.  12 

o.  14 

o.  19 

0.25 

0.28 

0.32 

0.40 

0.49 

o-54 

30 

0.25 

0.28 

0.32 

0.36 

O.42 

0.48 

0-54 

0.66 

0.78 

0.87 

40 

0.30 

o-35 

0.41 

0.48 

O.6O 

0.67 

0.77 

0.92 

1.  08 

1.20 

50 

0.41 

0.46 

0.52 

o-59 

0.79 

0.89 

0.98 

1.16 

1.38 

i-53 

60 

0.52 

0.60 

0.68 

0.79 

0-99 

I.  II 

1.23 

1.46 

1.70 

1.87 

70 

0.63 

0.74 

0.85 

0.98 

I.  2O 

1.32 

1-45 

1.70 

1.99 

2.  21 

80 

0.75 

0.87 

I.OI 

i-i5 

1-38 

i-53 

1.70 

1.98 

2.29 

2-54 

90 

0.87 

0.99 

I.I3 

1.28 

1.62 

1.82 

1.94 

2.25 

2.60 

2.89 

IOO 

0.98 

I.  12 

1.29 

1.47 

1.82 

2.03 

2.  20 

2-55 

2.92 

3-24 

1  20 

— 



— 

1.88 

2.28 

2.49 

2.68 

3-i3 

3-59 

3-96 

140 

— 



— 

— 

2-75 

2.97 

3.22 

3-75 

4.24 

4-69 

160 

— 



— 

—  - 

3-35 

3-80 

4-35 

4.92 

5-45 

180 

— 



— 

— 

•  — 

4-37 

4-99 

5-63 

6,22 

200 

— 



— 

— 

— 

— 

5.68 

6-34 

6.98 

2  2O 

— 



— 

— 

— 

— 

— 

— 

7-05 

7.82 

1 



SMITHSONIAN  TABLES 


TABLES  194,  195. 
CORRECTION    FOR    TEMPERATURE    OF    MERCURY   IN    THERMOMETER 

STEM    (continued). 

TABLE  194.  -  Stem  Correction  lor  Thermometer  of  Jena  Glass  (0°-360°  0). 

Degree  length  i  to  1.6  mm.;  /=the  observed  temperature;   /=  that  of  the  surrounding  air 
one  dm.  away ;  ;/  =  the  length  of  the  exposed  thread. 


CORRECTION  TO  BE  ADDED  TO  THERMOMETER  READING.* 

t  —  V 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

n 

10° 

20 

O.O2 
O.I3 

0.03 
0.15 

0.05 
0.18 

0.07 

O.22 

O.I  I 

0.29 

0.17 
0.38 

O.2I 
0.46 

0.27 

0-33 
0.6  1 

0.38 
0.67 

10° 

20 

30 
40 

0.24 

°-35 

0.28 
0.41 

o-33 
0.48 

0-39 
0.56 

0.48 
0.68 

0-59 
0.82 

0.70 
0.94 

0.78 
1.04 

0.88 
1.16 

0.97 
1.28 

3° 
40 

50 

0.47 

0.53 

0.62 

0.72 

0.88 

1.03 

I.I7 

I.3, 

1.44 

i-59 

50 

60 

0-57 

0.66 

0.77 

0.89 

1.09 

1.25 

1.42 

1.58 

1.74 

1.90 

60 

70 

0.69 

0.79 

0.92 

1.  06 

1.30 

1.47 

1.67 

1.86 

2.04 

2.23 

70 

80 

0.80 

0.91 

1.05 

1.  21 

1.52 

1.71 

1.94 

2.15 

2-33 

2-55 

80 

90 

0.91 

1.04 

1.19 

1.38 

i-73 

1.96 

2.2O 

2.42 

2.64 

2.89 

90 

IOO 

1.02 

1.18 

1.56 

1.97 

2.18 

2-45 

2.70 

2.94 

3-23 

IOO 

IIO 

- 

- 

- 

I.78 

2.19 

2-43 

2.70 

2.98 

3.26 

3-57 

no 

120 

- 

- 

- 

I.98 

2-43 

2.69 

2-95 

3-26 

3-58 

3-92 

1  20 

130 

_ 

_ 

_ 

_ 

2.68 

2.94 

3-20 

3.56 

3.89 

4.28 

130 

140 

— 

— 

— 

— 

2.92 

3.22 

3-47 

3.86 

4.22 

4.64 

140 

I5° 

— 

— 

— 

- 

3-74 

4-15 

4-.S6 

5.01 

J5° 

160 

- 

— 

— 

— 

— 

— 

4.00 

4.46 

4.90 

5-39 

160 

170 

1  80 

- 

- 

- 

- 

- 

- 

4.27 
4-54 

4.76 
5-07 

5-24 
5-59 

5-77 
6.15 

170 

1  80 

190 
200 

- 

- 

- 

- 

- 

: 

5-70 

5-95 
6.30 

6.54 
6.94 

190 

200 

210 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

- 

6.68 

7-35 

210 

220 

7.04 

7-75 

220 

*  See  Hovestadt's  "  Jena  Glass"  (translated  by  J.  D.  and  A.  Everett)  for  data  on  changes  of  thermometer  zeros. 


TABLE  195.  —Stem  Correction  lor  a  so-called  Normal  Thermometer  of  Jena  Glass  (0°-100°  0). 

Divided  into  tenth  degrees ;  degree  length  about  4  mm. 


CORRECTION  TO  BE  ADDED  TO  THE  READING  f. 

t—  t' 

30° 

35° 

40° 

45° 

50° 

55° 

60° 

65° 

70° 

75° 

80° 

85° 

IO 
20 

0.04 

O.T2 

0.04 

0.12 

0.05 
0.13 

0.05 
0.14 

0.05 
0.15 

0.06 
0.16 

0.06 
0.17 

0.07 
0.18 

O.o8 
0.19 

0.09 

O.2O 

O.IO 
O.22 

O.IO 

0.23 

30 

O.2I 

0.22 

0.23 

0.24 

0.25 

0.25 

0.27 

0.29 

0.31 

0.33 

o-35 

0.37 

40 

£ 

70 

0.28 
0.36 
0-45 

O.29 
0.38 
0.48 

0.31 
0.40 
0.51 

o-33 
0.42 

o-53 

0-35 
0.44 

o-55 

0-37 
0.46 

0-57 
0.66 

0-39 
0.48 
0.60 
0.69 

0.41 
0.50 
0.03 
0.71 

0-43 

i& 

o-75 

0-45 

°-57 
0.69 
0.8  1 

0.48 

0.61 

0-73 
0.87 

0.51 

0.65 
0.78 

0.92 

80 
90 

_ 

_ 

— 

— 

_ 

_ 

0.76 

0.8  1 
0.92 

0.87 
0.99 

^ 

I.OO 

1.  06 

1.  20 

IOO 

_ 

1.  10 

1.18 

L_ 

1.34 

SMITHSONIAN  TABLES. 


IQ2 


TABLES  196-199. 
THERMOMETERS. 

TABLE  196.  — Oas  and  Mercury  Thermometers. 


If  /H,  /M,  'cos,  'i6,  «69,  'T,  are  temperatures  measured  with  the  hydrogen,  nitrogen,  carbonic  acid, 
lu>  59m>  and  "  verre  dur  "  (Tonnelot),  respectively,  then 

,H  _  /T  =  *~r^  E—  0-61859  +  0.004735  1./—  0.00001  1  577-'2]* 


[—0.33386+  0.0039910.^—  0.000016678.^]*. 
[—0.67039  -j-  0.0047351.  /  —  o.ooooi  1  577-'2]t 
—  0.31089  +  0.0047351-'  — 


*  Chappuis ;  Trav.  et  Mem.  du  Bur.  internal,  des  Poids  et  Mes.  6,  1888. 

t  Thiesen,  Scheel,  Sell;  Wiss.  Abh.  d.  Phys.  Techn.Reichanstalt,2, 1895;  Scheel;  Wied.  Ann.  58, 1896;  D.  Mech. 
Ztg.  1897. 

TABLE  197.   tH  -  tl6    ( Hydrogen -16m). 


0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 

.000° 

-.007° 

-OI3° 

—  .019° 

-025° 

-.031° 

—.036° 

—.042° 

—047° 

-.051° 

IO 

—.056 

-.061 

-.065 

—.069 

—.073 

—.077 

—.080 

—.084 

—.087 

—.090 

20 

—•093 

-.096 

-.098 

—  .101 

—.103 

-.105 

—.107 

—.109 

—  .no 

—.112 

3° 

—•"3 

—.114 

.115 

—.116 

—.117 

—.118 

—.119 

—  .119 

—.119 

—  .I2O 

40 

—.120 

—  .120 

.I2O 

—  .I2O 

—.119 

—.119 

—  .Il8 

—  .  1  1  8 

—.117 

.Il6 

g 

90 

—.103 
-.087 
—.058 
—.030 

—•"5 

—  .101 

—.081 
—  .056 
—.027 

—.114 
—.099 
—.078 

—•053 
—.024 

—•"3 
—.097 
—  .076 
—  .050 

—  .021 

—  .Ill 

-.096 
—.074 
—.048 
—.018 

—  .110 
—.094 
—.071 

—.045 
—.015 

—.109 
-.092 
-.069 
—.042 
—.012 

—.107 
—.090 
—.066 

—.039 
—  .009 

—.106 
-.087 
—  .064  ' 
—  .036 
—  .006 

—  .IO4 
-.085 
—  .O6l 

—•033 
—.003 

IOO 

.OOO 

TABLE  198.    tH  — 169    (Hydrogen- 59m). 


0° 

,o 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 

.000° 

-.003° 

—.006° 

—.009° 

—.011° 

-.014° 

—.016° 

—.018° 

—.020° 

—.022° 

IO 

20 

30 

—.024 

—•035 
—.038 

-.02| 
—  .036 
—•037 

—.027 
-036 

—.037 

—.028 
—•037 
—.037 

—  .030 
—•037 
—•037 

—.031 

-.037 
—  .036 

—.032 
—.038 
—.036 

—035 

—•034 
—.038 

—035 

—•035 
—.038 

—•034 

40 

—•034 

—•033 

—.032 

—.032 

—.031 

—  .030 

—  .029 

—.028 

—.028 

—.027 

50 

—.026 

—.025 

—  .024 

—.023 

—  .022 

—  .021 

—  .O2O 

—  .OI9 

—.Ol8 

—.017 

60 

—  .016 

—.015 

—.015 

—  .OI4 

—  .013    !   —  .OI2 

—.Oil 

—  .OIO 

—.009 

—.008 

70 

—.008 

—.007 

—.006 

—.005 

—.005 

—.004 

—.003 

—.003 

—  .002 

—  .OOI 

80 

—  .001 

—  .001 

.000 

.000 

+  .001 

+  .OOI 

+  .00  1 

+  .002 

+.002 

+  .002 

90 

+.002 

+  .002 

+  .002 

+  .OO2 

+  .002 

+  .002 

+  .OOI 

+  .001 

+  .001 

.000 

IOO 

.000 

TABLE  199.   (Hydrogen  - 161"),  (Hydrogen  —  69"1). 


-5° 

—  10° 

-15° 

—20° 

-25° 

-30° 

-35° 

ta  —  tie 
tH  —  t69 

+0.04° 

+0.02° 

+0.08° 
+0.04° 

+O.I3° 

+0.07° 

+  O.I9° 

+0.10° 

+0.25° 
+0.14° 

+0.32° 

+0.18° 

+0.40° 
+0.23° 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  2OO,  2O1 . 
AIR  AND   MERCURY  THERMOMETERS. 

TABLE  200.    IAIR  — t16.    (Air  —  IB™.) 


00. 

0° 

,o 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

O 

.000 

—.006 

—  .012 

—.017 

—  .022 

—.027 

-.032 

—.037 

—.041 

—.045 

IO 

^.049 

—  °53 

X 

—  .O6l 

-.065 

—.068 

—.071 

—.074 

—.077 

—.080 

20 

-.083 

—.086 

—.089 

—.091 

—.093 

—.095, 

—.097 

—.099 

—  .IOI 

—  .102 

3° 

—.103 

—.104 

—.105 

—.I06 

—.107 

—.I08 

—.109 

—  .IIO 

—  .IIO 

—  .110 

40 

—  .110 

—  .110 

—  .Ill 

—  .Ill 

—  .110 

—  .110 

—  .110 

—.109 

-'.109 

—.108 

5° 

—.107 

—.107 

—.106 

—.105 

—  .IO4 

—.103 

—  .102 

—  .101 

—.100 

—.098 

60 

-.096 

—  -°95 

—.093 

—.092 

—.090 

—.088 

—.086 

-.084 

—.082 

—.080 

70 

—.078 

—  .076 

—.074 

—.072 

—  .070 

-.067 

-.065 

—.062 

—  .060 

—057 

80 

—.054 

—.052 

—.049 

—.047 

—.044 

—  .041 

—•°39 

-.036 

—•034 

—.031 

90 

—.028 

—.025 

—.023 

—  .O2O 

—.017 

—.014 

—  .on 

—.009 

—.006 

—.003 

IOO 

.000 

+.003 

4-.oo6 

+.008 

+  .011 

+  .014 

+.017 

+.019 

+.022 

+  .025 

no 

+.028 

+.030 

+.033 

+  .035  |     +.038 

+  .041 

+.043 

+.046 

+  .048 

+  -O$O 

120 

+'°53 

+•055 

+•057 

-j_.o6o 

+.062 

+  .064 

+.066 

+.068 

+  .070 

+  .072 

130 

+.074 

+.076 

+.078 

+.080 

+.081 

+  .083 

+.084 

+.086 

+  .087 

140 
I50 

+.090 
+.098 

+.091 
+.098 

+.092 
+.098 

+•093 
+.099 

+.094 
+.099 

+  •095 
+  .099 

+.096 
+.098 

+.096 

+  .097 

+  .097 
+.097 

1  60 

170 

+.097 
+.084 

+•082 

+•095 
+.080 

+.094 
+.078 

+.093 
+.076 

+  .092 
+  •073 

+.090 
+.071 

+!o68 

+  .065 

+  .086 
+  .062 

180 

+.059 

+.055 

+.052 

+.048 

+.045 

+  .041 

+•037 

+•033 

+  .028 

+  .023 

190 

+.019 

+.014 

+.009 

+.004 

—  .OOI 

—.007 

—.013 

—  .019 

—.025 

—.031 

200 

—.038 

—.045 

—.051 

—.058 

—.066 

—.073 

—.080 

—.088 

-.096 

—  lOq 

2IO 

—  -"3 

—  .122 

—.130 

—•139 

—.148 

—  .158 

—.168 

—.177 

-.187 

-.198 

2  2O 

—.208 

—  .219 

—.230 

—.241 

—.252 

—  .264 

—•275 

-.287 

—.300 

—.312 

230 

—•325 

—  .338 

—'351 

-365 

-.378 

—•392 

—.407 

—.421 

—436 

—•450 

240 

—.466 

—  .481 

—•497 

—•529 

—•546 

-.562 

—579 

—•597 

—  .614 

250 

-.632 

—  .650 

—.668 

—  .687 

-.706 

—•725 

—745 

-.76; 

-.785 

-.805 

260 

—.825 

—.846 

-.867 

—.889 

—.911 

—•933 

—955 

—.978 

—  I.OOI 

—  I.O25 

270 

—  1.048 

—  I.O72 

—  1.096 

—  1.  121 

—  1.146 

—1.171 

—  1.196 

—  1.222 

—1.248 

—1.274 

280 

—1.301 

-I.328 

-1.356 

—1.384 

—1.412 

—1.440 

—1.469 

-1.498 

—  1.528 

-I.  q58 

290 

-1.588 

—  1.618 

—1.649 

-1.680 

—1.711 

—1-743 

—1.776 

—1.  808 

—1.841 

—1.874 

300 

-1.908 

Note:    See  Circular  8,  Bureau  of  Standards  relative  to  use  of  thermometers  and  the  various 
precautions  and  corrections. 

TABLE  201.    tAiR— tB9.    (Air— 69m.) 


°c. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

IOO 

.000 

.000 

.000 

.OOO 

.000 

.000 

.000 

.000 

.000 

.OOO 

no 

.000 

.000 

.000 

—  .OOI 

—  .OOI 

—  .001 

—  .001 

—  .001 

—  .OO2 

—  .OO2 

120 

130 

—  .002 

—.004 

—  .002 

—.004 

.002 

—  .005 

—  .OO2 
—.005 

—  .002 

—.006 

-.003 

—  .006 

—  .003  1  —  .003 

.006     ;     .007 

—.004 
—.007 

—  .004 
—.008 

140 

—.008 

—.008 

—  .009 

—.009 

—  .010 

—  .010 

—.Oil 

—  .Oil 

—  .012 

—  .OI2 

150 

—.013 

—.013 

—  .014 

—.015 

—  .016 

—  .016 

—.016 

—.017 

—.018 

—.019 

160 

—  .019 

—  .020 

—  .021 

—  .O2I 

—  .022 

—.023 

—.024 

—.025 

—  .026 

—.027 

170 

—.028 

—.029 

—.030 

—.031 

—.032 

—•033 

—.034 

—.035 

—•037 

—.038 

1  80 
190 

—•039 
—.052 

—.040 
—.053 

—  .041 

—•055 

-.043 
—  .056 

—.044 
—.057 

—•045 
—.059 

—  .046 

—.060 

-062 

—.049 
—.064 

—.051 
-.066 

200 

—.067 

SMITHSONIAN  TABLES. 


194 


TABLES   202-2O4. 


GAS,    MERCURY,    ALCOHOL,    TOLUOL,    PETROLETHER,    PENTANE, 

THERMOMETERS. 
TABLE  202.  —  t!i— tji  (Hydrogen-Mercury). 


Temper- 
ature, C. 

Thurincer 
Glass.* 

Verre  dur. 
Tounelot.t 

Resistance 
Glass.* 

English 
Crystal 
Glass.* 

Choisv-le- 
Roi.* 

I22m* 

Nitrogen 
Thermometer. 
TB—  TM.t 

CO2  Ther- 
mometer. 
TH-T0(vt 

o 

o 

0 

o 

0 

0 

c 

0 

o 

O 

.OOO 

.000 

.000 

.000 

.OOO 

.000 

.000 

.OOO 

IO 

—•075 

—.0^2 

—.066 

—.008 

—.007 

—.005 

—.006 

—.025 

20 

—  .085 

—.108 

—  .001 

—  .004 

—.006 

—  .010 

—.043 

3° 

—  .'56 

—.102 

—  -I31 

+.017 

+  .004 

—  .002 

—  .Oil 

—•054 

40 

—  .168 

—.107 

—  .140 

+•037 

+  .014 

+  .OO  I 

—  .Oil 

—•059 

£ 

—.166 
—.150 

—.103 
—.090 

—  '35 
—.119 

+•057 
+.073 

+  .025 
+  •033 

+  .004 
+  .008 

—.009 
—.005 

—•059 
—•°53 

70 

—.124 

—.072 

—.095 

+.079 

+  .037 

+  .009 

—  .OOI 

—.044 

80 

—.088 

—  .OCO 

—.068 

+  .070 

+  .032 

+  .007 

+  .OO2 

—.031 

90 

—.047 

-.026 

—.034 

+.046 

+  .022 

+  .006 

+  .003 

—.016 

100 

.000 

.000 

.000 

.000 

.000 

.000 

.OOO 

.000 

*  Schlosser,  Zt.  Instrkde.  ai,  1901. 


t  Chappuis,  Trav.  et  mem.  du  Bur.  Intern,  des  Poids  et  Mas.  6, 


TABLE  203.  —  Comparison  of  Air  and  High  Temperature  Mercury  Thermometers. 

Comparison  of  the  air  thermometer  with  the  high  temperature  mercury  thermometer,  filled  under 

pressure  and  made  of  59UI  glass. 


Air. 

59m. 

Air. 

59m. 

0 

o 

0 

0 

0 

0. 

375 

3854 

100 

100. 

400 

412.3 

200 

200.4 

425 

440.7 

300 

304.1 

450 

469.1 

325 
35° 

330.9 
358.1 

475 
500 

498.0 
527-8 

Mahlke,  Wied.  Ann.  1894. 


TABLE  204.  —  Comparison  of  Hydrogen  and  Other  Thermometers. 

Comparison  of  the  hydrogen  thermometer  with  the  toluol,  alcohol,  petrolether,  and  pentane  ther- 
mometers (verre  dur). 


Hydrogen. 

Toluol* 

Alcohol  I.* 

Alcohol  II.* 

Petrolether.t 

Pentane.J 

0 

o 

0 

o 

0 

o 

O 

0.00 

O.OO 

0.00 

_ 

O.OO 

—  IO 

—20 

-8.54 

—  16.90 

—9-31 
—  18.45 

—9.44 

—  18.71 

— 

—9-03 
—17.87 

—3° 

—  25.10 

—27.44 

-27.84 

— 

—26.55 

—40 

-50 

—  60 

—  33-  r  5 
—41.08 
—48.90 

—36.30 
—45-05 

—53-71 

-36.84 

—45-74 
—54-55 

—  42.6 

—35-04 
—43-36 

—  5r-5° 

—70 

-56.63 

—62.31 

—  63.31 

— 

—  59.46 

—  IOO 

— 

_ 

—80.2 

—82.28 

—150 

- 

_ 

_ 

—  1  13.0 

—116.87 

—200 

~ 

•™ 

—140.7 

—  146.84 

*  Chappuis,  Arch.  sc.  phys.  (3)  18,  1892.  t  Holborn,  Ann.  d.  Phys.  (4)  6,  1901.  I  Rothe,  unpublished. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  2O5-2O7. 

TABLE  205. — Platinum  Resistance  Thermometers. 

Callendar  has  shown  that  if  we  define  the  platinum  temperature,  pt,  by  pt  =  ioo<{  (R  —  R0) 
/(Rioo—  Ro)  }• ,  where  R  is  the  observed  resistance  at  t°  C.,  R0  that  at  O°,  R100  at  100°,  then  the  re- 
lation between  the  platinum  temperature  and  the  temperature  t  on  the  scale  of  the  gas  thermo- 
meter is  represented  by  t  —  pt  =  S-{  t/  100  —  i  }-t/ioo  where  8  is  a  constant  for  any  given  sample 
of  platinum  and  about  1.50  for  pure  platinum  (impure  platinum  having  higher  values).  This  holds 
good  between  —  23°  and  450°  when  5  has  been  determined  by  the  boiling  point  of  sulphur  (445°.) 

See  Waidner  and  Burgess,  Bui.  Bureau  Standards,  6,  p.  149,  1909.  Also  Bureau  reprints  124, 
143  and  149. 

TABLE  206. — Thermodynamic   Temperature   of  the  Ice  Point,   and  Seduction  to 
Thermodynamic  Scale. 

Mean  =  273.13°  C.  (ice  point). 

For  a  discussion  of  the  various  values  and  for  the  corrections  of  the  various  gas  thermometers  to 
the  thermodynamic  scale  see  Buckingham,  Bull.  Bureau  Standards,  3,  p.  237,  1907. 
Scale  Corrections  for  Gas  Thermometers. 


Temp. 

c°. 

Constant  pressure  =  100  cm. 

Constant  vol.,  p0  =  100  cm,  t0  =  O°C 

He 

H 

N 

He 

H 

N 

—  240° 

_ 

+  1.0 

.. 

+0.02 

+0.18 

_ 

—   200 

+0.11    . 

+    .26 

— 

+    .01 

+    .06 

— 

—    ICO 

-f  .04 

+    -03 

+0.40 

.OOO 

+    .OIO 

+0.06 

—    5° 

+     .OI2 

+    .02 

+    .12 

.000 

+    .004 

+    .02 

+    25             —  .003 

—    .003 

—   .020 

.000 

.OOO 

—    .006 

+     50 

—    -003 

—    -003 

—   -025 

.000 

.OOO 

.OO6 

+     75 

—    -003 

—   -003 

—   .017 

.000 

.OOO 

—    .OO4 

+  150 

-j-    200 

+    -007 

+    .01 

+    .01 
+    .02 

+    .04 
+    .11 

+  .000 
.000 

+    .001 
+    .002 

+    .01 

+  -04 

+  45° 

+0.04 

+  -5 

o.oo 

+O.OI 

+    .2 

+  1000 

+0.3 

+  1-7 

— 

— 

-f-  7 

+  15°° 

+3- 

+  1-3 

See  also  Appendix,  p.  438. 


TABLE  207.— Standard  Points  for  the  Calibration  of  Thermometers. 


Substance. 

Point. 

Atmos- 
phere. 

Crucible. 

Temperatures. 

Nitrogen  Scale. 

Thermodynamic. 

Water 
Naphthalene 
Benzophenone 
Cadmium 

boiling,  760  mm. 
melting  or  solidifv. 

air 
air 

graphite 

IOO.OO 
2  1  8.0 

305-85l 
320.8    - 

-O.I 
-O.2 

100.00 

218.0 

305-9 
320.9 

Zinc 

«        «<        (t    ' 

" 

" 

4I9-3    - 

r°-3 

419.4 

Sulphur 
Antimony 
Aluminum 

boiling,  760  mm. 
melting  or  solidify, 
solidification 

CO2 

graphite 

444-4  5  : 
629.8   - 
658.5    - 

-O.I 

Io.5 
-0.6 

444.55 
630.0 

658.7 

Silver 

Cold 

melting  or  solidify. 

(«                U               « 

" 

H 
it 

960.0   - 
1062.4   - 

-0.7 
1  0.8 

vJOltl 

t(          «         « 

H 

II 

1082.6   \ 

-0.8 

Copper 
Li2SiO8 

melting 

air 

platinum 

I20I.O    = 

-  I.O 

Diopside,  pure 
Nickel 

melting  or  solidify. 

H  and  N 

magnesia  and 
Mg.  aluminate 

I39I.2     - 

I  2.0 

Cobalt 

«        «i        « 

" 

magnesia 

1489.8     - 

-2.0 

Palladium 

«        <«        «< 

air 

" 

1549.2     - 

-  2.O 

Anorthite,  pure 

melting 

" 

platinum 

1549-5    ~ 

I  2.O 

Platinum 

1 

. 

••••^••B 



mOSOSSm 

:5-* 

••••M 

•••••••^•^••••^•i 

*  Thermoelectric   extrapolation,      t  Optical   extrapolation, 
m^v  anH  «Vi<iman    Journal  de  Physique,  1912.     Mesure  des  temperatures  elevees.)     A  few  additional  points 
are?H.boaS^-TS26°;  0 ^boils-ffioiCO,,  sublimes- 78.5°;  Hg.  freezes -38.87°;  Alumina  melts  2000°; 
Tungsten  melts  3400°. 

SMITHSONIAN  TABLES. 


196  TABLES  208-209. 

TABLE   208.  — Standard  Calibration  Curve  for  Pt  — Pt.  Rh.  (10%  Rh.)  Thermo-Element. 

Giving  the  temperature  for  every  100  microvolts.  For  use  in  conjunction  with  a  deviation  curve  determined  by  cali- 
bration of  the  particular  element  at  some  of  the  following  fixed  pornts: 


Water 

boiling-pt. 

IOO.O 

643mv 

Silver 

Naphthalene 

217-95 

1585 

Gold 

Tin 
Benzophenone 

melting-pt. 
boiling-pt. 

231.9 
305.9 

1706 
2365 

Copper 
LLSiO, 

Cadmium 

melting-pt. 

320.9 

2503 

Diopside 

Zinc 

"         ** 

419.4 

3430 

Nickel 

Sulphur 
Antimony 
Aluminum 

boiling-pt. 
melting-pt. 

444-55 
630.0 
658.7 

3672 
5530 
5827 

Palladium 
Platinum 

melting-pt. 


960.2 
1062.6 
1082.8 

1201. 

I3QI-5 

1452.6 

IS49-S 
1755- 


Qiumv. 
10296 
10534 
11941 
14230 
14973 

16144 
18608 


E 

0 

IOOO. 

2OOO. 

3000. 

4000. 

5000. 

6000. 

7000. 

8000. 

9000. 

E 

micro- 
volts. 

TEMPERATURES,    °C. 

micro- 
volts. 

0. 

ICO. 

0.0 

17.8 

147  -I 
159-7 

$1 

374-3 
384-9 

478.1 
488.3 

578.3 
588.1 

675.3 
684.8 

769.5 
778.8 

861.1 

870.1 

950-4 
959-2 

0. 
TOO. 

200.      ; 

34-5 

I72.I 

287.7 

395-4 

498.4 

597-9 

694-3 

788.0 

879.1 

968.0 

!    200. 

300. 

50.3 

184.3 

298.7 

405.9 

508.5 

607.7 

703-8 

797-2 

888.1 

976.7 

300. 

400. 

65.4 

196.3 

309-7 

416.3 

5l8.6 

617-4 

713-3 

806.4 

897.1 

985-4 

400. 

500. 

80.0 

208.1 

32O.6 

426.7 

528.6 

627.1 

722.7 

815-6 

906.1 

994-1 

500. 

600. 

94.1 

219.7 

331-5 

437-1 

538.6 

636.8 

732-1 

824.7 

915.0 

1002.8 

600. 

700. 

107.8 

231.2 

342.3 

447-4 

548.6 

646.5 

741-5 

833.8 

923-9 

1011.5 

700. 

800. 

121.  2 

242.7 

353-0 

457-7 

558.5 

656.1 

750.9 

842.9 

932.8 

I02O.I 

800. 

000. 

134-3 

254.1 

363-7 

467.9 

568.4 

665.7 

760.2 

852.0 

941.6 

1028.7 

900. 

IOOO.      i 

I47.I 

265.4 

374-3 

478.1 

578.3 

675-3 

769-5 

861.1 

950.4 

1037.3 

IOOO. 

E 

'      10000. 

I  IOOO. 

12000. 

13000. 

14000.     :     15000. 

16000. 

17000. 

18000. 

E 

micro- 
volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

0. 

1037.3 

II22.2 

1205.9 

1289.3 

1372.4 

1454-8 

1537-5 

1620.9 

1704.3 

0. 

100. 

1045-9 

II30.6 

1214.2 

1297-7 

1380.7 

1463-0 

1545-8 

1629.2 

1712.6 

100. 

200. 

i    1054-4 

II39-0 

1222.6 

1306.0 

1389-0 

1471.2 

I554-I 

1637.6 

1721.0 

200. 

300. 

1062.9 

II47-4 

1230.9 

I3I4-3 

1397-3 

1479.4 

1562.4 

1645.9 

1729.3 

300. 

400. 

1071.4 

II55.8 

1239-3 

1322.6 

1405-6 

1487-7 

1570.8 

1654-3 

1737.7 

400. 

500. 

!     1079-9 

1164.2 

1247-6 

1330-9 

1413-8 

1496.0 

I579-I 

1662.6 

1746.0 

500. 

000. 

j    1088.4 

II72.5 

1255-9 

1339-2 

1422,0 

1504-3 

1587-5 

1670.9 

1754.3 

600. 

700. 

1096.9 

Il8o.9 

1264.3 

1347-5 

1430.2 

1512.6 

1595-8 

i679-3 

700. 

800. 

1105.4 

II89.2 

1272.6 

1355-8 

1438.4 

1520.9 

1604.2 

1687.6 

800. 

900. 

i    1113-8 

II97-6 

I28l.O 

1364-1 

1446.6 

1529-2 

1612.5 

1696.0 

900. 

IOOO. 

II22.2 

1205-9 

1289.3 

1372-4 

1454.8 

1537-5 

1620.9 

1704.3 

IOOO. 

TABLE  209.  — Standard  Calibration  Curve  lor  Copper  —  Constantan  Thermo-Element. 

For  use  in  conjunction  with  a  deviation  curve  determined  by  the  calibration  of  the  particular  element  at  some  of  the 
following  fixed  points: 

Water,  boiling-point,  100°,  4276  microvolts;  Naphthalene,  boiling-point,  217.95,  10248 mv.;  Tin,  melting-point,  231.9, 
11009  mv.;  Benzophenone,  boiling-point,  305.9,  15203  mv.;  Cadmium,  melting-point,  320.9,  16083  mv. 


E. 

0 

IOOO. 

2OOO. 

3OOO. 

4OOO. 

5000. 

6000. 

7000. 

8000. 

9000. 

E 

micro-  1 
volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

0. 

0.00 

25.27 

49.20 

72.08 

94.07 

II5-3I 

135-91 

155-95 

175-50 

194-62 

0. 

100. 

2.60 

27.72 

51-53 

74-31 

96.23 

117.40 

137-94 

157-92 

177-43 

196.51 

100. 

200. 

5-17 

30.15 

53-85 

76.54 

98.38 

119.48 

139.96 

159.89 

179.36 

198.40 

200. 

300. 

7-73 

32-57 

56.16 

78.76 

100.52 

121.56 

141.98 

161.86 

181.28 

200.28 

300. 

400. 

10.28 

34.98 

58.46 

80.97 

102.66 

123.63 

143-99 

163.82 

183.20 

202.16 

400. 

500. 

12.81 

37.38 

60.76 

83.17 

104.79 

125.69 

146.00 

165.78 

185.11 

204.04 

500. 

600. 

15-33 

39-77 

63.04 

85-37 

106.91 

127-75 

148.00 

167.73 

187.02 

205.91 

600. 

700. 

17-83 

42.15 

65.31 

87.56 

109.02 

129.80 

150.00 

169.68 

188.93 

207.78 

700. 

800. 

20.32 

44-51 

67-58 

89.74 

III.  12 

131-84 

151-99 

171.62 

190.83 

209.64 

800. 

000. 

22.80 

46.86 

69.83 

91.91 

113.22 

133-88 

153-97 

I73-56 

192.73 

211.50 

900. 

IOOO. 

25-27 

49-20 

72.08 

94-07 

"5-31 

135-91 

155-95 

175-50 

194.62 

213-36 

IOOO. 

E 

IOOOO. 

I  IOOO. 

I200O. 

13000.     14000. 

15000. 

16000. 

17000. 

18000. 

E 

micro- 
volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

o. 

100. 

213-36 
215.21 

231-74 
233.56 

249.82 
25I.6l 

267.60     285.13 
269.36     286.87 

302.42 
304-14 

319-49 
321.19 

336.36 
338.04 

353-09 

0. 
100. 

2OO. 

217.06 

235.38 

253.40 

271.12     288.61 

305-85 

322.88 

339-72 

200. 

300. 

218.91 

237-20 

255.18 

272.88     290.35 

307-56 

324-57 

341.40 

300. 

400. 

220.75 

239-01 

256.96 

274.64     292.08 

309.27 

326.26 

343-07 

400. 

5oo. 

222.59 

240.82 

258.74 

276.40     293.81 

310.98 

327-95 

344-74 

500. 

600. 

224.43 

242.63 

260.52 

278.15     295-54 

312.69 

329-64 

346.41 

600. 

700. 
800. 

226.26 
•  228.09 

244-43 
246.23 

262.29 
264.06 

279.90     297.26 
281.65     298.98 

314-39 
316.09 

331-32 
333-00 

348.08 
349-75 

700. 
800. 

000. 

1  229.92 

248.03 

265.83 

283.39     300.70 

317-79 

334-68 

351.42 

,   000. 

IOOO. 

i  231.74 

249-82 

267.60 

285.13     302.42 

319-49 

330.36 

353-09 

I  IOOO. 

Cf.  Day  and  Sosman,  Am.  Jour.  Sci.  29,  p.  93,  32,  p.  51;  ;  ibid.  R.  B.  Sosman,  30,  p.  i. 
SMITHSONIAN  TABLES. 


TABLES  21O-213. 
MECHANICAL  EQUIVALENT  OF    HEAT. 

TABLE  210. — Summary  of  Older  Work. 


197 


Taken  from  J.  S.  Ames,  L'equivalent  mecanique  de  la  chaleur,  Rapports  presentes  au  congres 

international  du  physique,  Paris,  1900. 
Reduced  to  Gram-calorie  at  20°  C.     (Nitrogen  thermometer). 


Joule      .... 

4.i6o,X  i  o7  ergs. 

V 
4.169  Xio7  ergs. 

Rowland     .     .     . 

4.181        "      " 

4.181        "      " 

Griffiths      .     .     . 

4.192        «      « 

4.184       "      " 

Schuster-Gannon 

4.189        "      " 

4.181        "       " 

Callendar-Barnes 

4.186        "      " 

4.178       «     " 

*  Admitting  an  error  of  i  part  per  1000  in  the  electrical  scale. 

The  mean  of  the  last  four  then  gives 

1  gram  (20°  0)  calorie  =  4.181  X  107  ergs.    See  next  table, 
x  gram  (15°  C.)  calorie  =  4.185  X  io7  ergs  assuming  sp.  ht.  of  water  at  20°  =  0.9990. 

TABLE  211.— (1915.)       Best  Value,  Electrical  and  Mechanical  Equivalents  of  Heat. 

Since  the  preparation  of  Dr.  Ames'  Paris  report,  considerable  work  has  been  done  on  the  me- 
chanical equivalent  of  heat,  including  recomputations  from  the  older  measurements  using  better 
values  for  some  of  the  electrical  relations,  etc.  Taking  all  the  available  material  into  account  the 
U.S.  Bureau  of  Standards  has  adopted,  provisionally,  the  relation 

1  (20°  C.)  gram-calorie  =  4.183  international  electric  Joules. 

No  exact  comparison  between  the  results  of  electrical  equivalent  and  mechanical  equivalent  of 
heat  measurements  can  be  made  without  exact  knowledge  of  the  relations  between  the  interna- 
tional and  absolute  electrical  units.  A  recent  absolute  measurement  of  absolute  resistance  by  F. 
E.  Smith  of  the  National  Physical  Laboratory  of  England  indicates  a  difference  of  one  part  in  2000 
between  the  international  and  absolute  ohms.  Pending  the  general  acceptance  of  some  definite 
figure  for  this  relation  it  is  useless  to  fix  upon  a  single  value  to  use  for  "  J  "  better  than  about  one 
part  in  a  thousand.  The  value 

4-183  international  joules  =  probably  4.184  mechanical  loules. 
This  value  is  made  the  basis  of  the  following,  table. 

TABLE  212. — Conversion  Factors  for  Units  of  Work. 


Joules. 

Foot-pounds. 

Kilogram- 
meters. 

20° 

Calories. 

British  ther- 
mal units. 

Kilowatt-hour*. 

Joule  .     .     .     .  = 
Foot-pound      .  = 

iV 

o.7376t 
i 

O.IO2Ot 
0-1383 

0.2390 
0.3240* 

0.0000476 
0.001285* 

0.2778X10-' 
0.3766X10-'* 

Kilogram-meter  = 
20°  Calorie  .     .  = 

9.807* 
4.184 

7-233 
3-o86t 

I 
0.4267  t 

2-344* 
I 

0.009293* 
0.003965 

2.724X10-'* 
I.I62XIO-' 

British  thermal 

unit      .    .     .  = 

I055- 

778.3! 

1  07.6! 

252.2 

I 

0.0002931 

i  Kilowatt-hour  .  = 

3  600  ooo. 

2  655  OOO.f 

367  loo.t 

860300. 

34". 

I 

The  value  used  for  g  is  the  standard  value,  980.665  cm.  per  sec.  per  sec. =32-174  feet  per  sec.  per  sec. 
*The  values  thus  marked  vary  directly  with  "  g." 
tThe  values  thus  marked  vary  inversely  with  "  g."    For  values  of     g     see  Tables  565-567. 

TABLE  213.— Value  of  the  English  and  American  Horsepower   (746  watts)  in  Local  Foot-pounds 
and   Kilogram-meters   per    Second   at   Various   Altitudes   and    Latitudes. 


Altitude, 

Kilogram-meters  per  second. 

Foot-pounds  per  second. 

Latitude. 

Latitude. 

o" 

30° 

45° 

60' 

90° 

0° 

30° 

45* 

60' 

90° 

o    km. 
1-5" 

3.0  " 

76.275 
76.297 
76.320 

76.175 
76.197 
76  .  22O 

76.074 
76.095 
76.119 

75-973 
75-995 
76.018 

75.873 
75.895 
75.918 

551-70 

551.86 
552-03 

550.97 
55i.i3 
55L30 

550.24 

550.41 
550.57 

549-52 
549-68 
549.85 

548.79 
548.95 
549-12 

SMITHSONIAN  TABLES. 


ing  TABLE  214. 

MELTING   POINTS  OF  THE  CHEMICAL   ELEMENTS- 

The  metals  in  heavier  type  are  often  used  as  standards. 

The  melting  points  are  reduced  as  far  as  possible  to  a  common  (thermodynamic)  temperature 
scale.  This  scale  is  defined  in  terms  of  Wien's  law,  with  Ca  taken  as  14,350,  and  on  which  the 
melting  point  of  platinum  is  1755°  C  (Nernst  and  Wartenburg,  1751;  Waidner  and  Burgess, 
1753;  Day  and  Sosman,  1755;  Holborn  and  Valentiner,  1770;  see  C.  R.  148,  p.  1177,  1909). 
Above  1100°  C,  the  temperatures  are  expressed  to  the  nearest  5°  C.  Temperatures  above  the 
platinum  point  may  be  uncertain  by  over  50°  C. 


Element. 

Melting 
point. 

Remarks. 

Element. 

Melting 
point. 
o°C 

Remarks. 

Aluminum 

658.7 

Most  samples 

Manganese.  . 

1230 

B  urgess-  Wallenberg. 

give  65  7  or  less 

Mercury.  .  .  . 

-38.87 

(Burgess). 

Molybdenum 

2535 

Mendenhall-Forsythe 

Antimony  . 

630.0 

Neodymium 

840? 

(Muthmann-  Weiss.) 

Neon  

-253? 

Argon  

-188 

Ramsay-Travers. 

Nickel  

1452 

Oay,    Sosman,    Bur- 

Arsenic. .  .  . 

850 

gess,  Wallenberg. 

Barium.  .  .  . 

850 

(Guntz.) 

Niobium.  .  .  . 

I7OO? 

Beryllium  .  . 

1280 

Nitrogen.  .  .  . 

—  211 

(Fischer-Alt.) 

Bismuth.  .  . 

271 

Adjusted. 

Osmium  .... 

About  2700 

(Waidner-B  urgess, 

unpublished.) 

Boron  

2200-2500? 

Oxygen  

-218 

Bromine.  .  . 

-7-3 

Palladium.  . 

1549  *  5 

(Waidner-B  urgess, 

Cadmium  .  . 

320.9 

Range:    320.7- 

Nernst-  Wartenburg, 

320.9 

Day  and  Sosman.) 

Caesium..  .  . 

26 

Range:     26.37- 

Calcium  .  .  . 

810 

25-3 
Adjusted. 

Phosphorus.  . 
Platinum.  .  . 

44.2 
J755  *  5 

See  Note. 

Carbon  .... 

(>3Soo) 

Sublimes. 

Potassium.  .  . 

62.3 

Cerium.  .  .  . 

640 

Praseodymium. 

940 

(Muthmann-  Weiss.) 

Chlorine.  .  . 

-101.5 

(Olszewski.) 

Radium  

700 

Rhodium  

J95o 

(Mendenhall-Inger- 

Chromium  . 

1615 

B  urgess-  Wai  ten- 

soll.) 

berg. 

Rubidium  .  .  . 

38 

Cobalt  

1480 

B  urgess-  Walten- 

Ruthenium.  . 

2450? 

berg. 

Samarium.  .  . 

1300-1400 

(Muthmann-  Weiss.) 

Scandium.  .  . 

? 

Copper.  .  .  . 

1083  *  3 

Mean,    Holborn- 

Selenium.  .  .  . 

217-220 

Day,         Day- 

Silicon  

1420 

Adjusted. 

Clement. 

Silver  

960.5 

Adjusted. 

Erbium  

Sodium  

97-5 

Fluorine.  .  . 

-223 

(Moissan-Dew- 

Strontium.  .  . 

Between  Ca  and  Ba? 

ar.) 

[S»    112.  8 

Various  Forms.     See 

Sulphur.  . 

j   Sit    119.  2 

Landolt-Bornstein. 

[S,-«io6.8 

Gallium  .  .  . 

30.1 

Germanium 

958 

Tantalum.  .  . 

2900 

Adjusted  from  Waid- 

Gold  

1063  .  o 

Adjusted. 

ner-Burgess  =  2910. 

Helium.  .  .  . 

<-27I 

Hydrogen.  . 

-259 

Tellurium.  .  . 

452 

Adjusted. 

Indium.  .  .  . 

155 

(Thiel.) 

Thallium.... 

302 

Iodine 

113     s 

R  H  n  CTP  *        T  T  1  T  T  v* 

T*Vi/-kWM     w 

7    AA7n  rrpnHnror 

•  A,5  •  o 

Ixcvllgc  .      112     1  1  j)  . 

A  11  Ori  urn  .  .  .  . 

^  I  7OO 

V.    \\  til  LLI1  UUI^. 

<Mo 

Iridium.  .  .  . 

2350? 

Tin  

231.9  ±  .2 

Iron  

1530 

Burgess-  Wai  ten- 

Titanium  .  .  . 
Tungsten  .  .  . 

1795 
3400 

i  urgess-  Wallenberg. 
Adjusted. 

berg. 

Krypton.  .  . 

-169 

(Ramsay.) 

Lanthanum 

810? 

(Muthmann- 

Uranium.  .  .  . 

<i8so 

Vloissan. 

Weiss.) 

Vanadium.  .  . 

1720 

J  urgess-  Wallenberg. 

Lead  

327  ^0.5 

Xenon  

-140 

iamsay. 

Ytterbium  .  . 

Yttrium  .... 

1490 

Lithium  .  .  . 

1  86 

(Kahlbaum.) 

Zinc  

419.4 

Magnesium 

651 

(Grube)    in    clay 

Zirconium.  .  . 

1700? 

"roost. 

crucibles,  635. 

SMITHSONIAN  TABLES. 


TABLE  215. 
BOILING-POINTS  OF  THE  CHEMICAL  ELEMENTS. 


I99 


Element. 

Range. 

Boiling- 
point. 

Observer;  Remarks. 

Aluminum 

0 

I800. 

Greenwood,  Ch.  News,  100,  1909. 

Antimony 

— 

1440. 

<»                                    «                        ft                      it                     << 

Argon 

- 

-I86.I 

Ramsay-Travers,  Z.  Phys.  Ch.  38,  1901. 

Arsenic 

449-450 

- 

Gray,  sublimes,  Conechy. 

>< 

>36o. 

Black,  sublimes,  Engel,  C.  R.  96.  1883. 

<< 

280-310 

- 

Yellow,  sublimes. 

Barium 

— 

— 

Boils  in  vacuo,  Guntz,  1903. 

Bismuth 

1420-1435 

1430. 

Barus,  1894;  Greenwood,  1.  c. 

Boron 

— 

— 

Volatilizes  without  melting  in  electric  arc. 

Bromine 

59-63              61  .  i 

Thorpe,  1880;  van  der  Plaats,  1886. 

Cadmium 

778. 

Berthelot,  1902. 

Caesium 

- 

670. 

Rufr-Johannsen. 

Carbon 

- 

3600. 

Conputed,  Violle,  C.  R.  120.  1895. 

" 

— 

— 

Volatilizes  without  melting  in  electric  oven. 

Moisson. 

Chlorine 

- 

-33-6 

Regnault,  1863. 

Chromium 

- 

2200. 

Greenwood,  Ch.  News,  100,  1909. 

Copper 

2100-2310 

2310. 

I.e. 

Fluorine 
Helium 

— 

-I87. 
-267. 

Moisson-Dewar,  C.  R.  136,  1903. 
Computed,  Tracers  Ch.  News,  86,  1902. 

Hydrogen 

—252.5-252.8 

—252.6 

Mean. 

Iodine 

>200. 

Iron 

_ 

2450. 

Greenwood,  1.  c. 

Krypton 

- 

•—151-7 

Ramsay,  Ch.  News,  87,  1903. 

Lead 

- 

I525- 

Greenwood,  1.  c. 

Lithium 

- 

1400. 

Ruff-Johannsen,  Ch.  Ber.  38,  1905. 

Magnesium 

— 

1  120. 

Greenwood,  1  c. 

Manganese 

- 

1900. 

"            " 

Mercury 

— 

357- 

Crafts;  Regnault. 

Molybdenum 

- 

3620. 

Langmuir,  Mackay,  Phys.  Rev.  1914. 

Neon 

— 

—239- 

Dewar,  1901. 

Nitrogen 

—195.7-194.4 

—IPS- 

Mean. 

Oxygen 

—  182.5-182.9 

—  182.7 

" 

Ozone 

- 

—119. 

Troost.  C.  R.  126,  1898. 

Phosphorus 

287-290 

288. 

Platinum 

- 

39io. 

Langmuir,  Mackay,  Phys.  Rev.  1914. 

Potassium 

667-757 

712. 

Perman;  Ruff-Johannsen. 

Rubidium 

696. 

Ruff-Johannsen. 

Selenium 

664-694 

690. 

Silver 

1955- 

Greenwood,  1.  c. 

Sodium 

742-757 

750. 

Perman  ;  Ruff-Johannsen. 

Sulphur 

444.7-445 

444-7 

Mean. 

Tellurium 

Deville-Troost,  C.  R.  91,  1880. 

Thallium 

_ 

1280. 

v.  Wartenberg,  25  Anorg.  Ch.  56,  1908 

Tin 

_ 

2270. 

Greenwood,  1.  c. 

Tungsten 

- 

5830. 

Langmuir.  Phys.  Rev.  1913. 

Xenon 

- 

—  109.1 

Ramsay,  Z.  Phys,  Ch.  44.  1903. 

Zinc 

916-942 

930. 

SMITHSONIAN  TABLES. 


200 


TABLES  216-218. 
TABLE  216.  —  Effect  of  Pressure  on  Melting  Point. 


Substance. 

Melting  point 
at  i  kg/sq.  cm 

Highest 
experimental 
pressure: 
kg/sq.  cm 

dt/dp 
at  i  kg/sq.  cm. 

At  (observed) 
for 
1000  kg/sq.  cm 

Reference 

F  

-38.85 
en.  7 

I2,OOO 
2,800 

O  .  005  I  I 
0.0136 

5-1* 
13-8 

I 
2 

\ 

' 
97.62 

I2,OOO 

0.00860 

+12.  3t 

4 

Bi                          .    . 

271.0 

I2,OOO 

-0.00342 

-3-  5t- 

4 

Sn  .  .  .           

231  .9 

2,000 

0.00317 

3-1? 

3 

Bi  
Cd  
Pb 

270.9 
320.9 
327.4 

2,OOO 
2,OOO 
2,OOO 

-0.00344 
o  .  00609 
0.00777 

-3-44 
6.09 

7-77 

3 
3 
3 

*  A  /  (observed)  for  10,000  kg/sq.  cm  is  50.8°. 

fNa  melts  at  177.5°  at  12,000  kg/cm2;    K  at  179-6°;  Bi  at  218.3°;    Pb  a 
obtains  melting  point  for  tungsten  as  follows:   i  atme,  3623°  K-    8,  3594;    18,  3572;  28,  3564. 
Phys.  Rev.  1917. 

References:  (i)  P.  W.  Bridgman,  Proc.  Am.  Acad.  47,  pp.  391-96,  416-19,  1911;  (2)  G. 
Tammann,  Kristallisieren  und  Schmelzen,  Leipzig,  1903,  pp.  98-99;  (3)  J.  Johnston  and 
L.  H.  Adams,  Am.  J.  Sci.  31,  p.  516,  1911;  (4)  P.  W.  Bridgman,  Phys.  Rev.  6,  i,  1915. 

A  large  number  of  organic  substances,  selected  on  account  of  their  low  melting  points,  have 
also  been  investigated:  by  Tammann,  loc.  cit.;  G.  A.  Hulett,  Z.  physik.  Chem.  28,  p.  629,  1899; 
F.  Korber,  ibid.,  82,  p.  45,  1913;  E.  A.  Block,  ibid.,  82,  p.  403,  1913;  Bridgman,  Phys.  Rev.  3, 
126,1914;  Pr.  Am.  Acad.  51,  55,  1915;  51,581,1916;  52,57,1916;  52,91,1916.  The  results 
for  water  are  given  in  the  following  table. 

TABLE  217. —  Effect  of  Pressure  on  the  Freezing  Point  of  Water  (Bridgman*). 


Pressure:  t 
kg/sq.  cm 

Freezing  point. 

Phases  in 

Equilibrium. 

I 

O.O 

Ice  I  —  liquid. 

I,OOO 

-8.8 

Ice  I  —  liquid. 

2,000 

—  20.  15 

Ice  I  —  liquid. 

2,115 

—  22.  O 

Ice  I  —  ice  III  — 

liquid  (triple  point). 

3,000 

—  18.40 

Ice  III  —  liquid. 

3,530 

-17.0 

Ice  III  —  ice  V  —  liquid  (triple  point). 

4,000 

-13-7 

Ice  V  —  liquid. 

6,000 

-  1.6 

Ice  V  —  liquid. 

6,380 

+  0.16 

IceV  —  iceVI- 

liquid  (triple  point). 

8,000 

12.8 

IceVI—  liquid. 

12,000 

37-9 

Ice  VI  —  liquid. 

16,000 

57-2 

Ice  VI  —  liquid. 

20,000 

73-6 

Ice  VI  —  liquid. 

*  P.  W.  Bridgman,  Proc.  Am.  Acad.  47,  pp.  441-558,  1912. 
t  i  atm.  -  i .  033  kg/sq.  cm. 

TABLE  218.  —  Effect  of  Pressure  on  Boiling  Point.  * 


Metal. 

Pressure. 

°C 

j  Metal. 

Pressure. 

°C 

Metal. 

Pressure. 

°C 

Bi 

10.  2  cm  Hg. 

1  200 

Ag 

26.3  cm  Hg. 

1780 

Pb 

20  .  6  cm  Hg. 

1410 

Bi 

25.7  cm  Hg. 

1310 

Cu 

10.0  cm  Hg. 

1980 

Pb 

6.3  atme. 

1870 

Bi 

6.3  atme. 

1740 

Cu 

25.7  cm  Hg. 

2180 

Pb 

11.7  atme. 

2100 

Bi 

11.7  atme. 

i95o 

Sn 

10.  i  cm  Hg. 

1970 

Zn 

11.7  atme. 

1230 

Bi 

16.5  atme. 

2060 

Sn 

26.  2  cm  Hg. 

2IOO 

Zn 

21.5  atme. 

1280 

Ag 

10.3  cm  Hg. 

1660 

Pb 

10.5  cm  Hg. 

1315 

Zn 

53  .  o  atme. 

1510 

*  Greenwood,  Pr.  Roy.  Soc.,  p.  483,  1910. 


SMITHSONIAN  TABLES. 


TABLE  219.  2OT 

DENSITIES  AND   MELTING   AND   BOILING   POINTS  OF   INORGANIC  COMPOUNDS- 


Substance. 

Chemical  formula. 

Density, 
about 

20°  C 

Melting 
point 
C 

Authority.  1 

Boiling 
point 

Pres- 
sure 
mm 

Authority.  1  1 

Aluminum  chloride  
nitrate  
oxide  
Ammonia  
Ammonium  nitrate  
sulphate  .  .  . 
phosphite.  . 
Antimony  trichloride.  .  . 
pentachloride 
Arsenic  trichloride  
Arsenic  hydride  

A1C13 
A1(N03)3  +  9H20 
A12O3 
NH3 
NH4NO3 
(NH4)2S04 
NH4H2P03 
SbCl3 
SbCl6 
AsCla 
AsH3 

4.00 

1.72 
1.77 

3-06 

2-35 
2.20 

190. 
72.8 

2050. 

-75- 
I65. 
140. 
123. 

73- 
3- 
-18. 
—  113  ^ 

2 
28 
3 

4 
5 

ii 
8 
6 

183.^ 
I34-* 

-33-5 

210.* 

150.* 
223. 

102. 
130.2 
—  CJ4.   g 

752 
76o 

76o 
68 
760 
760 

I 
7 

14 

23 
6 

Barium  chloride  
nitrate  .  . 

BaCl2 
Ba(NO3)2 

3-86 

^.  24 

960. 
C7C. 

ii 
24 

"       perchlorate  .... 
Bismuth  trichloride  .... 
Boric  acid  

Ba(C104)2 
BiCl3 
H3BO3 

4-56 
i  .46 

5°5- 
232-5 
185. 

10 

440. 

760 

— 

"     anhydride  
Borax  (sodium  borate).. 
Cadmium  chloride 

B203 
Na2B4O7 
CdCl2 

1.79 
2.36 

4O^ 

577- 
741- 
560. 

27 

2< 

ooo  =*= 

— 

Q 

"         nitrate  
Calcium  chloride  
chloride  .... 

Cd(NO3)2  +  4H2O 
CaCl2 
CaCl2  +  6H2O 

2.45 
2.26 

1.68 

59-5 
774-o 
29.  6 

2 

132. 

760 

4 

"        nitrate 

Ca(NO3)2 

2.36 

499- 

24 



, 



"        nitrate.   . 

Ca(NO3)2  +  4H2O 

1.82 

42  .3 

?6 

132.* 





11        oxide  

CaO 

2  .  7 

2570. 

28 





Carbon  tetrachloride  .  .  . 
trichloride  
"       monoxide  

ecu 

C2C16 
CO 

1-59 
1-63 

-24. 
184. 
—  207. 

22 

6 

76.7 

—  190. 

760 
760 

23 
6 

"       dioxide 

CO2 

i   ^6 

—  C7. 

7 

-80. 

subl. 

disulphide  .  .  . 

CS2 

i  26 

—  no. 

13 

46.  2 

760 



Chloric  (per)  acid  
Chlorine  dioxide  

HC104  +  H2O 
C1O2 

1.8* 

5°- 
-76. 

15 

3 

9-9 

731 

21 

Chrome  alum  

KCr(SO4)2  +  i2H2O 

i  83 

89. 

16 

nitrate  

Cr2(NO3)6  +  i8H2O 

37- 

2 

I7O. 

760 

2 

Chromium  oxide  
Cobalt  sulphate  
Cupric  chloride 

Cr203 
CoS04 
CuCl2 

5-04 
3-53 

•2      Q^ 

1990. 

97- 
498. 

28 

16 
9 

880.* 
* 

Cuprous  chloride  .... 

Cu2Cl2 

7    7 

421  . 

I  OOO  =*= 

760 

9 

Cupric  nitrate 

Cu(NO3)2  +  3H2O 

2    <X 

114.  5 

2 

170.* 

760 

2 

Hydrobromic  acid  
Hydrochloric  acid  
Hydrofluoric  acid  
Hydriodic  acid  
Hydrogen  peroxide  
phosphide  .  .  . 
sulphide  
Iron  chloride  

HBr 
HC1 
HF1 
HI 
H202 
PH3 
H2S 
FeCl3 

0.99 
r-s 

2.80 

-86.7 
-in.  3 
-92-3 
-51-3 

—  2. 
-132.5 

-86. 
301. 

3 
17 
6 

17 
18 
6 
3 

-68.7 

-83.1 
-36.7 

-35-7 
80.2 

-62. 

760 
755 
755 
760 

47 

17 
17 

2O 

'    nitrate  
"     sulphate  

Fe(N03)3  +  9H20 
FeSO4  +  yH2O 

1.68 
i  .90 

47.2 
64. 

2 

16 

-- 

- 

z 

Lead  chloride  .... 

PbCl2 

5  8 

500. 

9 

900  =*= 

760 

— 

metaphosphate  .  .  . 
Magnesium  chloride  
oxide  
nitrate  
sulphate  .  .  . 
Manganese  chloride.  .  .  . 
nitrate  ..... 
sulphate.  .  .  . 
Mercurous  chloride  
Mercuric  chloride  

Pb(P03)2 
MgCl2 
MgO 
Mg(N03)2  +  6H20 
MgS04  +  5H20 
MnCl2  +  4H2O 
Mn(N03)2  -f  6H20 
MnS04  +  sH20 
Hg2Cl2 
HgCl2 

2.18 
3-4 
1.46 
1.68 

2.01 
1.82 
2.09 
7.10 
5-42 

800. 
708. 
2800. 
90. 
150. 

87-5 
26. 

54- 

450  * 
282. 

9 

28 

2 

16 
19 

2 

16 

143- 

106. 
129. 

305- 

760 

760 
760 

2 

!Q 

2 

(i)  Friedel  and  Crafts;  (2)  Ordway;  (3)  Faraday;  (4)  Marchand;  (5)  Amat;  (b)  Olszweski;  (7)  Gibbs; 
(8)  Baskerville;  (9)  Carnelly;  (10)  Carnelly  and  O'Shea;  (n)  Ruff;  (13)  \VroblewskiandOlszewski;  (14)  Anschutz; 
(15)  Roscoe;  (16)  Tilden;  (17)  Ladenburg;  (18)  Staedel;  (19)  Clarke,  Const,  of  ^ature•,  (20)  Bruhl; 
(21)  Schacherl;  (22)  Tammann;  (23)  Thorpe;  (24)  Ramsay;  (25)  Lorenz;  (26)  Morgan;  (27)  Day; 
(28)  Kanolt.  *  Decomposes. 

SMITHSONIAN  TABLES. 


2O2  TABLE  219  (continued). 

DENSITIES  AND   MELTING   AND   BOILING    POINTS  OF   INORGANIC  COMPOUNDS- 


Substance. 

Chemical  formula. 

Density, 
about 

20°  C 

Melting 
point 

Authority.  1 

Boiling 

Pres- 
sure 
mm 

Authority.  1 

Nickel  carbonyl  .... 

NiC4O4 

I    32 

I 

47.° 

760 

nitrate  . 

Ni(NO3)2  4  6H2O 

2    OS 

56  7 

2 

136  7 

760 

2 

"      oxide  

NiO 

6  60 

"      sulphate  
Nitric  acid  
"      anhydride  
oxide  *  
peroxide  
Nitrous  anhydride  .  . 

NiSO4  4  7H2O 
HN03 
N206 
NO 
N204 
NoO3 

.98 
•52 
.64 
.27 

•49 

4S 

99- 
-42. 
30. 
-167. 
-9-6 
—  in  . 

3 
4 
5 

8 

7 

86. 
48. 
-153- 

21.6 

-2      C 

76o 
76o 
76o 
760 
760 

16 

9 
6 

oxide 

NoO 

—  IO2    A. 

8 

-89  8 

760 

g 

Phosphoric  acid  (ortho) 
Phosphorous  acid  

H3PO4 
H3PO3 

.88 
.65 

40  =»= 
72. 

Phosphorus  trichloride.  . 
oxychloride  .  . 
disulphide..  .  . 
pentasulphide 
sesquisulphide 
trisulphide  .  .  . 
Potassium  carbonate  .  .  . 
chlorate  . 

PC13 
POC13 
P3S6 
P2S5 
P4S3 
P2S3 
K2C03 
KC1O3 

.61 
.68 

2.00 

2.29 

2    34 

-in.  8 

297. 

275- 
168. 
290  ± 
909. 

3  S7 

10 

12 

I3 

14 

T  P 

76. 
108. 

522. 
400. 
490. 

76o 
76o 
760 
760 
76o 
760 

19 

25 

chromate  
cyanide  
perchlorate  .  .  . 
chloride  . 

K2Cr04 
KCN 
KC104 
KC1 

2.72 
1.52 
2.52 

975- 
red  h't 
610. 

17 
15 

410.  f 

760 



nitrate  
acid  phosphate 
acid  sulphate.  . 
Silver  chloride 

KNO3 
KH2P04 
KHSO4 
AeCl 

2.  10 

2-34 

2.35 

341- 

96. 

205. 

3 

400.  f 
dec. 

— 

nitrate 

45  L  • 

L5 

, 

perchlorate  
phosphate  
metaphosphate.  .  . 
sulphate  .  .  . 

AgC104 
Ag3P04 
AgP03 

•  60 

6.37 

486. 
849- 
482. 

18 

i5 



— 

Sodium  chloride  
hydroxide  
nitrate  
"       chlorate  . 

NaCl 
NaOH 
NaNO3 
NaClO3 

•  46 

2.17 

2.  I 
.2.  26 

800. 
3I5- 

~  .0 

ii 

27 

1005.  | 
1490. 

380.  f 

76o 



perchlorate  .... 
carbonate 

NaC104 
Na2CO3 

482. 

18 

t 

t 

— 

— 

carbonate  
phosphate  
metaphosphate  . 
pyrophosphate  . 
phosphite 

Na2CO3  4  ioH2O 
Na2HPO44  i2H2O 
NaP03 
Na4P207 
(H2NaPO3)2  4-5H2O 

!.46 

i-54 
2.48 

2-45 

34- 
38- 
617- 
970. 

3 

15 
30 

1 

— 

— 

sulphate  
sulphate  
hyposulphite.  .  . 
Sulphur  dioxide.  . 

Na2S04 
Na2SO4  4-  ioH2O 
Na2S203  +  5H20 
SOo 

2.67 
1.46 
i-73 

42  . 
884. 
32-38 
48.16 

ii 
17 

t 

— 

—  • 

Sulphuric  acid  
acid.. 

H2S04 
1  2H2SO4  +  H2O 

1-83 

10.4 

21 

338. 

760 

22 

acid  
acid  (pyro)..  . 
Sulphur  trioxide  
Tin.  stannic  chloride  .  .  . 
;     stannous  chloride.  . 
Zinc  chloride  
'    chloride  
;     nitrate  
'     sulphate  

H2S04  4  H20 
H2S207 
S03 
SnCl, 
SnCl2 
ZnCl2 
ZnCl2  4  3H20 
\0;),  46H2O 
XnSO,  4  7H20 

1.89 
1.91 

2.28 

2.91 
2.06 

2.  O2 

8-5 
35- 
16.8 

-33- 
250. 

365- 
6-5 
36.4 

So. 

22 

23 
24 
29 
26 

3 
3 

t 

44-9 
114. 
605. 
710. 

131- 

76o 
76o 
760 
760 

760 

., 

21)  %_w/ ( 

27)  Hevesy;"(28)  Retgers;  (29)  GriinauWV T.SO)' Richards  anTothers!' 

*  Under  pressure  138  mm  mercury,    f  Decomposes. 
SMITHSONIAN  TABLES. 


TABLE  220.  2O3 

DENSITIES,    MELTING-POINTS,    AND    BOILING-POINTS    OF    SOME 
ORGANIC  COMPOUNDS. 

N.B.  —  The  data  in  this  table  refer  only  to  normal  compounds. 


1 

Substance. 

Formula 

Temp. 

O  ("^ 

Den- 

sity. 

Melting- 
point 

Boiling-point. 

Authority. 

(a)  Paraffin  Series  :  CnH2n^_2. 

Methane*     . 

CH4 

-164. 

0.415 

-184. 

-I65. 

Olszewski,  Young. 

Ethanet  .... 

C2H6 

0 

.446 

—171.4 

—93- 

Ladenburg,      " 

Propane  .... 

C3H8 

0 

.536 

—195- 

—45- 

Young,  Hainlen. 

Butane     .... 

C4Hio 

o 

.60 

—135. 

i. 

Butlerow,  Young. 

Pentane  .... 

C5H12 

o 

•647 

—131. 

36.3 

Thorpe,  Young. 

Hexane   .... 

CeHi4 

17- 

.663 

—94- 

69. 

Schorlemmer. 

Heptane  .... 

C7Hie 

o 

.701 

—97. 

98.4 

Thorpe,  Young. 

Octane     .... 

C8H18 

o 

.719 

—56.6 

I25-5 

tt              <« 

Nonane   .... 

CoH-20 

0 

•733 

—  51- 

150. 

Krafft. 

Decane    .... 

CioH22 

o 

•745 

—  31- 

173- 

" 

Undecane    .     .     .     CnH24 

o 

•756 

-26. 

ii 

Dodecane     .     .     .     Ci2H2e 

0 

•765 

12. 

214. 

*< 

Tridecane    ...     Ci3H28 

o 

•771 

—6.' 

234- 

« 

Tetradecane     .     .     Ci4H30 

4. 

•775         5- 

252. 

U 

Pentadecane     .     . 

Ci5H32 

IO. 

.776        10. 

270. 

if 

Hexadecane 

C16H34 

18. 

•775 

18. 

287. 

" 

Heptadecane    .     .     Ci7H36 

22. 

•777 

22. 

3°3- 

M 

Octadecane       .     .     Ci8H38 

28.        .777 

28. 

u 

Nonadecane      .     . 

CigH4o 

32- 

•777 

32- 

33°- 

tl 

Eicosane  .... 

C2oH42 

37- 

•778 

37- 

I2I.§ 

« 

Heneicosane     .     . 

C2iH44 

40. 

•778 

40. 

« 

Docosane     .     .     . 

C22H46 

44- 

.778 

44- 

i36-5§ 

" 

Tricosane     .     .     . 

C23H48 

48. 

•779 

48. 

" 

Tetracosane      .     . 
Heptacosane    . 

C27H56 

£ 

•779 
.780 

£ 

f|f 

« 

Pentriacontane      .     C3iH64 

68. 

.781 

68 

I99-§ 

« 

Dicetyl    ....     C32H66 

70. 

.781 

70. 

2O5-§ 

« 

Penta-tria-contane 

C35H72 

75- 

.782 

75- 

33i4 

" 

(b)  Olefines,  or  the  Ethylene  Series  :  CnH2n. 

Ethylene      .     .     . 

C2H4 

_ 

0.610 

-169. 

—103. 

Wroblewski  or  Olszewski. 

Propylene    .     .     . 

C3H6 

- 

- 

—  180. 

—50.2 

Ladenburg,  Krugel. 

Butylene  .... 

C4H8 

—  13.5 

•635 

Sieben. 

Amylene      .     .     . 

- 

- 

36- 

Wagner  or  Saytzeff. 

Hexylene     .     .     . 

CeHj2 

0 

•7~6 

_ 

69. 

Wreden  or  Znatowicz. 

Heptylene   .     .     . 
Octylene  .... 
Nonylene     .     .     . 

C7H14 

19-5 

20. 

•703 
.722 
.767 

- 

I22.-I23- 

I4O.-I42. 

Morgan  or  Schorlemmer. 
Moslinger. 
Beilstein,  "  Org.  Chem." 

Decylene      .     .     . 

CjoH2o 

_ 

175- 

U                                 (i                           (4 

Undecylene      .     . 

CiiHgg 

20. 

•773 

196.-!  97. 

«                                «                           <« 

Doclecylene      .     . 

Ci2Ho4 

—  31- 

•795      —  31- 

2I2.-2I4. 

(t                                <«                           <« 

Tridecylene       .     . 

C13H2e 

T5- 

•774 

233- 

Bernthsen. 

Tetradecylene  .     . 

Ci4H28 

—  12. 

•794 

—12. 

1274          Krafft. 

Pentadecylene  .     . 

- 

.814 

_ 

247. 

Bernthsen. 

Hexadecylene  .     . 

Ci(;FI32 

4- 

.792 

4- 

1554 

Krafft,  Mendelejeff,  etc. 

Octadecylene   .     . 

Ci8H3e 

18. 

.791 

18. 

1794          Krafft. 

Eicosylene  .     .     . 

C2oH40 

o 

.871 

- 

390-400. 

Beilstein,  "Org.  Chem." 

Cerotene      .     .     . 

C27Hs4 

— 

58. 

— 

Bernthsen. 

Melene    .... 

C3oHeo 

•  _ 

_ 

62. 

U 

— 

*  Liquid  at — n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 

t  "  +  4-°  "      "     46 

J  Boiling-point  under  15  mm.  pressure. 

§  In  vacuo. 


SMITHSONIAN  TABLES. 


2O4  TABLE  22O  (continued). 

DENSITIES,    MELTING-POINTS,    AND    BOILING-POINTS    OF    SOME 
ORGANIC    COMPOUNDS. 


Substance. 

Chemical 
formula. 

Temp. 
C". 

Specific 
gravity. 

Melting- 
point. 

Boiling- 
point. 

Authority. 

(c)  Acetylene  Series  :  CnH2M_2. 

Acetylene 

C>H.> 

—80. 

.613 

—  8l. 

-85. 

Villard. 

Allylene      
Ethylacetylene    .     .     . 

v_x  »2  *  i*2 

C3H4 
C4H6 

—  1  10. 

—130. 

-23.5 

+8. 

Bruylants,   Kutsche- 

roff,  and  others. 

Propylacetylene  .     .     . 

C6H8 

_ 

_ 

- 

48.-50. 

Bruylants,  Taworski. 

Butylacetylene     .     .     . 
Oenanthylidene  . 

CeHio 

CyH^ 

_ 

_ 

"™ 

68.-70. 
loo.-ior. 

Taworski. 
Beilstein,    and    oth- 

ers. 

'  Caprylidene    .... 

C8Hi4 

0. 

0.771 

- 

I33--J34- 

Behal. 

Undecylidene  .... 

CnHao 

.- 

— 

2IO.-2I5- 

Bruylants. 

Dodecylidene       .     .     . 

CigHaa 

—  9- 

.810 

—  9- 

105.* 

Krafft. 

Tetradecylidene  . 
Hexadecylidene  .     .     . 

Ci4H26 
CieH3o 

+  6.5 

20. 

.806 
.804 

+  6-5 
20. 

160* 

a 
« 

Octadecylidene    .     .     . 

Ci8H34 

3°- 

.802 

30- 

184.* 

" 

(d)  Monatomic  alcohols  :  C,zH2W_j_IOH. 

Methyl  alcohol    .     .     . 

CH3OH 

o. 

0.8  1  2 

—97- 

66. 

Ethyl  alcohol  .... 

C2H5OH 

0. 

.806 

-114. 

78. 

Propyl  alcohol     .     .     . 

C3H7OH 

o. 

.817 

-127. 

97- 

From  Zander,  "  Lieb. 

Butyl  alcohol  .... 

C4H9OH 

o. 

.823 

— 

117. 

Ann."  vol.  224,  p.  85, 

Amyl  alcohol  .... 

C6HUOH 

o. 

.829 

- 

138. 

and  Krafft,  "  Ber." 

Hexyl  alcohol      .     .     . 

C6H13OH 

0. 

•833 

— 

:57- 

vol.  16,  1714, 

Heptyl  alcohol    .     .     . 

C7H15OH 

o. 

.836 

l~36. 

176. 

"      19,  2221, 

(  )ctyl  alcohol  .... 

C8H17OH 

o. 

•839 

'—  18. 

J95- 

'      23,  2360, 

Nonyl  alcohol      .     .     . 

C9H19OH 

o. 

.842 

—  5- 

213. 

and  also  Wroblew- 

Decyl  alcohol      .     .     . 

CioHaiOH 

+  7- 

•839 

+  7- 

231. 

.  ski  and  Olszewski, 

Dodecyl  alcohol  .     .     . 

Ci2H25OH 

24. 

.831 

24. 

143* 

"  Monatshefte," 

Tetradecyl  alcohol  .     . 

Ci4H2gOH 

38- 

.824 

38- 

167* 

vol.  4,  p.  338. 

Hexadecyl  alcohol  .     .   CiCH33OH 

5°- 

.818 

5°- 

190.* 

Octadecyl  alcohol    .     .   Ci8H37OH 

59- 

.813 

59- 

211.* 

(e)  Alcoholic  ethers  :  CWH2JI+2O. 

Dimethyl  ether   .     .     . 

C2HCO 

_ 

_ 

_ 

-23.6 

Erlenmeyer,  Kreich- 

baumer. 

Diethyl  ether  .... 

C4H100 

4- 

Q-731 

—  117 

+  34-6 

Regnault,  Olszewski. 

Dipropyl  ether     .     .     . 

C6H140 

0. 

•763 

— 

90.7 

Zander  and  others. 

1  >i-iso-propyl  ether  .     . 

C6H140 

o. 

•743 

_ 

69. 

" 

Di-n-butyl  ether  .     .     . 

C8H180 

0. 

.784 

- 

141. 

Lieben,  Rossi,  and 

others. 

c-butvl  ether   .     . 

C8H180 

21. 

.756 

_ 

121. 

Kessel. 

I)i-iso-butyl      "        .     . 

C8H180 

T5- 

.762 

_ 

122. 

Reboul. 

I)i-iso-amyl      "        .     . 

CioHaaO 

0. 

•799 

- 

1  70.-I  75. 

Wurtz. 

Di-sec-hexyl     "        .     . 

C12H20O 

- 

- 

203--208. 

Erlenmeyer  and 

Wanklyn. 

I)i-norm-octyl  "       .     . 

C16H840 

17- 

.805 

- 

280.-282. 

Moslinger. 

(f)  Ethyl  ethers  :  CWH2W+2O. 

Ethyl-methyl  ether  .     . 

C8H80 

0. 

0.725 

_ 

II. 

Wurtz,  Williamson. 

"     propyl       •'       .     . 

<   r,H,,<> 

20. 

°-739 

_ 

63--64- 

Chancel,  Briihl. 

"     is<>-prnpyl  ether  . 

CCH,,0 

o. 

•745 

_ 

54- 

Markownikow. 

"     norm-butyl  ether 

C,H,;O 

o. 

.769 

_ 

92. 

Lieben,  Rossi. 

"     iso-butyl  ether     . 

CeHl40 

— 

•751 

— 

78.-8o. 

Wurtz. 

"     iso-amyl  ether 

C7Hi6O 

18. 

.764 

_ 

112. 

Williamson  and 

others. 

"     norm-hexyl  ether 
"     norm-heptyl  ether 

C8H180 
CfHsoO 

1  6. 

.790 

- 

'34--I37- 
165. 

Lieben,  Janeczek. 
Cross. 

"     norm-octy!  ether 

*  ji»I  I'jsO 

17- 

•794 

— 

1  82.-!  84. 

Moslinger. 

*  Boiling»pofat  (inder  15  mm.  pressure. 

t  Liquid  at  — n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 


SMITHSONIAN  TABLES. 


205 


TABLE  220  (concluded). 

DENSITIES    AND    MELTING    AND    BOILING    POINTS    OF   SOME    ORGANIC    COMPOUNDS. 

(g)   MISCELLANEOUS. 


Substance 

Chemical  formula. 

Density  and 
temperature. 

Melting 
point  C 

BoilinR 
point  C 

Authority. 

Acetic  acid  

CH3COOH 

1.115           o° 

I6.7 

118.5 

Young,  '09 

Acetone  

CH3COCH3 

0.812          o 

-94.6 

56.1 

Aldehyde  

C2H4O 

0.806          o 

—  I2O. 

+20.  8 

Aniline  

CeHsNH, 

i  .  038          o 

-8. 

183.9 

Beeswax  

0.96  =fc 

62. 

Benzoic  acid  

C7H602 

I-2Q3          4 

121. 

249. 

Benzene 

C6H6 

o  870        20 

?    48 

80.2 

Richards 

Benzophenone  .  .  . 

(C6H5)2CO 

w  •  ^  /  V 

i  .  090        50 

O  •  T'*-' 

48- 

305-9 

Holborn- 

Henning 

Butter  

0.86-7 

7O  =*= 

Camphor  

C10H16O 

0.99          10 

ov 

176. 

209. 

Carbolic  acid  .... 

C6H5OH 

1  .  060           2  1 

43- 

182. 

Carbon  bisulphide 

CS2 

1.292          o 

-no. 

46.  2 

"       tetrachlor- 

ide    . 

CCL, 

1.582            21 

—  T.Q 

76   7 

Young 

Chlorbenzene  .... 

C6H5C1 

I.  Ill            15 

O      ' 
-40. 

/  w  *    / 

132. 

V"""O 

Chloroform 

CHC13 

12^7               O 

-65 

61.2 

Cyanogen  .  .  . 

C2N2 

0  / 

0 
—  3<. 

—  21  . 

Ethyl  bromide  .  .  . 

C2H5Br 

i-45           15 

OO 

-117. 

38.4 

chloride  .  .  . 

CoH5Cl 

0.918          8 

-141  .6 

14- 

"      ether  

C4H100 

0.736          o 

-118. 

34-6 

"      iodide  

C2H5I 

1-944        14 

— 

72. 

Formic  acid  

HCOOH 

i  .  242          o 

8.6 

100.8 

Gasolene  

0.68  ± 

— 

70-90 

Glucose  

CHO(HCOH)4CH2OH 

1-56 

146. 

— 

Glycerine  

C3H803 

i  .  269          o 

20. 

290. 

lodof  orm  

CHI3 

4.01          25 

119. 

— 

Lard  

29   ± 

— 

Methyl  chloride.  . 

CH3C1 

0.992     -24 

-103.6 

-24.1 

Methyl  iodide  

CH3I 

2.285        15 

-64. 

42.3 

Naphthalene  .... 

C6H4-C4H4 

1-152        15 

80. 

218. 

Holborn- 

Henning 

Nitrobenzene  .... 

C6H502N 

I.  212         7.5 

5- 

211. 

Nitroglycerine  .  .  . 

C3H5N309 

I.  60 



Olive  oil  

0.92 

20  =*= 

300  * 

Oxalic  acid  

C2H204-2H20 

1.68 

I9O. 

1  Paraffin  wax,  soft. 

— 

38-52 

350-390 

"     hard 

— 

52-56 

390-430 

Pyrogallol  

C6H3(OH)3 

i  .  46         40 

133- 

293- 

Spermaceti  

o  o";          i^ 

45  =t 



Starch  

CeHioOs 

vo              o 
1.56 

none 



Sugar,  cane  

CwHaOu 

1.588           20 

160. 



Stearine  

(C1SH3502)3C3H6 

0.925           65 

7i- 



Tallow,  beef  

0.94              15 

27-38 



"       mutton  .  . 

0-94              15 

32-41 



Tartaric  acid  .... 

C4H606 

1-754 

170. 



Toluene  

CcHsCHs 

0.882        oo 

-92. 

110.31 

Richards 

Xylene  (o)  

C6H4(CH3)2 

0.863        20 

-28. 

142. 

"        (m)  

C6H4(CH3)2 

0.864        20 

54- 

140. 

"        (P).  

C6H4(CH3)2 

0.861        20 

J5- 

I38. 

SMITHSONIAN  TABLES- 


206 


TABLES  221-223.    MELTING-POINTS, 

TABLE  221.  —  Melting-point  of  Mixtures. 


Metals. 

Melting-points,  C°. 

Reference.  1 

Percentage  of  metal  in  second  column. 

o% 

10% 

30% 

30% 

40% 

50% 

60% 

70% 

80% 

90% 

100% 

Pb.  Sn. 

326 

295 

276 

262 

240 

220 

190 

I85 

200 

216 

232 

i 

Bi. 

322 

290 

— 

179 

'45 

126 

168 

205 

— 

268 

7 

Te. 

322 

710 

790 

880 

917 

760 

600 

480 

-410 

425 

446 

8 

Ag. 
Ni. 

328 

460 
360 

545 
420 

590 
400 

620 

370 

650 

330 

70S 
290 

775 
250 

840 
2OO 

90S 
130 

959 
96 

9 

Cu. 

326 

870 

920 

925 

945 

95° 

955 

985 

1005 

1020 

1084 

2 

Sb. 

326 

250 

275 

330 

395 

440 

490 

525 

560 

600 

632 

16 

Al.  Sb. 

650 

750 

840 

925 

945 

950 

970 

1000 

1040 

1010 

632 

17 

Cu. 

650 

630 

600 

560 

540 

580 

610 

755 

930 

1055 

1084 

18 

Au. 

655 

675 

740 

800 

855 

9'5 

970 

1025 

1055 

675 

1062 

10 

Ag. 

650 

625 

615 

600 

590 

58o 

575 

570 

650 

750 

954 

17 

Zn. 

654 

640 

620 

600 

580 

560 

530 

510 

475 

425 

419 

ii 

Fe. 

653 

860 

1015 

1  1  10 

"45 

"45 

1220 

1315 

1425 

1500 

'SIS 

3 

Sn. 

650 

645 

'  635 

625 

620 

605 

590 

57° 

54o 

232 

'7 

Sb.  Bi. 

632 

610 

590 

575 

555 

54° 

520 

470 

405 

330 

268 

16 

Ag. 

630 

595 

57° 

545 

520 

500 

505 

545 

680 

850 

959 

9 

Sn. 

622 

600 

570 

525 

480 

430 

395 

350 

310 

255 

232 

19 

Zn. 

632 

555 

S'o 

540 

570 

565 

540 

525 

S'o 

470 

419 

17 

Ni.  Sn. 

'455 

1380 

1290 

1200 

"35 

1290 

1305 

1230 

1060 

800 

232 

17 

Na.  Bi. 

96 

425 

520 

590 

645 

690 

720 

73° 

7'5 

570 

268 

13 

Cd. 

96 

125 

185 

245 

285 

325 

33° 

34° 

360 

390 

322 

13 

Cd.  Ag. 

322 

420 

520 

610 

700 

760 

805 

850 

895 

940 

954 

I7 

XI. 

321 

300 

285 

270 

262 

258 

245 

230 

210 

235 

302 

M 

Zn. 

322 

280 

270 

295 

3*3 

327 

34° 

355 

370 

390 

419 

ii 

Au.  Cu. 

1063 

910 

890 

895 

9°5 

925 

975 

IOOO 

IO25 

1060 

1084 

4 

Ag. 

1064 

1062 

1061 

1058 

1049 

1039 

1025 

1006 

982 

963 

5 

Pt 

1075 

1125 

1  100 

1250 

1320 

1380 

1455 

'53° 

1610 

1685 

1775 

20 

K.  Na. 

62 

'7-5 

—  IO 

—3-5 

5 

ii 

26 

41 

58 

77 

97-5 

15 

Sf 

Cu  Ni. 

62.5 
1080 

'33 
1180 

.65 

188 

205 

9° 
215 

I  IO 
220 

135 
240 

162 

280 

265 
305 

301 

13 

Ag! 

1082 

1035 

1240 

990 

1290 
945 

I32O 

910 

870 

830 

788 

814 

875 

I455 

96o 

*  7 
9 

Sn. 

1084 

1005 

890 

755 

725 

680 

630 

580 

53° 

440 

232 

12 

Zn. 

1084 

1040 

995 

930 

900 

880 

820 

780 

700 

580 

419 

6 

Ag.  Zn. 

959 

850 

755 

7°5 

690 

660 

630 

610 

57° 

505 

419 

1  1 

Sn. 

959 

870 

630 

55° 

495 

450 

420 

375 

300 

232 

9 

Na.  Hg. 

96.5 

90 

80 

70 

60 

45 

22 

55 

95 

215 

13 

1  Means,  Landolt-Bornstein-Roth  Tabellen. 

2  Friedrich-Leroux,  Metal.  4,  1907. 

3  Gwyer,  Zs.  Anorg:.  Ch.  57,  1908. 

4  Means,  L.-B.-R.  Tabellen. 

5  Roberts- Austen  Cliem.  News,  87,  2,  1903. 

6  Shepherd  J.  ph.  ch.  8,  1904. 

7  Kapp,  Diss.,  Konigsberg,  1901. 

8  Fay  and  Gilson,  Trans.  Am.  Inst.  Min.  Eng.  Nov. 

9  Heycock  and  Neville,  Phil.  Trans.  iSgA,  1897. 
10  "         "     I94A,  201,  1900. 


ii   Heycock  and  Neville,  J.  Chem.  Soc.  71,  1897. 


Phil.  Trans.  202A,    i,    1903. 

13  Kurnakow,  Z.  Anorg.  Chem.  23,  439,  1900. 

14  30,  86,  1902. 

15  30,  109,  1902. 

16  Roland-Gosselin,  Bui.  Soc.  d'Encour.  (5)    i,    1896. 

17  Gautier,  "       "  "         (5)    i,      " 

18  Le  Chatelier,  "       "  "         (4)    10,    573, 

1895. 

19  Reinders,  Z.  Anorg.  Chem.  25,  113,  1896. 

20  Erhaid   and    Schertel,   Jahrb.    Berg-u.    Hiittenw- 

Sachsen.  1879,  17. 


TABLE  222.  —  Alloy  ol  Lead,  Tin,  and  Bismuth. 


Per  cent. 

Lead  .     .     . 
Tin     
Bismuth.     .     .     . 

32.0 
'5-5 
52-5 

25.8 
.9.8 
54-4 

25.0 
»5-o 
60.0 

43-o 
14.0 
43-o 

33-3 
33-3 
33-3 

10.7 
23.1 
66.2 

50.0 
33-o 
17.0 

35-8 
52.1 

12.  1 

20.  o 
60.0 

20.0 

70.9 
9.1 
20.0 

Solidification  at 

96° 

IOlO 

•25-- 

128° 

145° 

148° 

161° 

181° 

l82° 

234° 

Charpy,  Soc.  d'Encours,  Paris,  1901. 


TABLE  223.  -  Low  Melting-point  Alloy. 


I 

Jer  cent 

Cadmium  .... 
Tin    .... 

10.8 

IO.2 

I4.8 

13-1 

17  8 

6.2 

7-' 

6-7 

Lead     .     . 

Bismuth     .... 

50.1 

50-4 

52.2 

48.8 

34-4 
50.0 

39-7 
53-2 

43-4 

49-9 

Solidification    at 

65-5° 

67-5° 

68.5° 

68.5° 

76.50 

89-5° 

95° 

Drewitz,  Diss.  Rostock,  1902. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  224.  2.OJ 

TRANSFORMATION   AND    MELTING  TEMPERATURES  OF  LIME-ALUMINA- 
SILICA  COMPOUNDS  AND    EUTECTIC    MIXTURES. 

The  majority  of  these  determinations  are  by  G.  A.  Rankin.     (Part  unpublished.) 


Substance. 


CaSi03  . 
CaSiO3  . 
Ca2Si04  . 


Ca3Si2O7  . 
Ca3SiO5  . 

Ca3Al206  . 
Ca5Al6Oi4 
CaAL04  . 


Al2Si05  . 
CaAl2Si2O8 
Ca2A]2SiO7 
Ca3Al2SiO8 


CaO      A12O3        SiO2 


48.2 
48.2 


51.8 

51.8 

35- 

35- 

35- 

41.8 


73.6  26.4 

62.2  37-8  — 
47-8  52.2  - 
354  64.6 

2t8  Hi 

36.6 


20.  i 

40.8      37.2 

5°-9      3°-9 


37-i 
43-3 

22.0 
18.2 


Transformation. 


Melting 

a  to  ft  and  reverse 

Melting  

7  to  )8  and  reverse 

&  to  a  and  reverse 

Dissociation  into  Ca2SiO4  and 

liquid 

Dissociation  into  Ca2SiO4  and 

CaO 

Dissociation  into  CaO  and  liquid 

Melting 

Melting 

Melting 

Melting 

Melting 

Melting 

Dissociation  into  Ca2SiO4+ 

Ca2Al2SiO7  and  liquid     .     . 


Temp. 


I  540°  ±2° 
I2OO   -\-2 

2130  -4^10 
675  ±5 

I42O   -j-2 

1475  ±5 


1335  ±5 


EUTECTICS. 


EUTECTICS. 


Crystalline  Phases. 


%CaO    A1203      Si02 


Melting 
Temp. 


Crystalline  Phases. 


%CaO     A12O3     SiO2 


Meltin 
Temp. 


CaSiO3,SiO2 
Ca,SiO3  j 

3CaO,2SiO2     I 
Ca,SiO4  j 

CaO.  j 

Al2Si05)SiO2 
Al2SiO5,Al2O3 
CaAl2Si2O8      1 
CaSiO3  ] 

CaAl2Si2O8      1 
Si02  j 

CaAl2Si2O8      i 
SiO2,CaSiO3    \ 
Ca2Al2SiO7       i 
Ca2Si04 
A1203 

CaAl2Si2O8      j 
CaAl2Si2O8      I 
Al2Si05,SiO2  j 
Ca2Al2SiO7      i 
Ca3AlioOi8       J 
CaoAl2SiO7      j 
CaAl204 
Ca2Al2SiO7 
CaAl2O4 
Ca3Al10018 
CaAl2Si2O8      I 
Ca2Al2Si07      j 
Ca2Al2SiO7      ; 
Ca3Si207 
CaSi03 
Ca2Al2Si07 
CaSi03  j 


37- 

54-5  — 

67.5  - 

-  '3- 

—  64. 


34-i 
10.5 
23.2 
49.6 

!9-3 
9.8 

35- 
37-8 

37-5 
30.2 
47.2 
45-7 


18.6 

19-5 
14.8 

23-7 
39-3 
19.8 
50.8 
52-9 
S3-2 
36.8 
1 1.8 
13.2 


63- 

45-5 

32-5 

87. 

36. 

47-3 

70. 

62. 

26.7 

41.4 

70.4 

14.2 
9-3 
9-3 

33- 

41. 

41.1 


1436° 


2065^ 

1610 
1810 

1299 

1359 
1165 

'545 
1547 
1345 
'552 
1512 

1505 
1385 
1310 
1316 


CaAl2Si2O8 

Ca2Al2SiO7 

CaSiO3 

CaAl2Si2O8 

Ca2Al2SiO7 

A1203 

Ca2SiO4 


a2SiO4  ) 

aAl2O4 
a5A!6Oi4       ) 


38.        20.        42. 
29-2     39-        31-8 
49-5      43-7        6.8 


1265° 

1380 

1335 


QUINTUPLE   POINTS. 


Ca2Al2Si07 

Ca3Si07 

Ca2SiO4 

Ca2Al2SiO7 

Ca2Si04 

CaAl2O4 

CaAl2Si2O8 

A1203 

Al2SiO6 


48.2      11.9      39.9 


Ca2Al2SiO7 
A1203 


48.3      42. 


9-7 


15-6     36-5      47-9 


31.2      44.5      24.3 


1335 


1512 


1475 


QUADRUPLE   POINTS. 


3CaO.2SiO2 
2CaO.Si02 


55-5      — 


44-5 


H75 


The  accuracy  of  the  melting-points  is  5  to  10  units.    Geophysical  Laboratory.     See  also  Day  and  Sosman,  Am.  J. 
of  Sc.  xxxi,  p.  341,  ign. 

SMITHSONIAN  TABLES. 


2O8  TABLE  225. 

LOWERING    OF    FREEZING-POINTS    BY    SALTS    IN    SOLUTION. 

In  the  first  column  is  given  the  number  of  gram-molecules  (anhydrous)  dissolved  in  1000  grams 
of  water;  the  second  contains  the  molecular  lowering  of  the  freezing-point ;  the  freezing-point 
is  therefore  the  product  of  these  two  columns.  After  the  chemical  formula  is  given  the  molecular 
weight,  then  a  reference  number. 


rt  M 

13  M 

-<*  i 

**  M 

g.  mol. 
looo  g.  H,O 

Molecul 
Lowerii; 

g.  mol. 
.     looog   H2O 

Molecul 
Lowerir 

g.  mol. 
looo  g.  H2O 

1! 

g.  mol. 

1! 

looo  g.  H2O 

Pb(N03).>,  331-0: 

I,  2. 

0.0500 

347° 

0.4978 

2.02° 

MgCU,  95.26:  6, 

4- 

0.000362 

5-5° 

.1000 

3-42 

.8112 

2.OI 

O.OIOO 

5fl° 

.001204 

5-3° 

.2000 

3-32 

I-5233 

2.28 

.0500 

4-98 

.002805 

5-J7 

.500 

3-26 

BaCL,,  208.3:  3,6,  13. 

.1500 

4-96 

.005570 

4  97 

1.  000 

3-14 

0".00200 

5-5° 

.3000 

5.186 

•01737 

4.69 

LiNO;(,  69.07  :  9. 

.00498 

5-2 

.6099 

5-^9 

•5OI5 

2.99 

0.0398 

3-4° 

.OIOO 

KC1,  74.60:  9,  17-19. 

Ba(NO;,),,  261.5  : 

.1671 

3-35 

.O2OO 

4-95 

0.02910 

3-54° 

0.000383 

X>  5-6° 

.4728 

3-35 

.04805 

4.80 

.05845 

3-46 

.001259 

5.28 

1.0164 

3-49 

.100 

4.69 

.112 

3-43 

.002681 

5-23 

A12(S04)3,  342-4  : 

10. 

.2OO 

4.66 

•3139 

341 

.005422 

0.0131 

5-6° 

.500 

4.82 

.476 

3-37 

.008352 

5.04 

.0261 

4-9 

.586 

5-03 

I.OOO 

3.286 

Cd(N03)2,  236.5: 

3. 

.0543 

4-5 

•750 

5.21 

1.989 

3-25 

0.00298 
.00689 

5-25 

.217 

4-03 
3-83 

CdCl,,  183.3:  3,14- 

0.00299           5.0° 

3.269 

NaCl,  58.50:  3,  20 

3-25 

12,  16. 

.01997 
.04873 

5.18 
5-15 

CdS04,  208.5:  i,  ii. 

0.000704            3.35° 

.00690 
.0200 

4.8 
4.64 

0.00399 
.OIOOO 

3-7° 

AgNO3,  167.0  :  4, 

5- 

.002685 

3-05 

4.11 

.0221 

3-55 

0.1506 

3-3f 

.01151 

2.69 

.0818 

3.93 

•04949 

3-51 

.5001 

2.96 

.03120 

2.42 

.214 

3-39 

.I08l 

348 

.8645 

2.87 

•1473 

2<I3 

3.03 

•2325 

3-42 

1-749 

2.27 

.4129 

i.  80 

.858 

2.71 

•4293 

3-37 

2-953 

•5   A  -ft 

1.85 

•7501 

1.76 

1.072 

2-75 

.700 

3-43 

3.550 
0.0560 
.1401 
•3490 

KNO3,  101.9:  6,  7 
O.OIOO 
.O2OO 
.0500 
.100 

3.82 
3.58 
3-28 

3-5 

3-5    ! 

3.31  ; 

K2SO4,  174.4:  3*5*6,10,12.: 
0.00200                5.4° 
•00398                5.3 
.00865                4.9 
.0200                    4.76 
.0500                   4.60 

.1000              4.32 

.2OO                       4.O7 

CuCl2,  134.5  :  9- 
0.0350 
•'337 

.7149 

CoCU,  129.9:  9. 

©".0276 
.1094 

4-9° 
4.81 
4.92 
5-32 

5-o° 
4-9 

NH4Cl,53-52:6, 
O.OIOO 
.0200 

•0350 
.IOOO   • 
.2000 
.4OOO 
.7OOO 

3-50 
3-43 
3-396 
3-393 
3-4i 

.200 

3-f9 

•454 

3-87 

.2369 

5-°3 

LiCl,  42.48:  9,  '5- 

.250 
.500 

3.08; 
2-94 

CuSO4,  159.7:  i,  4.  ii- 
0.000286             ^.f> 

•5389 

5-30 
5-5 

0.00992 

•0455 

3-7° 
3-5 

•750 

2.87 

.000843 

3-'5 

CaCL,  m.o:  5,  13-16. 

.09952 

3-53 

1.  000 

2.66 

.002279 

3-°3 

O.OIOO 

e.i° 

.2474 

3-5° 

NaN03,  85.09:  2,6,7        i 

.006670 

2-79 

.05028 

4-85 

.5012 

3.61 

O.OIOO 

3-6°  j 

.01463 

2.59 

.1006 

4-79 

•7939 

3-7  1 

.0250 

3-46 

.1051 

2.28. 

•5°77 

5-33 

BaBr2,  297.3:   ,4. 

.0500 

3-44 

•2074 

1.95 

.946 

5-3 

O.I  00 

5-10 

.2000 

3-345 

.4043 

1.84 

2.432 

8.2 

.150 

4.9 

.500 

3-24 

.8898 

1.76 

11.5 

.2OO 

5.00 

•5o>5 

3-30  i 

MgSO4,  120.4:  i, 

4,  n. 

3-829 

14.4 

•5°0 

5.18 

1.  000 

3.1  5 

0.00067  5 

3-29 

0.0478 

S-2 

AlBr.,,  267.0:  9. 

1.0030 

3-03  '. 

.002381 

3.10 

•153 

4.91 

0.0078 

1.4° 

NH4NO3,  80.11  :  6,  8.        \ 

.01263 

2.72 

•331 

5-i5 

•0559 

1.2 

O.OIOO 
.0250 

3-6°  : 
3-50  ; 

.0580 
.2104 

2.65 
2-23 

.612 
.998 

5-47 
6-34 

.1971 

•4355 

1.07 
1.07 

i   Hausrath,  Ann.  Phys.  9,  1902. 

ii    Kahlenberg, 

.  Phys.  Ch.  <;,  1901. 

2  Leblanc-Noyes,  Z.  Phys.  Ch.  6,  1890. 

12  Abegg,  Z.  Phys.  Ch.  20,  1896." 

i  Jones,  Z.  Phys.  Ch.  ii,  1893. 

4  Raoult,  Z.  Phys.  Ch.  2,  1888. 

5  Arrhenius,  Z.  Phys.  Ch.  2,  1888. 

6  Loomis.  Wk-d.  Ann.  57,  1806. 

7  Jones,  Am.  Chem.  J.  27,  1902- 

8  Jones-Caldwell,  Am.  Chem.  J.  25,  1901 

9  Biltz,  Z.  Phys.  Ch.  40,  1^2. 

10  Jones-Mackay,  Am.  Chem.  J.  19,  '897. 


13  Jones-Getman,  Am.  Ch.  J.  27,  1902. 

14  Jones-Chambers,  Am.  Ch.  J.  23,  1900. 

15  Loomis,  Wied.  Ann.  60,  1897. 

16  Roozeboom,  Z.  Phys.  Ch.  4,  1889. 

17  Raotilt,  Z.  Phys.  Ch.  27,  1898. 

18  Roloff,  Z.  Phys.  Ch.  18,  1895. 

iO  Kistiakowsky,  Z.  Phys.  Ch.  6,  1890. 

_     . ,,  .  20  Loomis,  \Vied.  Ann.  51,  1894. 

Compiled  from  Landolt-Bomstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES- 


TABLE  225  (continued).  2O9 

LOWERING   OF    FREEZING-POINTS    BY    SALTS    IN    SOLUTION  (continued). 


U     £ 

JS  5* 

*"  M 

— 

~^~ 

mol.  

"s  -r 

£  « 

g.  mol. 

3.H 
0    U 

g.  mol 

"g-c 

g.  mol. 

*~  £ 
w  h 

looo  g.  H,O 

11 

looo  g.  H2O 

II 

1000  g.  H2O 

IJ 

1000  g.  H,0 

Jj 

CdBr2,  272.3  :  3,  14. 

KOH,  56.16:  i,  15,  23. 

Na.,SiO3,  122.5:  15. 

0.472 

2.20° 

0.00324 

5fl 

0.00352 

0.01052 

6.4° 

•944 

2.27 

.00718 

4.6 

.00770 

3-59 

.05239 

5-86 

1.620 

2.60 

.03627 
.0719 

3-84 
3-39 

.O2OO2 
.05006 

3-44 
3-43 

.1048 
.2099 

5.28 
4-66 

(COOH)2,  90.02  : 
O.OIOO2 

4,  '5- 

3-3° 

.1122    ' 

3.18 

.1001 

3-42 

•5233 

3-99 

.02005 

3-*9 

.220 

2.96 

.2003 

3-424 

HC1,  36.46  : 

.05019 

3.03 

440 

2.76 

230 

3-5° 

'-3,  6,  13 

18,  22. 

s 

.1006 

281 

.800 
CuBr,,  223.5  :  9- 
0.0242 

2-59 

-       T   O 

-465              3-57 

CH;JOH,  32.03  :  24,  25. 
o.oioo             1.8° 

0.00305 
.00695 
.OIOO 

*P 

3-6 

.2022 

.366 
.648 

••"j 

2.64 
2.56 

2.T. 

.0817                5.1 
•2255                5.27 
.6003                5.89 
CaBr.,,  200.0:  14. 
0.0871                5.1° 
.1742               5.18 
.3484               5.30 
.5226               5.64 
MgBr.,,  184.28  :   14. 
0.0517                5.4° 
.103                  5.16 
.207                  5.26 

.0301 
.2018 
1.046 
3-4i 

6.200 
C2H5OH,  46.04: 

I,  12,   17 
O.OOO4O2 
.004993 

.0100 

.02892 

.0705 

.1292 

1.82 
1.811 
1.86 
1.88 
1.944 

24-27 
i67° 

J.Si 

1.707 
1.85 
1.829 

.01703 

.0500 

.1025 

.2000 

.3000 
.464 

.516 

1.003 
1.032 

1.500 

2.000 

2.U5 
3-OOO 

3-59 
3-59 

3-57 
3.612 
3-68 
3-79 
3-95 
4.10 
4.42 
4-97 
4-52 
6.03 

C3H5(OH)3,  92.06 
O.O2OO 
.I008 
.2031 

•535 
2.40 

5-24 
(C2H5)20,  74-08: 
O.OIOO 

.0201 

.1011 

.2038 

J 

24,25. 

1.86° 
1.86 
1.85 
1.91 
1.98 
2.13 

'1.6' 
1.67 
1.72 
1.702 

•5T7 

KBr,  119.1  :  9,  21. 

0.0305 

vo 

3.61° 

.2024 

•5252 

1.0891 

1.832 
1.834 
1.826 

3-053 
4.065 

4^57 

4.90 

5-67 
6.19 

Dextrose,  180.1  :  24,  30. 
0.0198               1.84° 
.0470              1.85 

.1850 
.6801 
.250 
•500 

3-49 
3-30 
3-78 
3.56 

1.760 

3.901 
7.91 

1  1.  1  1 

1.83 
1.92 

2.O2 
2.12 

HN03,  63.05  :  3,  13,  15. 

0.02004          3-55° 
•05015          3-50 
.0510            1.71 

.1326              1.87 
.4076  .            1.894 
I.IO2                    1.921 
Levulose,  180.1  :  24,  25. 

Cdlo,  366.1  :  3,  5,  22. 

18.76 

I.8l 

.1004 

3.48 

O.O2OI 

1.87° 

O.OO2  1  0 

—  .^S'-/' 

4-5 

0.0173 

1.  80 

.1059 

3-53 

.2050 

1.871 

.00020 
_    /- 

4.0 

.0778 

1.79 

.2015 

3-45 

•554 

2.01 

.O2O62 
.04857 

3-52 
2.70 

K2CO3,  138.30  :  6 

O.OIOO 

•250 
.500 

3-50 
3.62 

1.384 

2.77 

2.32 
3-04 

.1360 

2-35 

.0200 

4-93 

I.OOO 

3.80 

Ci2H22On,  342.2:  i 

24,  26. 

•333 

2.13 

.0500 

4.71 

2.000 

4.17 

0.000332 

1.90° 

.684 

2.23 

.100 

4-54 

3-000 

4.64 

.001410 

1.87 

.888 

2.51 

.200 

4-39 

H3P02,  66.0:  29. 

.009978 

1.86 

KI,  166.0  :  9,  2. 

Na2CO3,  106.10  :  6 

0.1200 

2.90° 

.O2OI 

i.SS    1 

0.0651 

3-5° 

O.OIOO 

5-T° 

.2542 

2.75 

.1305 

1.88 

.2782 
.6030 

3-50 
3-42 

.O2OO 
.0500 

4-93 
4.64 

I.07I 

2-59 
2-45 

H2S04,  98.08  : 

13,  20,  31-3  V 

1.003 

3-37 

.IOOO 

4.42 

H8P08,8a.o:  4,5. 

O.OO46I 

4.8° 

SrI2,  341.3:  22. 

.2OOO 

4.17 

0.0745 

3.0° 

.OIOO 

4.49 

0.054 

5>l0 

Na.,SO3,  126.2  :  28 

.1241 

2.8 

.O2OO 

4-32 

.108 

S-2 

0.1044 

4.51° 

.2482 

2.6 

.0461 

4.10 

.216 

5-35 

•3397 

3-74 

I.OO 

2.39 

.100 

3-96 

•327 

5-52 

.7080 

3-38 

H3PO«,  98.0  :  6,  22. 

.2OO 

3-85 

NaOH,  40.06:  15. 

Na,HPO4,  142.1: 

22,  29. 

O.OIOO 

2.8° 

.400 

3-98 

O.O2OO2 

3-45° 

"o.oiooi 

5-o° 

.0200 

2.68 

I.OOO 

4.19 

.05005 

3-45 

.02003 

4.84 

.0500 

2.49 

1.500 

4-96 

.IOOI 

3-41 

.05008 

4.60 

.1000 

2.36 

2.000 

5.65 

.2000 

3-407 

.1002 

4-34 

.2000 

2.25 

2.500 

6-53 

1-20  See  page  217. 

21  Sherrill,  Z.  Phys.  Ch.  43,  1903. 

22  Chambers-Frazer,  Am.  Ch.  J.  23,  1000. 

23  Noyes-Whitney,  Z.  Phys.  Ch.  15,  1894. 

24  Loomis,  Z.  Phys.  Ch.  32,  1900. 

25  Abegg,  Z.  Phys.  Ch.  15,  1894. 

26  Nernst-Abegg,  Z.  Phys.  Ch.  15,  1894. 

SMITHSONIAN  TABLES. 


27  Pictet-Altschul,  Z.  Phys.  Ch.  16,  1895. 

28  Barth,  Z.  Phys.  Ch.  9,  1892. 

29  Petersen,  Z.  Phys.  Ch.  n,  1893. 

30  Roth,  Z.  Phys.  Ch.  43,  1903. 

31  Wildermann,  Z.  Phys.  Ch.  15,  1894. 

32  Jones-Carroll,  Am.  Ch.  J.  28,  1902. 

33  Jones-Murray,  Am.  Ch.  J.  30,  1903. 


210  TABLE  226. 

RISE   OF  BOILING-POINT  PRODUCED  BY  SALTS  DISSOLVED  IN  WATER.* 

This  table  gives  the  number  of  grams  of  the  salt  which,  when  dissolved  in  100  grams  of  water,  will  raise  the  boil- 
ing-point by  the  amount  stated  in  the  headings  of  the  different  columns.  The  pressure  is  supposed  to  be  76 
centimeters. 


Salt. 

1°C. 

2° 

3° 

4° 

5° 

7° 

10° 

15° 

20° 

25 

BaCl2+2H2O    . 

i 

5.0 

31-1 

47-3 

63.5 

(71-6  g 

ives  4° 

5  rise 

of  temp 

. 

CaCl2 

0.0 

"•5 

16.5 

2I.O 

25.0 

32.0 

4i-5       55-5 

69.0 

84-5 

Ca(N03)2  +  2H20     . 

I2.O 

25-5 

39-5 

53-5 

68.5 

IOI.O 

152-5 

240.0 

331-5 

443-5 

KOH 

4-7 

9-3 

17.8 

17.4 

20.5 

26.4 

34-5 

47-o 

57-5 

67-3 

KC>H3O2    . 

6.0 

I2.O 

1  8.0 

24-5 

31.0 

44.0 

63-5 

98.0 

134.0 

I7I-5 

KC1 

9.2 

I6.7 

23-4 

29.9 

36.2 

48.4 

(57.4  gives  a  rise  of  8°.  5) 

K2C03 

"•5 

22.5 

32.0 

40.0 

47-5 

60.5 

78.5 

W3-S 

127-5 

I52-5 

KClOg 

13.2 

27.8 

44.6 

62.2 

KI       . 

15.0 

3O.O 

45-o 

60.0 

74.0 

99-5 

134. 

185.0 

(220  gives  i8°.5) 

KXO3 

15.2 

3I.O 

47-5 

64-5 

82.0 

120.5 

188.5 

338-5 

K2C4H406  +  |H20    . 

18.0 

36.0 

S4-o 

72.0 

90.0 

126.5 

182.0 

284.0 

K.\uC4H4O6       . 

17-3 

34-5 

Si-3 

68.1 

84.8 

119.0 

171.0 

272.5 

390.0 

510-0 

KNaC4H4O6  +  4H2O 

25.0 

53-5 

84.0 

118.0 

157-0 

266.0 

554-0 

SS'o.o 

LiCl    .... 

3-5 

7.0 

IO.O 

12.5 

15.0 

20.0 

26.0 

35-o 

42-5 

50.0 

LiCl  +  2H2O      . 

6.5 

13.0 

19-5 

26.0 

32.0 

44-o 

62.0 

92.0 

123.0 

160.5 

MgCl2-f  6H2O  . 
MgSO4+7H2O 

II.O 

4i-5 

22.O 

87.5 

138.0 

44.0 
196.0 

55-° 
262.0 

77.0 

I  IO.O 

170.0 

241.0 

334-5 

NaOH 

4-3 

8.0 

"•3 

14-3 

17.0 

22.4 

30.0 

41.0 

51.0 

60.  i 

NaCl  .... 

6.6 

12.4 

17.2 

21.5 

25-5 

33-5 

(40.7 

gives  8°.8rise) 

NaNO3 

9.0 

18.5 

28.0 

38.0 

48.0 

68.0 

99-5 

156.0 

222.O 

NaC2H302  -f  3H2O   . 

14.9 

30.0 

46.1 

62.5 

79-7 

118.1 

194.0 

480.0 

6250.0 

Na2S2O3      . 

14.0 

27.0 

39-o 

49-5 

59-o 

77.0 

104.0 

152.0 

214.5 

311.0 

Na2HP04   . 

17.2 

34-4 

5'-4 

68.4 

85-3 

Na2C4H406  +  2H2O  . 

21.4 

44-4 

68.2 

93-9 

121.3 

183.0 

(237-3  gives  8°.4  rise) 

Na2S2O3  +  5H2O 

23.8 

50.0 

78.6 

108.1 

139-3 

216.0 

400.0 

1765.0 

Na2C03  -f  ioH20      . 

34-i 

86.7 

177.6 

369-4 

1052.9 

Na2B4O7  +  ioH2O     . 

39- 

93-2 

254.2 

898.5 

(5555-5  gives  4°-5  rise) 

NH4C1 

6.5 

12.8 

19.0 

24.7 

29.7 

39-6 

56.2 

88.5 

NH4NO3     . 

IO.O 

2O.O 

30.0 

41.0 

52-0 

74-o 

108.0 

172.0 

248.0 

337-o 

(NH4)2SO4 

154 

3O.I 

44.2 

58.0 

71.8 

99-i 

(115.3  gives  108.2) 

SrCl2  +  6H2O    . 
Sr(\03)2     .         .         . 

20.0 
24.0 

4O.O 

45-° 

60.0 
63.6 

81.0 
81.4 

103.0 
97.6 

150.0 

234.0 

524.0 

C4H606       .         .         . 

r.,ll.-04  4-  2lI20 
C6H807  4-  H20 

17.0 
I9.O 
29.0 

34-4 
40.0 
58.0 

52.0 
62.0 
87.0 

70.0 
86.0 
116.0 

87.0 

II2.O 

145.0 

123.0 
169.0 
208.0 

177.0 
262.0 
320.0 

272.0 
540.0 
553-o 

374-0 
1316.0 
952-0 

484.0 
50000.0 

Salt.                     40 

60° 

80° 

100° 

120° 

140° 

160°       180°       200°       240° 

CaCl2   .         .         .     137.5 

222.O 

314.0 

KOH   .        .        .      92.5 

I2I.7 

152.6 

185.0 

219.8 

263.1 

312.5      375.0      444.4    623.0 

NaOH          .        .      93.5 
NH4NOa      .        .    682.0 

1  50.8        230.0 
I37O.O     24OO.O 

345-c 
4Q9Q.O 

526.3 

8C47.0 

800.0 

00 

J333-o   2353.0   6452.0       - 

C4H6Ofl        .        .    980.0 

3774-0 

infinity  gives  170) 

*  Compiled  from  a  paper  by  Gerlach,  "  Zeit.  f.  Anal.  Chem."  vol.  26. 
SMITHSONIAN  TABLES. 


TABLE  227. 


211 


FREEZING    MIXTURES.* 

Column  i  gives  the  name  of  the  principal  refrigerating  substance,  A  the  proportion  of  that  substance,  B  the  proper- 
tion  of  a  second  substance  named  in  the  column,  C  the  proportion  of  a  third  substance,  D  the  temperature  of  the 
substances  before  mixture,  E  the  temperature  of  the  mixture,  /''the  lowering  of  temperature,  G  the  temperature 
when  all  snow  is  melted,  when  snow  is  used,  and  H  the  amount  of  heat  absorbed  in  heat  units  (small  calories  when 
A  is  grams).  Temperatures  are  in  Centigrade  degrees. 


Substance. 

A 

B 

C 

D 

E 

F 

G 

H 

NaC2H3O2  (cryst.) 

35 

H2O-ioo 

_ 

10.7 

—  4-7 

154 

_ 

_ 

NH4C1  . 

30 

"        " 

— 

18.4 

— 

_ 

NaNO3. 

75 

"        " 

— 

13.2 

—  5.3 

I8.5 

— 

_ 

Na2S2O3  (cryst.)    . 

no 

"        " 

- 

10-7 

—  8.0 

18.7 

- 

- 

KI. 

140 

"       " 

- 

10.8 

—  11.7 

22.5 

- 

— 

CaCl«  (cryst.) 

250 

11                 U 

- 

10.8 

—  12.4 

23.2 

_ 

_ 

NH4N08       • 

60 

"         " 

— 

13.6 

-13.6 

27.2 

— 

_ 

(NH4)2S04    .         . 

25 

"      5° 

NH4NO3-25 

26.0 

- 

- 

NH4C1  . 

25 

«            u 

"          " 

— 

— 

22.0 

— 

— 

CaCl2     . 

25 

«       tt 

"          " 

- 

- 

20.0 

_ 

_ 

KN03    . 

25 

U                 it 

NH4Cl-25 

- 

— 

2O.O 

_ 

_ 

Na2SO4 

25 

u           u 

u             u 

_ 

_ 

I9.O 

_ 

_ 

NaNO3. 

25 

«           « 

«            .< 

- 

- 

17.0 

_ 

- 

K2SO4  . 

10 

Snow  100 

— 

— 

—  1.9 

0.9 

_ 

Na2CO3  (cryst.)     . 

20 

u            u 

_ 

— 

2.O 

1.0 

_ 

_ 

KN08    . 

13 

U                 U 

- 

— 

-2.8S 

1.85 

- 

- 

CaCl2     . 

3° 

u            « 

- 

— 

IO-9 

9-9 

— 

—    ' 

NH4C1  . 
NH4N03 

25 
45 

«   ;; 

: 

z 

-I5-4 
—  16.75 

14.4 

x5-75 

: 

: 

NaN03  . 

5° 

u            u 

~ 

— 

—  17-75 

16.75 

~ 

- 

NaCl      . 

33 

U                 « 

- 

— 

—  21.3 

20.3 

- 

- 

"    1.097 

— 

— 

—  37-0 

36.0 

—37.0 

o.o 

"     1.26 

— 

— 

—  36.0 

35-o 

—30.2 

17.0 

H2SO4+H2O 
(66.i%H2S04) 

;;  1-38 
"  4^32 

- 

— 

—  35-0 
—  30.0 
—  25-0 

34-o 
29.0 
24.0 

—25.0 
—12.4 
—7.0 

27.0 
133-0 
273.0 

7.92 

- 

— 

—  2O.O 

19.0 

—  3-1 

553-0 

"  13.08 

- 

—  I 

—  16.0 

15.0 

—  2.1 

967.0 

"  0.35 

— 

o 

— 

— 

0.0 

52.1 

"       49 

— 

0 

— 

- 

—  19.7 

49-5 

"       .61 

— 

0 

— 

- 

—  39-0 

40-3 

CaCl2  +  6H2O      - 

.70 
"       .81 

_ 

o 

0 

_ 

_ 

—  54-9t 
—  40-3 

30.0 
46.8 

"     1-23 

- 

0 

- 

- 

—  21.5 

88.5 

"     2.46 

— 

o 

— 

- 

—  9.0 

192.3 

"     4-92 

- 

0 

- 

-. 

—  4.0 

392-3 

Alcohol  at  4°       j 

77 

"   73 
CO2  solid 

_ 

0 

—  30.0 
—  72.0 

_ 

_ 

_ 

Chloroform    . 

- 

U                 (( 

- 

- 

—  77.0 

- 

- 

- 

Ether     . 

— 

«           « 

- 

— 

—  77.0 

— 

— 

— 

Liquid  SO2    . 

_ 

"           " 

_ 

_ 

—  82.0 

- 

- 

_ 

H20-.75 

- 

20 

5.0 

- 

- 

33-o 

•94 

— 

20 

—  4.0 

— 

— 

21.0 

"       " 

— 

10 

—  4.0 

— 

— 

34-o 

"       " 

— 

5 

—  4.0 

— 

— 

40.5 

Snow     " 

_ 

o 

—  4.0 

— 

_ 

122.2 

NH4N03       . 

H2O-i.20 

~ 

10 

—  14.0 

- 

-  , 

17.9 

Snow     " 

- 

0 

—  14.0 

- 

- 

129.5 

H2O-i.3i 

— 

ro 

—  17.5! 

- 

— 

10.6 

Snow     " 

_ 

o 

—  17.5! 

— 

_ 

I3I-9 

H2O-3.6i 

~ 

10 

—  8.0 

- 

- 

0.4 

Snow     " 

0 

—  8.0 

327.0 

*  Compiled  from  the  results  of  Cailletet  and  Colardeau,  Hammerl,  Hanamann,  Moritz,  Pfanndler,  Rudorf,  and 
Tollinger. 

t  Lowest  temperature  obtained. 

SMITHSONIAN  TABLES. 


212 


TABLE  228. 


CRITICAL  TEMPERATURES,  PRESSURES,  VOLUMES,    AND  DENSITIES  OF 

GASES.* 

6  =  Critical  temperature. 

P  =  Critical  pressure  in  atmospheres. 

<f>  =  Critical  volume  referred  to  volume  at  o°  and  76  centimeters  pressure. 

d  =  Critical  density  in  grams  per  cubic  centimeter. 

a,  b,  Van  der  Waals  constants  in  (p  +  ~^)     (  v  ~  b  )  =  l  +  at' 


Substance. 

e 

P 

<*> 

d 

a  X  io6 

b  X  io8 

Observer 

Air          ... 

—  140.0 

39-0 

_ 

_ 

257 

1560 

, 

Alcohol  (C2H6O)  . 

243.6 

62.76 

0.00713 

0.288 

2407 

3769 

2 

-        (CH40)    . 

239.95 

78.5 

— 

— 

I898 

2992 

3 

Ammonia 

130.0 

115.0 

- 

- 

798 

1606 

4 

Argon     . 

—117.4 

52.9 

— 

— 

259 

1348 

5 

Benzene 

288.5 

47-9 

— 

0.305 

3726 

5370 

Bromine 

302.2 

0.00605 

1.18 

1434 

2O2O 

6 

Carbon  dioxide 

31.2 

73- 

0.0044 

0.46 

717 

1908 

- 

"        monoxide  . 

—141.1 

35-9 

— 

— 

275 

1683 

7 

disulphide 

273- 

72.9 

0.0090 

- 

2316 

3430 

8 

Chloroform     . 

260.0          54.9 

— 

— 

2930 

445° 

9 

Chlorine 
Ether      '.        !        '. 

141.0 
146.0 
197.0 

83-9 
93-5 

35-77 

0.01584 

0.208 

"57 
1063 
3496 

2259 
2050 
6016 

4 

10 

ii 

"          ... 

194.4 

35-61 

0.01344 

0.262 

3464 

6002 

3 

Ethane   . 

32.1 

49.0 

— 

— 

1074 

2848 

12 

Ethylene 
Helium  . 

<—  268.0 

51-1 
2.3 

_ 

~ 

886 
5 

2533 
700 

' 

Hydrogen 
"          chloride  . 

—  240.8 
5I-25 

14. 
86.0 

_ 

_ 

42 
692 

880 
1726 

15 

«                « 

52-3 

86.0 

_ 

0.6  1 

I731 

4 

"          sulphide  . 

1  00.0 

88.7 

- 

- 

888 

1926 

i 

Krypton 

—  62.5 

54-3 

— 

- 

462 

1776 

5 

Methane 

—81.8 

54-9 

- 

- 

376 

1557 

" 

—95-5 

50.0 

— 

— 

357 

1625 

4 

Neon 

<  —  205.0 

29. 

— 

— 

— 

- 

5^3 

Nitric  oxide  (NO)  . 

—93-5 

71.2 

- 

- 

257 

1160 

i 

Nitrogen 

—  146.0 

35-o 

— 

0.44 

259 

1650 

i 

"        monoxide 

• 

(N20) 

35-4 

75-° 

0.0048 

0.41 

720 

1888 

4,17 

Oxygen  . 
Sulphur  dioxide 

—  118.0 
T55-4 

50.0 
78-9 

0.00587 

0.6044 
0-49 

273 
1316 

1420 
2486 

i 

9,17 

Water     . 

358.1 

— 

0.001874 

0.429 

— 

— 

6 

. 

374- 

217-5 

" 

1089 

1362 

16 

(1)  Olszewski,  C.  R.  98,  1884;  99,  1884;  100, 

1885;    Beibl.  14,  1890;   Z.  Phys.  Ch.  16, 
1893. 

(2)  Ramsay-Young,  Tr.  Roy.  Soc.  177,  1886. 

(3)  Young,  Phil.  Mag.   1900. 

(4)  Dewar,  Phil.  Mag.  18, 1884  ;  Ch.  News,  84, 

1901. 

(5)  Ramsay,  Travers,  Phil.  Trans.  16,  17,  1901. 

(6)  Nadejdme,  Beibl.  9,  1885. 

(7)  Wroblewski,  Wied.    Ann.    20,    1883 ;    Stz. 

\Vien.  Ak.  91,  1885. 

(8)  Batelli,  1890. 


(9)  Sajotschewsky,  Beibl.  3,  1879. 
(io)  Knietsch,  Lieb.    Ann.    259,  1890. 
(n)  Batelli,  Mem.  Torino  (2),  41,  1890. 

(12)  Cardozo,  Arch.  sc.  phys.  30,  1910. 

(13)  Kamerlingh-Onnes,    Comno.    Phys.   tab. 

Leiden,    1908,   1909,    Proc.   Amst.   n, 
1908,  C.  R.  147,  1908. 

(14)  Olszewski,  Ann.  Phys.  17,  1905. 

(15)  Ansdell,  Chem.  News,  41,  1880. 

(16)  Holborn,  Baumann  Ann.   Phys.  31,  19101 

(17)  Cailletet,  C.  R.  102, 1886;  104,  1887. 


'Abridged  for  the  most  part  from  Landolt  and  Bornstein's  "Phys.  Chem.  Tab." 


SMITHSONIAN  TABLES. 


TABLE  229. 
CONDUCTIVITY    FOR   HEAT,   METALS  AND   ALLOYS- 


213 


The  coefficient  k  is  the  quantity  of  heat  in  small  calories  which  is  transmitted  per  second  through 
a  plate  one  centimeter  thick  per  square  centimeter  of  its  surface  when  the  difference  of  tempera- 
ture between  the  two  faces  of  the  plate  is  one  degree  Centigrade.  The  coefficient  k  is  found  to 
vary  with  the  absolute  temperature  of  the  plate,  and  is  expressed  approximately  by  the  equation 
kt  =  &0[i  +  a.(t  -  Jo)].  £o  is  the  conductivity  at  tQ,  the  lower  temperature  of  the  bracketed  pairs 
in  the  table,  kt  that  at  temperature  /,  and  a  is  a  constant,  kt  in  g-cal.  per  degree  C  per  sec.  across 
cm  cube  =  0.239  x  kt  in  watts  per  degree  C  per  sec.  across  cm  cube. 


Substance 

,c 

*i 

a 

i>    (j 

*aj  C 

Substance. 

/°C 

ftl 

a 

ji 

Aluminum  

-160 

0.514 

_ 

I 

Mercury  .... 

o 

0.0148! 

' 

18 

0.480 

u 

50 

0.0189; 

+.o°55 

7 

' 

IOO 

0.492 

+  .  0030 

2 

Molybdenum 

17 

0.346 

-.0001 

6 

* 

200 

o.  545 

Nickel  

-160 

O.  120 



i 

*          .... 

400 

o.  760 

+  .  OO2O 

3 

i 

18 

W.    X  A.\f 

o.  1420 

— 

2 

|          .... 

500 
600 

0.885 

I.OI 

+.0014 

3 

o 

IOO 

0.1425! 
0.1380  j 

-.00032 

3 

Antimony  .... 

0 
IOO 

0.0442  1 
o  0^06  f 

—.OOIO4 

4 



200 
7OO 

0.1325  I 

o  060    f 

-.00095 

3 

Bismuth  

-186 

•  ^ov^  j 
o.  025 



/  w 

IOOO 

^.  wuy      j 

o  064.  ! 

tt 

18 

o.  0194  1 

I2OO 

W  .  WVJlf.     I 

o  ot;8  I 

-.00047 

3 

« 

IOO 

0.0161  / 

-.0021 

2 

Palladium.  .  . 

18 

^O°  / 

0.1681  ! 

Brass  

-160 

0.181 



I 

it 

IOO 

w  '  *  W*-'O     V 

0.182    / 

+.0010 

2 

" 

17 

o.  260 



I 

Platinum.  .  .  . 

18 

0.1664! 

"    ,  yellow.  . 

o 

o.  204 

+.0024 

4 

M 

IOO 

0.1733  / 

+  .  0005  I 

2 

"    ,red.... 

o 

o.  246 

+.0015 

4 

Pt  10%  Ir  .. 

17 

0.074 

+.O002 

6 

Cadmium,  pure 

-160 

0.239 



i 

Pt  10  %  Rh  . 

17 

0.072 

+.0002 

6 

«               u 

18 

0.222  1 

O 

Platinoid...  . 

18 

0.060 



i 

Constantan.  .  . 

IOO 

18 

0.215; 

0.0540! 

-  .  00038 

2 

Potassium.  .  . 

5-o 
57-4 

0.232! 
0.216  / 

-.0013 

8 

(60  Cu+4o  Ni) 

IOO 

0.0640/ 

+.00227 

2 

Rhodium.  .  .  . 

17 

0.210 

-.OOIO 

6 

Copper,*  pure  . 

-160 
18 

IOO 

1.079 
0.918! 

o  .  908  J 

-.00013 

I 
2 

Silver,  pure.  . 

-160 
18 

IOO 

0.998 

1.006! 
0.992  J 

-.00017 

i 

2 

German  silver. 

0 

0.070 

+.0027 

4 

Sodium  

5-7 

\ 

0.321! 

3 

Gold  

17 

o  .  705 

—  .00007 

6 

u 

88.1 

0.288J 

—  .  OO  I  2 

Graphite  

17 

0.037 

+.0003 

6 

Tantalum.  .  . 

17 

0.130 

—.0001 

6 

Iridium  

17 

o.  141 

-  .  0005 

8 

" 

1700 

0.174 

— 

9 

Iron,f  pure  .  .  . 

18 

IOO 

o.  161  ! 
0.151  J 

-  .  0008 

2 

M 

1900 

2  IOO 

0.186! 
0.198? 

+.00032 

9 

Iron,  wrought. 

-160 
18 

0.152 
0.144! 

—  .  00008 

I 
2 

Tin... 

O 
IOO 

o.i55  I 
0.145  J 

-.00069 

4 

*  

. 

IOO 

O.I43/ 

,pure.... 

-160 

o.  192 

— 

i 

"    steel,  i% 

18 

0.108  1 

C  ......... 

IOO 

o.  107  / 

-.0001 

2 

Tungsten.  .  .  . 

17 

0.476 

-.0001 

6 

Lead,  pure  

-160 

0.092 

— 

I 

n        « 

18 

IOO 

0.083! 
0.081  / 

—.0001 

2 

Tungsten  — 

1600 

2OOO 

0.249! 
0.272  f 

+.00023 

10 

Magnesium.  .  . 

oto/ 

IOO) 

0.376 

— 

4 

M 

2400 

2800 

0.294! 
0-3I3J 

+.00016 

10 

Manganin  .... 

—  160 

0.035 

— 

I 

Wood's  alloy 

— 

0.319 

— 

7 

"  (84CU+4 

18 

0.0519! 

Zinc,  pure.  .  . 

-160 

0.278 

— 

i 

Nii2Mn) 

TOO 

0.0630) 

+  .  0026 

2 

" 

18 

0.2653! 

-.00016 

2 

IOO 

0.2619  / 

References:    (i)  Lees,   Phil.  Trans.   1908;    (2)  Jaeger  and  Diesselhorst,  Wiss.  Abh. 

Phys.  Tech.  Reich.  3,  1900;   (3)  Angell,  Phys.  Rev.  1911;    (4)  Lorenz;    (5)  Macchia, 
1907;   (6)  Barratt,  Pr.  Phys.  Soc.  1914;   (7)  H.  F.  Weber,  1879;   (8)  Hornbeck,  Phys. 

Rev.  1913;    (9)  Worthing,  Phys.  Rev.  1914;    (10)  Worthing,  Phys.  Rev.  1917. 

*  Copper:    100-197°  C,  kt  =  1.043;   100-268°,  0.969;    100-370°,  0.931;   100-541°,  0.902  (Her 
ing;  for  reference  see  next  page). 

flron:    100-727°  C,  kt  =  0.202;    100-912°,  0.184;    100-1245°,  0.191  (Hering). 
SMITHSONIAN  TABLES. 


214 


TABLES  230-231. 
CONDUCTIVITY   FOR   HEAT. 

TABLE  230.  —  Thermal  Conductivity  at  High  Temperatures. 
(See  also  Table  229  for  metals;  k  in  gram-calories  per  degree  centigrade  per  second  across  a  centimeter  cube.) 


Tempera- 

I 

Tempera- 

jj 

Material. 

ture, 

k 

K 

Material. 

ture, 

k 

s 

°C 

•8 

°C 

! 

Amorphous  carbon  .  .  . 

37-163 

.028-.  003 

Brick:  Carborundum 

150-1200 

.0032-.  027 

3 

170-330 
240-523 

.027-.  004 

.020-.  003 

Building       \ 
Terra-cotta  / 

15-1100 

.0018-.  0038 

3 

283-597 

.on-.  004 

Fire-clay  .... 

125-1220 

.003  2-.  O054 

3 

100-360 

.089 

Gas-retort  .  .  . 

100-1125 

.0038 

3 

100-751 

.124 

Graphite  .... 

300-700 

.024 

3 

100-842 

.129 

Magnesia  .... 

50-1130 

.002  7~.  007  2 

3 

Graphite  (artificial)  .  .  . 

100-390 

.338 

Silica  

100-1000 

.002   -.0033 

3 

100—546 

-324 

Granite  

100 

.0045—.  OO5O 

4 

100-720 

.306 

200 

.0043-.  0097 

4 

100-914 

.291 

500 

.0040 

4 

30—2830 

.162 

Limestone  

40 

.0046—.  OO57 

4 

2800-3200 

.002 

100 

.003  9-.  0049 

4 

90-110 

•55--  45 

350 

.0032-.  0035 

4 

180-120 

.44-.  34 

Porcelain  (Sfevres)  .  . 

165-1055 

.0030-.  0047 

3 

500-700 

.31-.  22 

Stoneware  mixtures  . 

70-1000 

.0029-.  0053 

3 

References:    (i)  Hansen,  Tr.  Am.  Electrochem.  Soc.  16,  329,  1909;     (2)  Hering,  Tr.  Am.  Inst.  Elect. 
Eng.  1910;     (3)  Bui.  Soc.  Encouragement,  in,  879,  1909;   Electroch.  and  Met.  Ind.  7,  383,  433,  1909;    (4) 
Poole,  Phil.  Mag.  24,  45,  1912;   see  also  Clement,  Egy,  Eng.  Exp.  Univers.  111.  Bull.  36,  1909;    Dewey,  Pro- 
gressive Age,  27,  772,  1909;   Woolson,  Eng.  News,  58,  166,  1907,  heat  transmission   by  concretes;    Richards, 
Met.  and  Chem.  Eng.  n,  575,  1913.    The  ranges  in  values  under  i  do  not   depend  on  variability  in  ma- 

terial but  on  possible  errors  in  method;   reduced  from  values  expressed  in  other  units. 

TABLE  231.  —  Thermal  Conductivity  of  Various  Substances. 


Substance,  temperature. 

kt 

Refer- 
ence. 

Substance,  temperature. 

kt 

Refer- 
ence. 

Aniline  BP  183°  C.,  —  160  

.000112 
.010 
.012 
.00050 
.OOOSI 
.0022 
.00013 
.004 
.00028 
•093 
.025 
.OO25 
.OOIlS 
.0028o 
.00324 
.OOOSl 
.OOI7O 
.OOlSl 
.00077 

•0053 
.0066 
.0050 
.038 
.0103 
.00029 
.0047  to 
.0056 
.0018 
.0063 
.0044 

i 

2 

3 

4 

4 
5 
5 

5 
5 
5 

5 

5 
5 
i 
6 
i 
i 
5 
5 
4 
6 
6 

6 
6 

Naphthalene  MP  79°  C.,  —  160  
Naphthalene  M  P  79°  C.  ,  o  

.0013 
.00081 
.00068 
.00062 
.00106 
.00065 
.00062 
.00039 
.0025 
.0586 
.0173 
•0133 
.0325 
.0167 
.0150 
.00033 
.00037 
.00045 
.00093 
.0055 

.00012 

:SB 

.00026 

.0012 
.0037 
.0037 
.00070 
.00022 
.00087 

5 
5 
S 
5 
5 
5 
5 
5 

6 

6 

6 

6 
7 

7 

5 
8 
9 

Naphthol  —  /3,  MP  122°  C.,  -160.. 
Naphthol,  o  

Carborundum  

Concrete,  cinder           ...    . 

Nitrophenol,  MP  114°  C.,  —  160  
Nitrophenol  o 

stone 

Diatomaceous  earth  

Paraffin  MP  54°  C.,  —  160  
Paraffin,  o 

Earth's  crust  

Fire-brick 

Porcelain  

Fluorite,  o.                

Glass*  window 

crown,  ojiri,  —  190  

Quartz  ||  to  axis  o 

CrOWn,  O3472,  0  

crown  OUT!   100.. 

Rock  salt,  o  

Rock  salt,  30  
Rubber,  vulcanized,  —  160  
Rubber,  o  

h'vy  flint  OIM,  —190  
h'vy  flint  oi«s,  o  
h'vy  flint  OIM,  100.  .  . 

Glycerine,  —  160  

Sand,  white  dry 

Granite       

Ice    —  160 

Iceland  spar,  —  190  

Iceland  spar  o    . 

Limestones,  calcite  )  

Marbles  dolomite   j  . 

Mica 

Flagstone  J    to  cleavage  

Micaceous  ||  to  cleavage  

Vulcanite                                    

References:   (i)  Lees,  Tr.  R.  S.  1905;    (2)  Lorenz;    (3)  Norton;    (4)  Hutton,  Blard;  (5)  Eucken,  Ann. 
d.  Phys.,  1911;  (6)  Herschel,  Lebour,  Dunn,  B.  A.  Committee,  1879;   (7)  Tansson,  1904;   (8)  Melmer,  1911; 
(9)  Stefan. 

SMITHSONIAN  TABLES. 


TABLE  232.  215 

THERMAL   CONDUCTIVITIES  OF  INSULATING   MATERIALS. 

Conductivity  in  g-cal.  flowing  in  i  sec.  through  plate  i  cm  thick  per  cm2  for  i°  C  difference 
of  temperature. 


Material. 

Conduc- 
tivity. 

Density. 
g/cm3 

Remarks. 

Air 

o  00006 

Horizontal  layer   heated  from  above 

Calorox 

o  000076 

o  064 

Fluffy  finely  divided  mineral  matter 

Hair  felt  

o  000085 

O    27 

Keystone  hair  

o  000003 

O    3O 

Felt  between  layers  of  bldg  paper 

Pure  wool  

o  000084 

O    IO7 

Firmly  packed 

«      « 

o  000084 

O    IO2 

a      a 
ii      u 

o  .  000090 

O   OOOIOI 

0.061 

O    O3O 

Loosely  packed. 
Very  loosely  packed 

Cotton  wool 

O   OOOIO 

Firmly  packed 

Insulite 

O   OOOIO2 

I    O 

Pressed  wood-pulp  —  rigid   fairly  strong 

Linofelt 

o  000103 

o  18 

Vegetable  fibers  between  layers  of  paper  — 

Corkboard  (pure)  
Eel  grass 

0.000106 

O   OOO  I  I 

0.18 

O    2  ^ 

soft  and  flexible. 
Inclosed  in  burlap. 

Flaxlinum 

o  000113 

o  18 

Vegetable  fibers  —  firm  and  flexible 

Fibrofelt 

o  000113 

o  18 

Rock  cork 

o  000119 

o  33 

Rock  wool  pressed  with  binder,  rigid. 

Balsa  wood     

O   OOOI2 

O    12 

Very  light  and  soft. 

Waterproof  lith.  .    .  . 

o  00014 

o.  27 

Rock  wool,  vegetable  fiber  and  binder,  not 

Pulp  board  
Air  cell  \  in.  thick  
Air  cell  i  in.  thick  
Asbestos  paper  

0.00015 
0.000154 
0.000165 
0.00017 

0.14 

o.  14 
o.  50 

flexible. 
Stiff  pasteboard. 
Corr.  asbestos  paper  with  air  space. 

11                     11                      U                «           <(            « 

Fairly  firm,  but  easily  broken. 

Infusorial  earth,  block  .  . 
Fire-felt,  sheet     

O.OOO2O 

o  000205 

0.69 

0.42 

Asbestos  sheet  coated  with  cement,  rigid. 

Fire-felt,  roll  

O.OOO22 

0.68 

Soft,  flexible  asbestos. 

Three-ply  regal  roofing.  . 
Asbestos  mill  board  .... 
Woods,  kiln  dried: 
Cypress  

O.OOO24 
O.OOO29 

O.OOO23 

0.88 
0.97 

0.46 

Flexible  tar  roofing. 
Pressed  asbestos,  firm,  easily  broken. 

White  pine  

O.OOO27 

0.50 

Mahogany  
Virginia  pine  
Oak 

0.00031 
0.00033 
O.OOO'K 

o-5S 
0-55 
0.61 

Hard  maple  

0.00038 

o.  71 

Asbestos  wood,  sanded.  . 

0.00093 

1.97 

Asbestos  and  cement,  very  hard,  rigid. 

Dickinson  and  van  Dusen,  Am.  Soc.  Refrigerating  Eng.  J.  3,  Sept.  1916. 
SMITHSONIAN  TABLES. 


2l6 


TABLES  233-234. 
CONDUCTIVITY   FOR   HEAT. 

TABLE  233. —  Various  Substances. 

kt  is  the  heat  in  gram-calories  flowing  in  i  sec.  through  a  plate  I 
drop  in  temperature. 


cm.  thick  per  sq.  cm.  for  i°C 


Substance. 


Asbestos  fiber  .... 
85%  magnesia  asbestos  . 
Cotton  .  . 


Eiderdown 


Lampblack,  Cabot  number  5 
Quartz,  mesh  200  .... 
Poplox,  popped  Na2SiO3  . 
Wool  fibers  . 


Density, 


0.201 
.216 

.021 
.IOI 
.0021 
.109 

•193 
1.05 
0.093 

.015 
.054 
.192 


500 

100 

500 

100 


500 
500 
200 
500 


.00019 
.00016 
.00017 

.000111 

.000071 
.00015 
.000046 

.000074 

.000107 

.00024 

.000091 

.000160 

.000118 

.000085 

.000054 


Substance. 


Asbestos  paper  .  . 
Blotting  paper  .  .  . 
Portland  cement  .  . 
Cork,  t,o°C  .  .  . 

Chalk 

Ebonite,  t,  49° .     .     . 
Glass, 'mean       .     .     . 
Ice.     ...... 

Leather,  cow-hide 
"         chamois  .     . 

Linen  

Silk      ....... 

Caen  stone,  limestone 
Free  stone,  sandstone 


0.00043 
.00015 
.00071 
.0007? 

.0020 

.00037 

.002 

.0057 

.00042 

.00015 

.OOO2I 

.000095 

.0043 

.0021 


Authority. 


Lees-Chorl- 
ton. 

Forbes. 
\  H,  L,  D, 
J      see  p.  205. 

Various. 

Neumann. 

I  Lees-Chorl- 
ton. 

[   H,  L,  D. 


Left-hand  half  of  table  from  Randolph,  Tr.  Am.  Electroch.  Soc.  XXI .,  p.  550,  1912  ;  kt  (Randolph's  values) 
is  mean  conductivity  between  given  temperature  and  about  io°C.  Note  effect  of  compression  (density).  The 
following  are  from  Barratt  Proc.  Phys.  Soc.,  London,  27,  81,  1914- 


Substance. 


Brick,  fire  . 
Carbon,  gas 
Ebonite      .     . 
Fiber,  red 
Glass,  soda 
Silica,  fused  . 


Density. 


'•73 
1.42 
1.19 
1.29 
2.59 
2.17 


at  2o°C.     at  ioo°C. 


.00110 

.0085 
.00014 

.00112 

.00172 

00237 


.00109 

.0095 

.00013 
.00119 
.00182 

.00255 


Substance. 


Boxwood  . 

Greenheart 

Lignumvitae 

Mahogany 

Oak.     .     . 

Whitewood 


Density. 


0.90 
1.08 
1.16 
°-55 
0.65 
0.58 


at  2o°C.     at  ioo°C. 


.00036 

.00112 
.OOO6O 
.00051 
.00058 
.00041 


.00041 
.00110 

.00072 
.00060 
.00061 

.00045 


The  following  values  are  from  unpublished  data  furnished  by  C.   E.  Skinner  of  the  Westinghouse  Co.,  Pitts- 
burgh, Penn.    They  give  the  mean  conductivity  in  gram-calories  per  sec.  per  cm.  cube  per  °C.  when  the  mean 

temperature  of  the  cube  is  that  stated  in  the  table.    Resistance  in  thermal  ohms  (watts/inch2/inch/°C.)  =  — 

10.6 

conductivity. 


Substance. 


Grams, 
per  cm3. 


Conductivity. 


00°  C.         200°  C.         300°  C.         400°  C.         500°  C 


Safe 
temp. 


Air-cell  asbestos 

Cork,  ground 

Diatomit 

Infusorial  earth,  natural     . 

"  "  h'd  pressed  blocks 
Magnesium  carbonate  .... 
Vitnbestos 


0.232 
.168 
.326 
.506 
.321 
•450 
.362 


0.00034 
.00015 
.00028 
.00034 
.00030 
.00023 
.00049 


0.00043 
.00019 
.00032 
.00032 
.00029 
.00025 
.00066 


0.00050 

.00037 
.00040 
.00033 
.00025 
.00079 


0.00042 
.00036 
.00090 


0.00046 


320 
i  Ho 
6cx) 

400 
300 
600 


TABLE   234. —  Water  and  Salt  Solutions. 


Substance. 

°c. 

k, 

Authority. 

Solution 
in  water. 

Density. 

°C. 

kt 

Authority. 

( 

0 

0.00150 

Goldschmidt,  'n. 

CuS04 

.160 

4-4 

o.ooi  18 

H.  F.  Weber. 

Water     \ 
( 

1  1 

25 

20 

.00147 
.00136 
.00143 

{  Lees,  '98. 
Milner,  Chattock,  '98 

KC1 
NaCl 

.026 

.T78 

'3- 
4-4 
26.3 

.001  i  6 

.  00  I  15 

•00135 

Graetz. 
H.  F.  Weber. 

H2S04 

.054 

20.5 

.00126 

{  Chree. 

** 

.180 

21. 

.TXM30 

ZnS04 

•'34 

4-5 

.00118 

}  H.  F.  Weber. 

.136 

4-5 

SMITHSONIAN  TABLES. 


TABLES  235-237. 
TABLE  235.  —  Thermal  Conductivity  of  Organic  Liquids. 


Substance. 

°C 

kt 

Ji 

(£ 

Substance. 

°C 

kt 

£ 
« 

« 

Substance. 

CC 

kt 

1 

Acetic  acid  
Alcohols:  methyl.  .  . 
ethyl  
amyl  
Aniline 

9-i5 
ii 
ii 

0 
0 

0-15 

.03472 
.0352 
.0346 
•  03345 
.03434 
•  Q3333 

i 

2 

2 

3 
I 

Carbon  disulphide. 
Chloroform  
Ether 

0 

0-15 
Q-iS 
25 
13 
13 

.03387 
.03288 
•  03303 
.0368 
•03355 
.03325 

3 

I 
I 

2 

5 

5 

Oils:  olive. 

0 

25 
o 

•03395 
.03425 
•03349 
.0344 
•01343 

4 
4 
3 

2 

3 

"     castor  

Glycerine  
Oils:  petroleum.  .  . 
turpentine.  . 

Vaseline 

Xylene  

Benzene  

References:  (i)  H.  F.  Weber;  (2)  Lees;  (3)  Goldschmidt;  (4)  Wachsmuth;  (5)  Graetz. 

TABLE  236.  —  Thermal  Conductivity  of  Gases. 


The  conductivity  of  gases,  kt  =  1(97  —  S)l*Cv,  where  7  is  the  ratio  of  the  specific  heats,  CP/CV,  and  fj.  is 
the  viscosity  coefficient  (Jeans,  Dynamical  Theory  of  Gases,  igi6).     Theoretically  kt  should  be  independent 
of  the  density  and  has  been  found  to  be  so  by  Kundt  and  Warburg  and  others  within  a  wide  range  of  pressure 
below  one  atm.     It  increases  with  the  temperature. 

Gas. 

rc 

kt 

Ref. 

Gas. 

t°C 

kt 

Ref. 

Gas. 

t°C 

kt 

Ref. 

Air*... 
At 
CO 

C02 

-191 
O 
100 

-183 

o 

IOO 
0 

-78 

0 

0.0000180 
0.0000566 
0.0000719 
0.0000142 
0.0000388 
o  .  0000509 
0.0000542 
0.0000219 
0.0000332 

C02 
C2H4 
He 

H2 
CH4 

IOO 
0 

-193 

0 
IOO 

-192 

0 
IOO 
0 

0.0000496 
0.0000395 
0.000146 
0.000344 
o  .  000398 
0.000133 
0.000416 
o  .  000499 
0.0000720 

4 

i 
4 

Hg 

N« 

02 

NO 

NzO 

203 
—191 
o 

IOO 

—  191 

0 
IOO 

8 

0 

o  0000185 
0.0000183 
0.0000568 
0.0000718 
0.0000172 
0.0000570 
0.0000743 
o  .  000046 
0.0000353 

3 

4 

References:   (i)  Eucken,  Phys.  Z.  12,  1911;  (2)  Winkelmann,  1875;  (3)  Schwarze,  1903;  (4)  Weber,  1917. 

*  Air:  k0=  5.22  (io~B)  cal.  cm  -1  sec.-1  deg.  C"1;  5.74  at  22°;  temp.  coef.  =  .0029  ;  Hercus-Laby,  Pr.  R.  Soc. 

190,  1919. 


TABLE  237.  —  Diffusivities. 

The  diffusivity  of  a  substance  =  A2  =  k/cp,  where  k  is  the  conductivity  for  heat,  c  the  specific  heat  and  p  the  density 
(Kelvin).     The  values  are  mostly  for  room  temperatures,  about  18°  C. 


Material. 

Diffusivity. 

Material. 

Diffusivity. 

Aluminum 

o  826 

Coal 

o  002 

o  139 

Concrete  (cinder)    

0.0032 

o  0678 

Concrete  (stone)     ...                

0.0058 

Concrete  (light  slag) 

o  006 

o  467 

Cork  (ground)  

0.0017 

Ebonite                                            

O.OOIO 

Gold 

i   182 

o  0057 

o  173 

Granite  

0.0155 

Ice                                     

O.OII2 

Lead 

O.OO92 

o  883 

Marble  (white)  

0.0090 

o  0327 

Paraffin                        .            

0.00098 

Nickel.  

0.152 
o.  240 

Rock  material  (earth  aver.)  
Rock  material  (crustal  rocks)  

O.OIlS 
0.0064 

o  243 

Sandstone       

0.0133 

Silver 

i   737 

Snow  (fresh)                        .            

O.OO33 

Tin                                

o.  407 

Soil  (clay  or  sand,  slightly  damp)  

0.005 

Zinc 

o.  402 

Soil  (very  dry)  .  .  . 

0.0031 

Air 

o  179 

Water                 

O.OOI4 

Asbestos  (loose)  

0.0035 

Wood  (pine,  cross  grain)  

0.00068 

Brick  (average  fire)           

0.0074 

Wood  (pine  with  grain)  

0.0023 

Brick  (average  building)                          .    . 

0.0050 

Taken  from  An  Introduction  to  the  Mathematical  Theory  of  Heat  Conduction,  Ingersoll  and  Zobel,  1913. 
SMITHSONIAN  TABLES. 


2l8 


TABLE  238. 
LINEAR   EXPANSION   OF  THE   ELEMENTS- 


In  the  heading  of  the  columns  /  is  the  temperature  or  range  of  temperature;  C  is  the  coefficient  of  linear  expansion; 
A\  is  the  authority  forC;  M  is  the  mean  coefficient  of  expansion  between  o°  and  100°  C;  a  and  0  are  the  coefficients 
in  the  equation  It  =  fc(i  +  at  +  /8t2),  where  lo  is  the  length  at  o°  C  and  It  the  length  at  t°  C;  At  is  the  authority  for 
a,  ft,  and  J/.  See  footnote  for  Molybdenum  and  Tungsten. 


Substance. 

t 

CX  io« 

,ll 

M  X  10^ 

a  X  io< 

0X108 

A« 

Aluminum  

40 

o  2313 

I 

O.  222O 

2 

600 

3 





—  191  to  +16 

0.1835 

4 



.23536 

.OO7O7 

5 

Antimony:  ||  to  axis  
_L  to  axis  

40 
40 

0.1692 
0.0882 

I 

I 

— 

Mean.           

40 

o.  1152 

I 

o.  1056 

.0923 

.OI32 

6 

Arsenic 

40 

o  0559 

I 

Bismuth:  ||  to  axis 

40 

o.  1621 

I 

_L  to  axis  

40 

O.I  208 

I 









Mean               .      ,  . 

40 

o.  1346 

I 

o.  1316 

.1167 

.OI49 

6 

Cadmium 

40 

o  .  3069 

I 

0.3159 

.2693 

.0466 

6 

Carbon:  Diamond 

40 

0.0118 

I 

Gas  carbon  
Graphite      

40 
40 

0.0540 
0.0786 

I 
I 

— 

.0055 

.00l6 

13 

Anthracite 

40 

o  2078 

I 

Cobalt  

40 

o.  1236 

I 









Copper  

40 

0.1678 

I 

0.1666 

.1481 

.Ol85 

6 

—  191  to  -|-i6 

o  1409 

4 

.  16070 

.00403 

5 

Gold  

40 

o.  1443 

i 

o.  1470 

•  1358 

.0112 

6 

—  170 

o  117 

15 

40 

o  4170 

I 





.  . 

Irirlium  
Iron:  Soft    . 

I48 
40 

0.088 

O    I2IO 

16 
i 

0.090 

— 



16 

Cast 

i 



Cast  

—  IQI  to  +16 

o  oS^o 

4 







Wrought  . 

—  18  to  100 

7 

.  11705 

.005254 

8 

Steel 

i 

09173 

.008336 

8 

Steel  annealed  
Lead 

40 
40 

0.1035 

i 

i 

0.1089 

.1038 
•  273 

.0052 
.OO74 

9 

6 

Lead  (cast) 

Magnesium  .  .  . 

40 

i 

o  261 



16 

Nickel 

40 

i 

13460 

.003315 

8 

16 

Osmium  

40 

i 



Palladium 

40 

11670 

.OO2l87 

8 

Platinum  

40 

i 

08868 

.001324 

8 

Potassium    . 

0-50 

Ruthenium  

40 

i 





Selenium      .  . 

40 

o  3680 

_ 

12 

Silicon 

Silver  

40 

18270 

.  OO4793 

8 

o  189 

1  6 

2    26 

Sulphur:  Cryst.  mean  
Tellurium.  .. 

40 

0.6413 

i 

1.180 
o  ^68? 

— 

— 

12 

Tin 

•  3 

,. 

6 

Zinc      

? 

o.  2290 

6 

Zinc  (cast) 

•   97 

References:  (i)  Fizeau;  (2)  Calvert,  Johnson  and  Lowe;  (3)  Chatelier;  (4)  Henning;  (5)  Dittenberger; 
(6)  Matthiessen;  (7)  Andrews;  (8)  Holborn-Day;  (9)  Benoit;  (10)  Pisati  and  De  Franchis;  (n)  Hagen;  (12) 
Spring;  (13)  Day  and  Sosman;  (14)  Griffiths;  (15)  Dorsey;  (16)  Griineisen. 

Tungsten:  (L  -  Lo)/Lo  =  4.44  X  io~«(r  -  300)  +  45  X  io~"(r  -  300)"  +  2.20  X  io~l3(T  -  300)'.  Lo  =  length 
at  300°  K.  Coefficient  at  300°  K  =  4.44  X  io~*;  1300°  K,  5.19  X  IQ-«;  2300°  K,  7.26  X  ie>-«.  Worthing,  Phys.  Rev. 
1917- 


Molybdenum:     Li  =  L*(i  +  5.151  X  io~«  +  0.00570**  X  io-«),  for  19°  to  -142°  C; 
0.00138*  X  io-«J,  for  io8Jto  +  305°  C;    Schad  and  Hidnert,  Phys.  Rev.  1919. 


The  Holborn-Day  and  Sosman  data  are  for  temperatures  from  20°  to  1000°  C. 
SMITHSONIAN  TABLES 


Lo(i+  s.oi/X  10-0 
The  Dittenberger,  o°  to  600°  C. 


TABLE  239. 
LINEAR  EXPANSION  OF  MISCELLANEOUS  SUBSTANCES. 


2IQ 


The  coefficient  of  cubical  expansion  may  be  taken  as  three  times  the  linear  coefficient.    /  is  the  temperature  or  range 
of  temperature,  C  the  coefficient  of  expansion,  and  A.  the  authority. 


Substance. 

1 

CX  io« 

A. 

Substance. 

t 

CX  io« 

A. 

Brass: 
Cast  
Wire  

o-ioo 

40 
o-ioo 

16.6-100 
16.6-350 

16.6-957 

40 
0-80 

16.7-25-3 
4-29 
25.3-35.4 
o-ioo 

50-60 
o-ioo 

—  191  to  +  16 

20 

—  20  to  —  i 
°78° 

o-ioo 
12-39 

15-100 
0-16 
16-38 
38-4Q 

40 

0.1875 
0.1930 
•i  783--  193 

0.1859 
0.1906 

0.1844 
0.2116 

0.1737 
0.1782 
0.1713 

o.  1708 

0.657-0.686 
0.770 
0.1523 
0.842 
o.  1950 
0.1836 

0.1523 
0.1552 

0.0833 
0.0828 
0.0891 
0.0897 
0.0954 
0.0788 

0.081 

0.058 
0.424 
1.983 
0.51 

0.2631  * 
0.0544 

0.2508 
0.238 
0.181 
0.117 
1.0662 
i  •  3030 
4.7707 

0.0884 

i 
i 

2 

3 
4 

5 
5 

5 

3 
6 
6 

2 

7 

1 

8 
4 

4 

I 
9 

10 

10 
II 
II 

12 

12 
13 
14 

IS 

6 
6 

i 
16 

i 

18 
18 

3 

Platinum  -silver: 

I  Pt  +   2Ag 

o-ioo 

20-700 

1000-1400 

0-80 

—  100  to  +  16 
0-80 
—  190  to  •+•  16 
16  to  500 
16-1000 

$ 

-160 
o-ioo 

16.6-254 
0-18 
o-ioo 

2.34 

10-26 
26-31 
31-43 
43-57 

o  1523 
0.0413 
0-0553 

0.0797 
0.0521 
0-1337 
—0.0026 
0.0057 
0.0058 
o  .  4040 
0.691 
0.300 
0.1933 

0.0832 
0.0836 
0.0472 

0.0937 
0.0773 

0  '°l2 

0.6300 
0.0800 

0.0951 
0.0257 

o  .  0649 
0.0565 
0.0361 
0.0638 
0.0492 
0.0541 
0.0658 

0.614 

0.325 

0-443 
0.404 
0.484 
0-544 
0-341 
0.484 
2.300 
3.120 
4.860 
15.227 

4 
19 
20 

6 

21 

6 

13 
26 
26 

3 
27 

27 

i 

8 
8 
8 

8 

8 
5 

22 
5 

23 
24 
24 
24 
24 
24 
24 
24 

24 

24 

24 
24 
24 

24 

24 
24 
24 
25 
25 
25 
25 

Porcelain  
Bayeux.  . 
Quartz: 
Parallel  to  axis  .  .  . 

Perpend,  to  axis... 
Quartz  glass  

Rock  salt...'..'.'.'.'.' 
Rubber,  hard  

Speculum  metal  
Topaz: 
Parallel    to    lesser 
horizontal  axis.  .  . 
Parallel  to  greater 
horizontal  axis.  .  . 
Parallel  to  vertical 
axis 

71.5  Cu4-  27.7  Zn  + 
o.aSn  +  o.sPb..  . 
71  Cu  +  29  Zn. 

Bronze: 
3  Cu  +  i  Sn  

86.3  Cu  +  9.7'  Sn  + 
4  Zn                 

«-6  Cu  +  l/hard 

Ef+|U 

Caoutchouc  

Constantan     

Ebonite  

Tourmaline: 
Parallel    to    longi- 
tudinal axis  
Parallel  to  horizon- 
tal axis  
Type  metal  
Vulcanite 

Fluor  spar:  CaFi  .... 

Gold-platinum: 
2  Au  +  i  Pt 

Gold-copper: 
2  Au  +  i  Cu  

Glass: 
Tube  

Wedgwood  ware.  .  . 
Wood: 
Parallel  to  fiber: 
Ash  
Beech 

Plate  
Crown  (mean)  

Chestnut  
Elm  
Mahogany  
Maple  
Oak 

Flint 

Jenather-|i6IU      \ 
mometer  1  normal  / 

59m-... 

Gutta  percha  
Ice  

Pine  
Walnut  
Across  the  fiber: 
Beech  
Chestnut  
Elm  

Iceland  spar: 
Parallel  to  axis  
Perpendicular  to  axis 
Lead-tin       (solder) 
2  Pb  4-  i  Sn 

Mahogany  
Maple 

Oak... 

Magnalium  

Pine..'  
Walnut 

Marble 

Wax:  White  

Paraffin    

Platinum-indium 
10  Pt  +  i  Ir  

References: 

(i)  Smeaton.                       (8)  Pfaff.                                           (15)  Mean. 
(2)  Various.                        (9)  Deluc.                                          (16)  Stadthagen. 
(3)  Fizeau.                        (10)  Lavoisier  and  Laplace.               (17)  Frohlich. 
(4)  Matthiessen.               (u)  Pulfrich.                                      (18)  Rodwell. 
(5)  Daniell.                        (12)  Schott.                                           (19)  Braun. 
(6)  Benoit.                        (13)  Henning.                                      (20)  Deville  and  Troost. 
(7)  Kohlrausch.                 (14)  Russner.                                        (21)  Scheel. 

(22)  Mayer. 
23)  Glatzel. 
24)  Villari. 
25)  Kopp. 
26)  Randall. 
(27)  Dorsey. 

SMITHSONIAN  TABLES. 


32O 


TABLE  24O. 
CUBICAL  EXPANSION  OF  SOLIDS, 


If  vz  and  v\  are  the  volumes  at  /2  and  t\  respectively,  then  7/2  =  ^(1  +  C&t),  C  being  the 
coefficient  of  cubical  expansion  and  A/  the  temperature  interval.  Where  only  a  single  temperature 
is  stated  C  represents  the  true  coefficient  of  cubical  expansion  at  that  temperature.* 


Substance. 

t  or  A/ 

CX  io« 

Authority. 

Antimony    

O-IOO 

0.3167 

Matthiessen 

Beryl        .     .     . 

O-IOO 

O.OICK 

Pfaff 

Bismuth 

O-IOO 

0.^048 

Matthiessen 

Copper    
Diamond      .... 

O-IOO 
40 

0.4998 

O.OK4 

Fizeau 

Emerald  . 

40 

0.0168 

Galena 

O—  IOO 

0.  q  q8 

Pfaff 

Glass,  common  tube  .     . 
"         hard  

O-IOO 
O-IOO 

0.276 

0.214 

Regnault 
it 

"         Jena,  borosilicate 
59I1I      .     .     . 
pure  silica  .     .     . 
Gold    

2O-IOO 

0-80 

O-IOO 

0.156 
0.0129 

0.4411 

Scheel 
Chappuis 
Matthiessen 

Ice  . 

—  ->o  1 

1.1250 

Brunner 

Iron 

O—  IOO 

O  7CCO 

Dulong   and   Petit 

Lead   
Paraffin        

O-IOO 
20 

0.8399 
588 

Matthiessen 
Russner 

Platinum      ... 

O-IOO 

J.UU 

o  ^65 

Dulong   and    Petit 

Porcelain,  Berlin  .     .     . 
Potassium  chloride   .     . 
nitrate      .     . 
"            sulphate  .     . 
Quartz 

20 

O-IOO 
O-IOO 

20 

O—  IOO 

0.0814 

1.094 

1.967 

1-0754 

o  ^840 

Chappuis  and  Marker 
Playfair  and  Joule 

Tutton 
Pfaff 

Rock  salt     

co-6o 

121  ''O 

Pulfrich 

Rubber              .... 

20 

487 

Silver            

O—  IOO 

t+.u/ 

o  cS^i 

Sodium 

•'O 

^-y^j1 

2  I  T.6)A 

Stearic  acid 

•}•>  8  4.C  c 

*•  i  jU4 

C     r 

Sulphur,  native     .     .     . 
Tin           .... 

JJ'°    45-i 

i3-2-5°-3 

O—  IOO 

2.23 

06889 

Zinc     

O-IOO 

o  8928 

(i 

*  For  tables  of  cubical  expansion  complete  to  1876,  see  Clark's  Constants  of  Nature,  Smithsonian  Collections,  280. 
SMITHSONIAN  TABLES. 


TABLE  241.  221 

CUBICAL   EXPANSION   OF  LIQUIDS. 

If  V0  is  the  volume  at  o°  then  at  t°  the  expansion  formula  is  Vt  =  V0  (i  +  at  +  ftfl  +  7/8). 
The  table  gives  values  of  a,  0  and  y  and  of  C,  the  true  coefficient  of  cubical  expansion,  at  20° 
for  some  liquids  and  solutions.  A/  is  the  temperature  range  of  the  observation  and  A  the 

authority. 


Liquid. 

u 

a  lo3 

/3io« 

YIO* 

Cl03 

at  20° 

A 

Acetic  acid 
1  Acetone 
i  Alcohol  : 
Amyl 
Ethyl,  30%  by  vol.      .     . 
"       50%         "          •     • 
"      99-3%    "         •    - 
"       500  atmo.  press.  . 
"     3000      "          "      . 
Methyl      
Benzene  ....... 

16-107 

0-54 

—  15-80 
18-39 

o-39 
27-46 
0-40 
0-40 
0-61 
11-81 
o-59 

18-25 
17-24 
—34-60 
0-50 
0-50 
0-76 
0-63 
-15-38 

o-33 

O-IOO 

o-33 

16-25 
36-157 

24-120 
0-29 
11-40 

0-30 
0-30 
—  9-106 
o-33 

1.0630 
1.3240 

0.9001 

0.2928 
0.7450 
I.OI2 

0.866 
0.524 
1.1342 
1.17626 
1.06218 

0.07878 
0.42383 
1.13980 
0.940 
0.581 
1.18384 
1.10715 
1-51324 
0-4853 

0.4460 
0.18182 
0.6821 
1.4646 

0.2695 
0.8340 

0.8994 
0.3640 

0-3599 

0.2835 

0-5758 
0.9003 
—0.06427 

0.12636 

3.8090 

0.6573 
10.790 

1.85 

2.20 

1.3635 
1.27776 
1.87714 

4.2742 
0.8571 
L37065 

0.89881 
4.66473 
2.35918 
0.4895 

0.215 
0.0078 
1.1405 

3-°93I9 

2.080 
0.10732 

1.396 
1.237 
1.258 

2.580 
—0.432 
1-9595 
8.5053 

1.0876 
—0.87983 

1.18458 
—11.87 
0.730 

0.8741 
0.80648 
—0.30854 

1.91225 

1:35*35 

—1.74328 
4.00512 

0.4446 

—0.44998 
—6.7900 

1.071 
1.487 

0.902 
1.  12 

I.I99 

1-237 
I.I32 

0.250 
0.458 
I.2I8 

1.236 

»-*73 

1.656 

0-505 

o-455 
0.18186 
0.721 
i.  608 

0-353" 
1.090 

0-955 
0.414 
0.410 

0.387 
0-558 
0-973 
0.207 

3 
3 

4a 
6 
6 
6 
i 
i 
5* 
5a 

2 

7 
7 
4* 
i 
i 
4b 
4b 
4a 
8 

9 
U 

10 

M 

7 
n 

12 

9 
9 
9 

Ib 

13 

1  Calcium  chloride  : 
5.8%  solution    .     .     . 

40.9%         "          •     •     • 
1  Carbon  disulphide    .     .     . 
500  atmos.  pressure 
3000       " 
Carbon  tetrachloride     ,     . 
'  Chloroform           .... 

1  Ether 

Hydrochloric  acid  : 
33.2%  solution  .... 
Mercury            

Qlj-yg   oil 

Pentane  

Potassium  chloride  : 
24.3%  solution  .... 
Phenol     .     ;     

Petroleum  : 
Density  0.8467  .... 
Sodium  chloride  : 
20.6%  solution  .... 
Sodium  sulphate  : 
24%  solution      .... 
Sulphuric  acid  : 
10.9%  solution  .... 

IOO  O% 

Turpentine 

Water      

AUTHORITIES. 
i.  Amagat:  C.  R.  105,  p.  1120;  1887.                    9.  Marignac:  Lieb.  Ann.,  Supp.  VIII,  p.  335; 
2.  Thorpe  :  Proc.  Roy.  Soc.  24,  p.  283;  1876.                    1872. 
3.  Zander:  Lieb.  Ann.  225,  p.  109;  1884.             10.  Spring:  Bull.  Brux.  (3)  3,  p.  331  ;  1882. 
4.  Pierre:  a.  Lieb.  Ann.  56,  p.  139;  1845.           n.  Pinette  :  Lieb.  Ann.  243,  p.  32;  1888. 
b.  Lieb.  Ann.  80,  p.  125;  1851.          12.  Frankenheim  :    Pogg.    Ann.    72,    p.  422; 
I  5.  Kopp  :  a.  Lieb.  Ann.  94,  p.  257;  1855.                         1847. 
b.  Lieb.  Ann.  93,  p.  129;   1855.            13.  Scheel:  Wiss.  Abh.  Reichsanstalt,  4,  p.  i; 
6.  Reel-enamel  :  Sitzber.  bayr.  Ak.  p.  327,   2                   1903. 
Abt.  ;  1866.                                                       14-  Thorpe  and    Jones:    J.   Chem.   Soc.   63, 
7.  Drecker  :   Wied.  Ann.  34,  p.  952  ;    1888.                      p.  273  ;   1893. 
8.  Emo:  Ber.  Chem.  Ges.  16,  1857;  1883. 

SMITHSONIAN  TABLES. 


222 


TABLE  242. 
COEFFICIENTS   OF  THERMAL   EXPANSION, 

Coefficients  of  Expansion  of  Gases. 
Pressures  are  given  in  centimeters  of  mercury. 


Coefficient  at  Constant  Volume. 

Coefficient  at  Constant  Pressure. 

Coeffi- 

X 

Coeffi- 

CJ 

Substance. 

Pressure 
cm. 

cient 
X 

j 

Substance. 

Pressure 
cm. 

cient 
X 

1 

IOO. 

c2 

100. 

*»; 
Qg 

Air         ... 

.6 

•37666 

i 

Air          ... 

76. 

•3671 

3 

. 

1.3 

•37172 

" 

. 

257- 

•3693 

ii 

IO.O 

.36630 

" 

"    0°-IOO°      . 

100.  1 

.36728 

2 

"           ... 

25-4 

.36580 

" 

Hydrogen    o°-ioo° 

IOO.O 

.36600 

" 

"           ... 

75-2 

.36660 

" 

"... 

200  Atm. 

•  H2 

9 

"    0°-IOO°      . 

100.  1 

•36744 

2 

"... 

400      "       |  .29  s 

"            ... 

76.0 

.36650 

3 

"... 

600      " 

.261 

« 

. 

2OO.O 

.36903 

it 

800      " 

.242 

" 

"               ... 

2OOO. 

.38866 

" 

Carbon  dioxide 

76. 

3 

"            ... 

IOOOO. 

4100 

it 

"      0°-20° 

51.8 

.37128 

2 

Argon    . 
(  urbon  dioxide 

76.0 

.3668 
.36856 

4 
3 

"    o°-40° 

"      0°-IOO° 

51.8 
51.8 

.37100 
•37°73 

It 

"         " 

1.8 

•36753 

i 

"      0°-20° 

99-8 

.37602 

" 

5.6 

.36641 

1C 

"      0°-IOO° 

99-8 

•37410 

M 

74-9 

•37264 

" 

"      0°-20° 

'37-7 

•37972 

0°-20°* 

51-8 

.36985 

2 

"      0°-IOO° 

•37/03 

o°-40° 

51.8 

it 

«        «    o°-7.5° 

2621. 

.1097 

6 

0°-IOO° 

51-8 

.36981 

it 

"  64°-  1  00° 

2621. 

•6574 

" 

0°-20° 

99-8 

•37335 

" 

Carbon  monoxide  . 

76. 

.3669 

3 

0°-IOO° 

99.8 

.37262 

Nitrous  oxide 

76. 

•3719 

"    0°-IOO° 

Carbon  monoxide  . 

IOO.O 

76. 

'16667      i 

Sulphur  dioxide     . 
it              (« 

76. 
98. 

•3903 
•3980 

*' 

Helium  . 

56.7      .3665" 

4 

O°-  T  I  Q° 

76. 

.4187 

10 

Hydrogen  i6°-i32° 

"            !£lT« 

.0077  .3328 
•025  1.3623 

6    i 

w*<-    £!£ 

i/o  r\r*v 

76. 

76. 

.4189 
.4071 

tt 

•47 

.3656 

" 

VapOl                   QO.^QQO 

76. 

•3938 

« 

ii 

•93 

.37002 

i 

0°-2470 

76. 

•3799 

ii 

. 

II.  2 
s 

.36548      " 

•                 •                 • 

76.4 

.36504      " 

0°-IOO° 

Nitrogen    13°-  13  2° 

IOO.O 

.06 

.36626          2 

.3021        6 

Thomson  has  given,  Encyc.  Brit.  "  Heat," 
the  following  for  the  calculation  of  the  ex- 

0°-20° 
0°-IOO° 

•53 

100.2 
IOO.2 
~>f\ 

.3290 

•36754         2 

pansion,  E,  between  o°  and  ioo°C.   Expansion 
is  to  be  taken  as  the  change  of  volume  under 
constant  pressure  : 

Oxygen  u°-i32°    . 
«        x?o"!320    ' 

70. 
.007 

ci 

.4161        6 

.3984        M 
7871 

Hydrogen,  E  =  .3662(1  —  .00049  F/z/), 
Air,             E  =  .3662(  i  —  .0026  V/v), 
Oxygen,       h  =  .3662(1  —  .0032    F/z>), 

(i 

O 

'7668; 

8 

Nitrogen,    E  =  .  3662(1  —  .0031    F/z>), 

! 

18^5 

•  j'J'J0.> 
.36600 

CO2             £  =  .3662(1—  .0164   V/v). 

Nitrous  oxide 
Sulph'r  dioxide  SOs 

75-9 
76. 
76. 

.36681 
•3676 
•3845 

2 

V/v  is  the  ratio  of  the  actual  density  of  the 
gas  at  o°  C  to  what  it  would  have  at  o°  C  and 
i  Atm.  pressure. 

i    Meleander,  Wied.  Beibl.  14,  1890;  Wied.           5  Chappuis,  Arch.  sc.  phys.  (3),  18,  1892. 

Ann.  47,  1892.                                                      6  Baly-  Ramsay,  Phil.  Mag.  (5),  38,  1894. 
2  Chappuis,  Trav.  Mem.  Bur.  Intern.  Wts.           7  Andrews,  Proc.  Roy.  Soc.  24,  1876. 

Meas.  13,  1903.                                                    8  Meleander,  Acta  Soc.  Fenn.  19,  1891. 

3  Regnault,  Ann.  chim.  phys.  (3)5,  1842.                9  Amagat,  C.  R.  in,  1890. 
4  Keunen-Randall,  Proc.  R.  Soc.  59,  1896.          10  Him,  Theorie  mec.  chaleur,  1862. 

SMITHSONIAN   TABLES. 


TABLE  243. 
SPECIFIC    HEAT   OF   THE   CHEMICAL   ELEMENTS- 


223 


Element. 

Range  *  of 
temperature, 
°C 

Specific 
heat. 

Refer- 
ence. 

Element. 

Range  *  of 
temperature, 

Specific 
heat. 

Refer- 
ence. 

Aluminum  . 

—  240.  6 

0092 

45 

Cobalt  

500 

18 

—  190  o 

0889 

45 

IOOO 

18 

« 

—  73-O 

190 

46 

« 

—182  to  +15 

0822 

" 

—  IQO  tO    —82 

.1466 

47 

« 

15-100 

.  1030 

<< 

—  76  to  —  i 

1962 

47 

Copper  t  . 

—  249.5 

0035 

<(        

+16  to  +100 
+16  to  +304 

.2122 

$ 

48 

-223 
—  185 

.0208 

O?32 

lo 

„        

-250 

.1428 
2089 

" 

-63 
+  25 

.0865 

46 

"        

IOO 

.2226 
2382 

" 

76 
84 

•0937 
OO^8 

51 

« 

500 

« 

IOO 

" 

16-100 

2122 

4 

« 

362 

.0997 

51 

Antimony  

15 

0489 

« 

900 

1259 

IOO 

0503 

» 

15-238 

.O95I 

43 

« 

ti 

—  181  to  13 

0868 

Arsenic,  gray  

O—  IOO 

O822 

3 

« 

23—100 

Arsenic,  black  
Barium  
Bismuth  

o-ioo 

—  l85  tO   +20 

-186 
o 

.0861 
.068 
.0284 
O3OI 

3 
4 

I 

Gallium,  liquid.  .  . 
solid  
Germanium  
Gold.  .  . 

12  tO  113 

12-23 

o-ioo 
—  185  to  +20 

.080 
-079 
•0737 

03? 

22 
22 
23 

„       

75 

20-IOO 

0309 
.O3O2 

6 

7 

Indium  .  .    . 

o-ioo 
o—  ioo 

.O3IO 

0570 

24 
13 

"       fluid 

280—380 

8 

Q^ge 

Boron  

o-ioo 

•307 

9 

—  191  to  —80 
9—98 

•0454 

49 

« 

—  76  to  —  o 

1677 

47 

Iridium 

—  186  to  +18 

O282 

26 

Bromine,  solid  

—  78  tO    —20 

.0843 

10 

18-100 

.O323 

26 

solid  

—  192  to  —80 

.0702 

49 

Iron  

—  223 

.0176 

46 

fluid  

13-45 

.  IO7 

ri 

-163 

.O622 

46 

Cadmium  

—  223 

.O308 

46 

< 

-63 

.  0961 

46 

—  173 

0478 

46 

< 

+37 

IO92 

46 

;•    ;::::::::: 

-73 

21 
IOO 

•0533 
•0551 

0570 

46 

2 
2 

cast  
wrought  

20-100 
15-100 

IOOO—  I  2OO 

.1189 
.1152 
I080 

27 
28 
28 

Caesium  
Calcium  

200 
300 
0-26 
—  l8S  tO   +20 

0-181 

•0594 
.0617 
.0482 
•157 
I7O 

2 
2 
12 

4 
13 

wrought  
hard-drawn  .  . 
hard-drawn.  . 

500 
0-18 

20-IOO 
—  185  tO   +20 
O  tO   +2OO 

.176 
.0986 
.1146 
.0958 
1175 

28 
29 
29 
4 
53 

Carbon,  graphite.  .  . 

—  191  to  —79 
—  76  to  —  o 

•0573 

•  I2SS 

47 

47 

'     

o  to  +300 
o  to  +400 

.1233 
.1282 

53 
53 

::      ::  ::: 

-50 
+11 
977 

.114 
.160 
467 

14 
14 
14 

'  ::::::::::::: 

o  to  +500 
o  to  +600 
o  to  +700 

.1338 
.1396 
.1487 

53 
53 

53 

«           « 

1730 

•  5° 

52 

' 

o  to  +800 

.1597 

53 

/  -244 

.  005 

50 

< 

o  to  +900 

.1644 

53 

Acheson 

\  —  186 

027 

50 

« 

o  to  +1000 

•  *557 

53 

Carbon,  diamond  .  .  . 

—  50 

.0635 

47 

« 

0  tO   +1100 

.1534 

53 

Cerium 

+n 
985 
o—  100 

.113 
•  459 

0448 

47 
47 
15 

Lanthanum  
Lead  

o-ioo 
—250 
—236 

.0448 
•  0143 
0217 

IS 
46 
46 

Chlorine,  liquid  .... 

0-24 

2262 

16 

—  193 

.0276 

46 

Chromium  

—  2OO 

0666 

17 

i 

—  73 

.0295 

46 

17 

, 

15 

0299 

«< 

IOO 

II2I 

17 

i 

IOO 

.0311 

2 

„         

600 

—  185  to  +20 

.1872 
086 

17 

"     '  flu'id  

300 

310 

•  0338 

2 

3° 

*When  one  temperature  is  given,  the  "true"  specific  heat  is  indicated,  otherwise  the  "mean"  specific  heat. 

1 0.3834  +  o.ooo2o(/  —  25)  intern,  j  per  g   degree  =  0.0917  +  0.000048 (*  —  25)  cabo  per  g  degree.      (Griffith, 
1913-) 
SMITHSONIAN  TABLETS. 


224 


TABLE  243  (continued). 
SPECIFIC    HEAT    OF    THE    CHEMICAL    ELEMENTS- 


Element. 

Range  *  of 
temperature, 

^ 

Refer- 
ence. 

Element. 

Range  *  of 
temperature, 

Specific 
heat. 

Refer- 
ence. 

Lead 

90 

2IO 

18-100 
16-256 

—  191  tO   —SO 

—  78  to  o 

-75  to  +19 

—  100 

o 
So 

IOO 
IQO 

—  185  to  +20 
60 
325 
625 

20-IOO 

-i88to  -79 
—  79  to  +15 
60 
325 

20-IOO 
—  IOO 
0 
IOO 

-77  to  -42 
—36  to  —3 
—  185  to  +20 

0 

85 

IOO 

250 

—  185  tO  +20 

60 
475 

20  tO  IOO 

—  185  to  +20 

IOO 
300 
500 
1000 

18-100 
19-98 

-i86to  +18 
o-ioo 
0-1265 

°-5  1 

13-36 
—  186  to  +20 
-186  to  +18 

IOO 

200 
500 
750 

IOOO 

1300 

2O-IOO 

20-500 

20-IOOO 

20-1300 

0.0312 

0.0334 

0.0310 
0.0319 
0.521 

0.595 

0.629 
0.5997 
0.7951 
0.9063 
I  .  0407 
1.3745 

O.222 
0.2492 
0.3235 
0-4352 
0.2492 
0.0820 

o.  1091 

0.  I2II 
0.1783 
O.I2II 
0.0979 

o.  1072 
O.H43 
0.0329 
0.0334 
0.032 
0.03346 
0.0328 
0.03284 
0.03212 
0.062 
0.0647 
0.0750 
o  .  0647 
0.092 
o.  1128 
o.  1403 

0.1299 

0.1608 
0.109 
0.0311 
0.0528 
0.0592 
0.0714 
o.  1829 

O.2O2 
0.178 
0.0293 
0.0275 
O.0330 
0.0349 
0.0365 
O.038I 
0.0400 
0.0319 
0.0333 
0.0346 
0.0359 

Si 
51 
43 
43 
47 
47 
47 
31 
3i 
3i 
3i 
31 
4 
7 
7 
7 
7 
49 
49 
49 
49 
49 
31 
31 
31 
47 
47 
4 
32 
32 

2 
2 

4 
7 
7 
7 
4 
18 
18 
18 
18 
26 

10 

26 
24 
24 
33 
33 
4 
26 
34 
35 
35 
35 
35 
35 
35 
35 
35 
35 

Potassium  

—  191  to  —80 
—  78  too 
—  185  to  +20 
10-97 

0 

o-ioo 
-188  to  +18 
—  185  to  +20 
-39  8 
+57-1 
232 
-238 
-213 
—  173 

+8 

o-ioo 

23 
IOO 

500 
17-507 
800 

007-1100 

—  185  tO   +20 

—  191  to  —83 

-77  to  o 
—  223 
-183 
-188  to  +18 
o-54 
0-52 
119-147 

—  185  tO   +20 
I4OO 

—  188  to  +18 
15-100 

—  185  tO  +20 
20-100 
O-IOO 

—  196  to  —79 
—  76  to  +18 
21-109 

250 

IIOO 
—  185  tO  +20 

o-ioo 

—  185  tO   +20 

o-ioo 

IOOO 
2000 

2400 
0-98 

0    -IOO 

-243 
—  193 
-153 

20-100 
IOO 

300 

o-ioo 

0.1568 
0.1666 
o.  170 
0.0580 
0.0802 
0.0611 
0.068 
0.123 
o.  1360 
0.1833 
o.  2029 
0.0146 
0.0307 
0.0447 
0.0540 
0.0560 
0.0559 
0.05498 
0.05663 
0.0581 

0.05987 

0.076 
0.0748 
0.253 
0.243 
0.276 
0.152 
0.219 
0.137 
0.1728 

o.  1809 

0.235 
0.033 
0.043 
0.047 
0.0483 

0.038 
0.0326 
0.0276 
0.0486 
0.0518 
0.0551 
0.05799 
0.0758 
0.082 
0.1125 
0.036 
0.0336 
0-0337 
0.042 
0.045 
0.028 
O.H53 
0.0144 
0.0625 
0.0788 
0.0931 
0.0951 
o.  1040 
o  .  0660 

47 
47 
4 
25 

13 
36 
4 
14 
14 
14 
46 
46 
46 
46 
46 
13 

2 
2 

34 
43 
18 
18 
4 
47 
47 
46 
46 
36 
33 
33 

2 

4 

36 
37 

4 

3 

26 
26 
30 
18 
18 
4 
39 
4 
40 
52 

52 

52 
41 
4° 
46 
46 
46 
27 

2 
2 
42 

(i    

Rhodium 

Lithium  

Rubidium  
Ruthenium  
Selenium  
Silicon  .  . 

,     ;;;;  

Silver  .  '.  

i 

Magnesium  

H 

i< 

4I     

Manganese  

;  ::::::::::: 

4     'fluid!!!!!! 
Sodium  

"          

«i 

Mercury,  sol  
"         lici 

tl     

Sulphur  
rhombic  . 
"       monoclin. 
liquid  .  .  . 
Tantalum  

Molybdenum  

Nickel  '.'.'.:: 

Tellurium  
"         crys.  .  . 
Thallium  

Thorium 



Tn  

cast  
'      fluid  
'      fluid 

Osmium  
Palladium 

Titanium  

Phosphorus,  red.  .  . 
yellow, 
yellow. 
Platinum  

Tungsten  

lt        

••    ::::::::: 

Vanadium  
Zinc 

"    

M 

ii 

::    ::::::::: 

M 

M 

Zirconium  

*  When  one  temperature  is  given,  the  "true"  specific  heat  is  indicated,  otherwise  the  "mean"  specific  heat.    See 
page  226  for  references. 

SMITHSONIAN  TABLES. 


TABLE  244. 

HEAT  CAPACITIES.   TRUE  AND   MEAN   SPECIFIC   HEATS.   AND 
LATENT   HEATS  AT  FUSION. 


225 


The  following  data  are  taken  from  a  research  and  discussion  entitled  "Die  Temperatuiv 
Warmeinhaltskurven  der  technisch  wichtigen  Metalle,"  Wiist,  Meuthen  und  Durrer,  For- 
schungsarbeiten  herausgegeben  vom  Verein  Deutscher  Ingenieure,  Springer,  Heft  204,  1918. 

(a)  There  follow  the  constants  of  the  equation  for  the  heat  capacity:  W  =  a  +  bt  +  cf2;  for 
the  mean  specific  heat:  5  =  at~l  +  b  +  ct;  and  for  the  true  specific  heat:  s'  -  b  +  ict\  also  the 
latent  heats  at  fusion.  (See  also  Table  243,  pp.  223-224.) 


Ele- 
ment. 

Tempera- 
ture 
range. 

a 

b 

c  X  io« 

La- 
tent 
heat. 

cal./g 

Ele- 
ment. 

Tempera- 
ture 
range. 
°C 

a 

b 

cXio« 

La- 
tent 
heat 
cal./g. 

Cr 

0-1500 



o.  10233 

33-47 

_ 

Ag 

0-961 

_ 

0.05725 

5.48 

26.0 

Mo 

0-1500 

— 

0.06162 

10.99 

— 

961-1300 

53-17 

0.00710 

28.30 

— 

W 

0-1500 

— 

0.03325 

1.07 

—  - 

Au 

0-1064 

0.03171 

1.30 

15-9 

Pt 

0-1500 

— 

0.03121 

3-54 

-  — 

1064-1300 

26.35 

0.01420 

8.52 

Sn 

0-232 

— 

0.06829 

13.8. 

Cu 

0-1084 

o.  10079 

3.05 

41.0 

232-1000 

14-33 

0.07020 

-18.30 

1084-1300 

130.74 

-.04150 

65.6 

Bi 

0-270 

0.03141 

5-22 

IO.2 

Mn 

0-1070 

0.12037 

25.41 

36.6 

270-1000 

10.31 

0.03107 

5-41 



II3O-I2IO 

-7.41 

0.17700 

— 

24.14* 

Cd 

0-321 

— 

0.05550 

6.28 

10.8 

1230-1250 

3-83 

o.  19800 

— 

— 

32I-IOOO 

6.30 

0.06952 

6-37 

— 

Ni 

0-320 

o.  10950 

52.40 

56.1 

Pb 

0-327 

— 

0.03591 

-11.47 

5-47 

330-1451 

0.41 

0.12931 

O.II 

1-33* 

327-1000 

6.07 

0.02920 

3-30 

— 

1451-1520 

50.21 

0.13380 

— 

— 

Zn 

0-419 

— 

0.08777 

43.48 

23.0 

Co 

0-950 

— 

0.09119 

40.77 

58.2 

419-1000 

14-34 

0.13340 

—  16.  10 

1100-1478 

22.OO 

o.i  1043 

14-57 

14.70* 

Sb 

0-630 

0.05179 

3.00 

38.9 

1478-1600 

57-72 

o.  14720 

— 

630-1000 

39-42 

0.05090 

2.96 

— 

Fe 

0-725 

o.  10545 

56.84 

49-4 

Al 

0-657 

— 

O.  222OO 

38.57 

94.0 

785-919 

-I.63 

0.1592 

— 

6.56* 

657-1000 

102.39 

0.21870 

24.00 

— 

919-1404 

18.31 

0.14472 

0.05 

6.67* 

1405-1528 

-77-18 

o.  21416 

— 

1.94* 

1528-1600 

70.03 

0.15012 

*  Allotropic  heat  of  transformation:   Mn,  1070-1130°;   Ni,   320-330°;   Co,  950-1100°;   Fe, 

725-785°;  9*9°  *  i;  1404-5°  *  0.5. 

(b)  TRUE  SPECIFIC  HEATS. 


°c 

Pb 

Zn 

Al 

Ag 

Au 

Cu 

Ni 

Fe 

Co 

Quartz. 

o°C 

0-0359 

0.0878 

O.  222O 

0.0573 

0.0317 

0.1008 

0.1095 

0.1055 

0.0912 



100 

0.0336 

0.0965 

o.  2297 

0.0583 

0.0320 

o.  1014 

0.1200 

O.II68 

0.0993 

0.2372 

2OO 

0.0313 

o.  1052 

0.2374 

0.0594 

0.0322 

O.  IO2O 

0.1305 

o.  1282 

0.1073 

0.2416 

300 

0.0290 

O.II39 

0.2451 

0.0605 

0.0325 

o.  1026 

0.1409 

0.1396 

0.1154 

o.  2460 

4OO 

0.0266 

o.  1226 

0.2529 

0.0616 

0.0328 

0.1032 

0.1294 

0.1509 

0.1235 

0.2504 

500 

0.0259 

0.1173 

o.  2606 

0.0627 

0.0330 

o.  1038 

0.1294 

0.1623 

0.1316 

0.2548 

600 

0.0252 

o.  1141 

0.2683 

0.0638 

0.0333 

0.1045 

0.1294 

0.1737 

0.1396 

0.2592 

700 

0.0246 

o.  1109 

0.2523 

0.0649 

0.0335 

O.I05I 

0.1295 

0.1850 

0.1477 

0.2636 

800 

0.0239 

o.  1076 

0.2571 

0.0660 

0.0338 

0.1057 

0.1295 

0.1592 

0.1558 

0.2680 

9OO 

0.0233 

o.  1044 

o.  2619 

0.0671 

0.0341 

0.1063 

0.1295 

0.1592 

0.1639 

0.2724 

1000 

0.0226 

O.  IOI2 

0.2667 

0.0637 

0.0343 

o.  1069 

0.1295 

0.1448 

— 

0.2768 

IIOO 

— 



— 

o  .  0694 

0.0329 

o.  1028 

o.  1296 

0.1448 

0.1424 

0.2812 

I2OO 

— 



— 

0.0750 

0.0346 

0.1159 

0.1296 

0.1448 

0.1454 

0.2856 

1300 

— 



— 

0.0807 

0.0364 

o.  1291 

o.  1296 

0.1449 

0.1483 

o.  2900 

.  1400 

— 



— 

— 

— 

— 

o.  1296 

0.1449 

0.1512 

0.2944 

I5OO 

— 



— 

— 

— 

— 

0.1338 

o.  2142 

0.1472 

0.2988 

I6OO 

0.1501 

0.1472 

For  more  elaborate  tables  and  for  all  the  elements  in  upper  table,  see  original  reference. 
SMITHSONIAN  TABLES. 


226  TABLE  245. 

ATOMIC  HEATS  (60°  K).  SPECIFIC  HEATS  (60°  K).  ATOMIC  VOLUMES  OF  THE  ELEMENTS. 
The  atomic  and  specific  heats  are  due  to  Dewar,  Pr.  Roy.  Soc.  SgA,  168,  1913. 


Ele- 
ment. 

Specific 
heat 
-223°  C. 

Atomk 
heat 

-223°C 

Atomic 
volume 

Ele- 
ment 

Specific 
heat 
—223°  C. 

Atomic 
heat 
-223  °C 

Atomic 
volume. 

Ele- 
ment. 

Specific 
heat 
-  223°  C. 

Atomic 
heat 

-223°C. 

Atomic 
volume. 

Li 

o.  1924 

1-35 

13-0 

Cr 

0.0142 

0.70 

7.6 

Sn 

0.0286 

3-41 

20.3 

Gl 

0.0137 

0.125 

4-9 

Mn 

0.0229 

1.26 

7-4 

Sb 

0.0240 

2.89 

18.2 

B 

O.O2I2 

0.24 

4-5 

Fe 

0.0175 

0.98 

7-i 

I 

0.0361 

4-59 

25.7 

C* 

0.0137 

o.  16 

5-i 

Ni 

0.0208 

1.22 

6-7 

Te 

0.0288 

3-68 

21.2 

ct 

0.0028 

0.03 

3-4 

Co 

0.0207 

I.  22 

6.8 

Cs 

0.0513 

6.82 

71.0 

Na 

O.I5I9 

3-50 

23-6 

Cu 

0.0245 

1.56 

7-i 

Baf 

0.0350 

4.80 

36.6 

Mg 

0.0713 

1.74 

14.1 

Zn 

0.0384 

2.52 

9.2 

La 

0.0322 

4.60 

22.6 

Al 

0.0413 

I.  12 

IO.O 

As 

0.0258 

1.94 

15-9 

Ce 

0.0330 

4.64 

20.3 

Sit 

0.0303 

0.86 

14.2 

Se 

0.0361 

2.86 

18.5 

W 

0.0095 

i-75 

9.8 

Si§ 

0.0303 

0.77 

11.4 

Br 

0.0453 

3-62 

24.9 

Os 

0.0078 

1.49 

8-5 

P 

Rb 

0.0711 

6.05 

55-8 

Ir 

0.0099 

1.92 

8.6 

yel. 

0.0774 

2.40 

17.0 

Srlf 

0.0550 

4.82 

34-5 

Pt 

0.0135 

2.63 

9.2 

P 

Zr 

0.0262 

2.38 

21.8 

Au 

0.0160 

3-i6 

IO.  2 

red 

0.0431 

1-34 

13-5 

Mo 

0.0141 

1.36 

9-3 

Hg 

0.0232 

4-65 

14.8 

S 

0.0546 

i-7S 

16. 

Ru 

0.0109 

i.  ii 

9.0 

Tl 

0.0235 

4-80 

17.2 

Cl 

0.0967 

3-43 

24.6 

Rh 

0.0134 

1.38 

8-5 

Pb 

0.0240 

4.96 

I8.3 

K 

0.1280 

S-oi 

44-7 

Pd 

0.0190 

2.03 

9.2 

Bi 

0.0218 

4-54 

21.3 

Ca 

0.0714 

2.86 

25-9 

Ag 

0.0242 

2.62 

10.2 

Th 

0.0197 

4-58 

21.  I 

Ti 

O.O2O5 

0.99 

10.7 

Cd 

o  .  0308 

3-46 

13.0 

U 

0.0138 

3-30 

12.8 

*  Graphite.        f  Diamond. 


Fused.         §  Crystallized. 


Impure. 


References  to  Table  243: 

(1)  Bontschew. 

(2)  Naccari,  Atti  Torino,  23,  1887-88. 

(3)  Wigand,  Ann.  d.  Phys.  (4)  22,  1907. 

(4)  Nordmeyer-Bernouli,    Verh.    d.    phys. 

Ges.  9,  1907;   10,  1908. 

(5)  Giebe,  Verh.  d.  phys.  Ges.  5,  1903. 

(6)  Lorenz,  Wied.  Ann.  13,  1881. 

(7)  Stiicker,  Wien.  Ber.  114,  1905. 

(8)  Person,  C.  R.  23,  1846;   Ami.  d.  chim. 

(3)  21,  1847;    24,  1848. 

(9)  Moisson-Gautier,  Ann.  chim.  phys.  (7) 

17,  1896. 
(10)  Regnault,  Ann.  d.  chim.  (3)  26,  1849; 

63,  1861. 
(n)  Andrews,  Pog.  Ann.  75,  1848. 

(12)  Eckardt-Graefe,  Z.  Anorg.  Ch.  23,  1900. 

(13)  Bunsen,  Pogg.  Ann.  141,  1870;    Wied. 

Ann.  31,  1887. 

(14)  Weber,  Phil.  Mag.  (4)  49,  1875. 

(15)  Hillebrand,  Pog.  Ann.  158,  1876. 

(16)  Knietsch. 

(17)  Adler,  Beibl.  27,  1903. 

(18)  Pionchon,  C.  R.  102-103,  1886. 

(19)  Tilden,  Phil.  Trans.  (A)  201,  1903. 

(20)  Richards,  Ch.  News,  68,  1893. 

(21)  Trowbridge,  Science,  8,  1898. 

(22)  Berthelot,  Ann.  d.  chim.  (5)  15,  1878. 

(23)  Pettersson-Hedellius,  J.  Pract.  Ch.  24, 

1881. 

(24)  Violle,  C.  R.  85,  1877;  87,  1878. 

(25)  Regnault,  Ann.  d.  chim  (2)   73,  1840; 

(3)  63,  1861. 

(26)  Behn,  Wied.  Ann.  66,  1898;    Ann.  d. 

Phys.  (4)  i,  1900. 

SMITHSONIAN  TABLES. 


(27)  Schmitz,  Pr.  Roy.  Soc.  72,  1903. 

(28)  Nichol,  Phil.  Mag.  (5)  12,  1881. 

(29)  Hill,  Verh.  d.  phys.  Ges.  3,  1901. 

(30)  Spring,  Bull,  de  Belg.  (3)  u,  1886;  29, 

1895. 

(31)  Laemmel,  Ann.  d.  Phys.  (4)  16,  1905. 

(32)  Barnes-Cooke,  Phys.  Rev.  16,  1903. 

(33)  Wiegand,  Fort.  d.  Phys.  1906. 

(34)  Tilden,  Pr.  Roy.  Soc.  66,  1900;  71,  1903; 

Phil.  Trans.  (A)  194,  1900;  201,  1903. 

(35)  White,  Phys.  Rev.  12,  436,  1918. 

(36)  Dewar,  Ch.  News,  92,  1905. 

(37)  Kopp,  Phil.  Trans.  London,  155,  1865. 

(38)  Nilson,  C.  R.  96,  1883. 

(39)  Nilson-Pettersson,  Zt.  phys.  Ch.  i,  1887. 

(40)  Mache,  Wien,  Ber.  106,  1897. 

(41)  Bliimcke,  Wied.  Ann.  24,  1885. 

(42)  Mixter-Dana,  Lieb    Ann.  169,  1873. 

(43)  Magnus,  Ann.  d.  Phys.  31,  1910. 

(44)  Harper,  Bull.  Bureau  of  Stds.   n,  p. 

259,  1914. 

(45)  Nernst,  Lindemann,  1910,  1911. 

(46)  Nernst,  Dewar. 

(47)  Kosef,  Ann.  d.  Phys.  36,  1911. 

(48)  Magnus,  Ann.  d.  Phys.  31,  1910. 

(49)  Estreicher,  Straniewski,  1912. 

(50)  Nernst,  Ann.  d.  Phys.  36,  395,  1911. 

(51)  King,  Phys.  Rev.  n,  1918. 

(52)  Worthing,  Phys.  Rev.  12,  1918. 

(53)  Harker,   Pr.   Phys.    Soc.   London,    19, 

703,  1905;    Fe  .01;  C  .02;   Si  .03;  S 
.04;  P,  Mn  trace. 


TABLES  246-247. 

TABLE  246.— Specific  Heat  of  Various  Solids. 


227 


Solia. 

Temperature 
°C. 

Specific  heat. 

Au- 
thority. 

Alloys  : 
Bell  metal  
Brass,  red  
"      yellow     
80  Cu  +  20  Sn    
88.7CuH-ii.3Al     
German  silver    . 
Lipowitz  alloy  :  24-97Pb  +  10.  13  Cd  +5O.66BI 
+  14.24  Sn         .... 
«              << 

15-98 
0 
0 

14-98 

20-IOO 
0-100 

5-50 

100-150 

0.0858 
.08991 
.08831 
.0862 
.  10432 
.09.464 

•0345 
.0426 

R 

L 

R 
Ln 
T 

M 

Rose's  alloy:  27.5  Pb  +48.9  Bi  +23.6  Sn      . 

Wood's  alloy:  25.85  Pb'-f  6.99  Cd  +  52.43  Bi 
+  i4.73Sn        . 
(fluid)     
Miscellaneous  alloys  : 
17.5  Sb  +  29-9  Bi-f-  i8.7Zn  +  33.9Sn      • 
37.1  Sb+62.9Pb     
39.9Pb  +  6o.iBi      
"    (fluid)  

—77-20 
20-89 

5-50 
100-150 

20-99 
10-98 
16-99 

144—  7cg 

•0356 
.0552 

.0352 
.0426 

•05657 
.03880 
•03165 

.omoo 

S 
u 

M 

« 

R 
P 

63.7Pb  +  36.3Sn    
46.7Pb  +  53-3Sn    
63  8Bi  -|-36.2Sn     

12-99 
10-99 

20-QQ 

.04073 
.04507 

04001 

R 

« 

46.9  Bi  +53-1  Sn    
Gas  coal  
Glass,  normal  thermometer  :6"i    .... 
French  hard  thermometer     .... 
"       crown  ...               
"       flint       ....               . 

20-99 
20-1040 
19-100 

10-50 

10-50 

.04504 

•3I45 

.161 
.  117 

W 

z 

H  M 

Ice     . 

_!88  252 

.  146 

D 

.28^ 

« 

_!8  78 

•  463 

{< 

India  rubber  (Para)            ...... 

,        ' 

?-IOO 

.481 

GT 

Mica         

20 

.  10 

Paraffin    

—  20-    +3 

.3768 

R  W 

—  19  |-20 
0-20 

.60^0 

fluid         
Vulcanite        
Woods     ....               

35-40 
60-63 

20-100 
20 

.622 
.712 
•3312 
•3-7 

B 
AM 

TABLE  247.— Specific  Heat  of  Water  and  of  Mercury. 


Specific  Heat  of  Water. 

Specific  Heat  of  Mercury. 

Temper- 
ature,°C. 

Barnes. 

Rowland. 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Barnes 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Specific 
Heat. 

Temper- 
!  ature,°C. 

Specific 
Heat. 

-s 

•oiSS 

_ 

_ 

60 

0.9988 

0.9994 

0 

0.03346  i 

90 

0.03277 

0 

.0091 

1.0070 

i  .0094 

65 

•9994 

i  .0004 

5 

.03340  i 

IOO 

.03269 

+  5 

.0050 

1.0039 

1.0053 

70 

1.  000  1 

1.0015 

10 

.03335 

no 

.03262 

10 

.0020 

i.  0016 

1.0023 

80 

1.0014 

1.0042 

15 

.03330 

120 

.03255 

IS 

.0000 

I.OOOO 

1.0003 

90 

1.0028 

1.0070 

20 

•03325 

130 

.03248 

20 

0.9987 

.9991 

0.9990 

IOO 

1.0043 

I.OIOI 

25 

.03320  j 

140 

.03241 

25 

.9978 

.9989 

.9981 

120 

— 

1.0162 

30 

•03316  ; 

150 

.0324 

30 

•9973 

.9990 

.9976 

140 

- 

1.0223 

35     ;    .03312 

170 

.0322 

35 

.9971 

.9997 

.9974 

1  60 

— 

1.0285 

40 

.03308 

190 

.0320 

40 

•9971 

1.0006 

.9974 

ISO 

— 

1.0348 

50 

.03300 

210 

.0319 

45 

•9973 

1.0018 

.9976 

200 

— 

1.0410 

60 

.03294 

— 

50 

•9977 

1.0031 

.9980 

220 

- 

i  .0476 

70 

.03289 

- 

- 

55 

.9982 

1.0045 

.9985 

1 

80            .03284 

Barnes's  results  :  Phil.  Trans.  (A)  199,  1902;   Phys.  Rev.  15,  1902;  16,  1903.     (H  thermometer.) 
Bousjfteld,  Phil.  Trans.  A  211,  p.  199,  1911.  Barnes-Rcgnault's  as  revised  by  Peabody  ;  Steam  Tables. 

The  mercury  data  from  o°  C  to  80,  Barnes-Cooke  ( H  thermometer);  from  90°  to  140,  mean  of  Winklemann,  Naccari 
and  Milthaler  (air  thermometer);  above  140°,  mean  of  Narcari  and  Milthaler. 


228 


TABLES  248-260. 
TABLE  248.  — Specific  Heat  of  Various  Liquids. 


Liquid. 

Temp. 

•c. 

Spec. 

heat. 

Au- 
thority. 

Liquid. 

Temp. 

Spec. 

heat. 

Au- 
thority. 

Alcohol  ethyl 

-20 
0 
40 

5-10 
15-20 
15 
30 
50 

IO 

40 

65 
-15 

0 
+  20 
-20 
0 
+  20 
-20 
O 
+  20 
12-15 
12-14 
13-17 

53 
65 

0.5053 
0.548 
0  .  648 
O.SQO 

0.601 
0.514 
0.520 
0.529 
0.340 
0.423 
o.'482 
0.764 

0-775 
0.787 
0.695 
0.712 
0.725 
0.651 
0.663 
0.676 
0.848 
0.951 
0.975 

0.464 
0.482 

R 

« 
« 
« 

G 

H-D 
t« 

DMG 

« 

i 
i 

Pa 

B 

« 

Ethyl  ether  

0 
15-50 
18 
18 
18 
18 
18 
18 
80-85 
90-95 
14 
28 

5-4 
6.6 

0 

21-58 
17-5 
17-5 
17-5 

IO 

65 
85 

20-52 
20-52 

0.529 
0.576 
0.876 

0-975 
0.942 
0.983 
0.791 
0.978 
0.396 
0.409 
0.350 
0.362 
0-434 
0.438 
0.471 
0.387 
0.411 
o.  511 
0.980 
0.938 
0.903 
0.364 
0.490 
0-534 
0.842 
0.952 

R 
E 
TH 

« 

u 
« 
(1 

B 
(i 

A 
u 

W 
HW 

u 

W 
R 

Pa 
« 

M 

(( 

H-D 

Ma 
fi 

Glycerine  ... 

<«          « 

KOH  +  3oH2O  '. 

"         -j-  100  "      

NaOH  +  5oH2O  

Anilin 

"         +  100    "     

n 

•NaCl  +  ioH2O  

« 

"     +200"  
Naphthalene,  C10H8  

Benzole  C6H6 

«             « 

"      C6H6 

Nitrobenzole  

CaClj,  sp.  gr.  1.^14  

u 

U            It 

"      I.2o'.'. 
«          « 

«          « 

citron  

olive  

sesame  
turpentine 

"      j  26 

Petroleum 

«        « 

ii             U 

CuSo4  +  50  H2O  

Sea  water,  sp.  gr.  1.0043. 
;'   1-0235. 
"       "       "     "   1.0463. 
Toluol  CeHs 

+  200  "      
4-  400  "      
Diphenylamine, 
Ci2HnN                 .    .  . 

u 

ft 

ZnSO4  +  50  HoO  

« 

"          +  200"       

References:     (A)  Abbot;   (B)  Batelli;  (E)  Emo;   (G)  Griffiths;   (DMG)  Dickinson, 
Mueller,  and  George;  (H-D)  de  Keen  and  Deruyts;  (Ma)    Marignac;   (Pa)    Pagliani; 
(R)  Regnault;    (Th)  Thomsen;    (W)  Wachsmuth;    (Z)  Zouloff;  (HW)  H.  F.  Weber. 

TABLE  249.  —  Specific  Heat  of  Liquid  Ammonia  under  Saturation  Conditions. 

Expressed  in  Calories^  per  Gram  per  Degree  C.     Osborne  and  van  Dusen, 

Bui.  Bureau  of  Standards,  1918. 


Temp. 
°C 

o 

I 

2 

3 

4 

5 

6 

7 

8 

9 

-40 

.062 

.061 

.060 

•059 

.058 

.058 

•057 

.056 

•055 

•055 

-30 

.070 

.069 

.068 

.067 

.066 

•065 

.064 

.064 

.063 

.062 

-20 

.078 

.077 

.076 

•075 

.074 

.074 

•073 

.072 

.071 

.070 

-10 

.088 

.087 

.086 

-085 

.084 

.083 

.082 

.081 

.080 

.079 

-    0 

.099 

.098 

.097 

.096 

.094 

•093 

.092 

.091 

.090 

.089 

+  o 

.099 

.100 

.101 

.103 

.  104 

.105 

.106 

.108 

.109 

.110 

+  10 

.  112 

•113 

.114 

.116 

.117 

.118 

.  120 

.  122 

.123 

.125 

+  20 

.126 

.128 

.129 

•131 

.132 

•134 

.136 

•137 

•139 

.141 

+30 

.142 

.144 

.146 

.148 

.ISO 

.152 

•154 

.156 

1.158 

.160 

+40 

.162 

.164 

.166 

I.  169 

.171 

•173 

.176 

.178 

1.181 

.183 

TABLE  250.  —  Heat  Content  of  Saturated  Liquid  Ammonia. 

Heat  content  =  H  =  €  +  pv,  where  €  is  the  internal  or  intrinsic  energy.     Osborne  and  van 
Dusen,  Bui.  Bureau  of  Standards,  1918. 


Temperature  .  .  . 

H  =  e  +  pv  

-50° 
-53-8 

-40° 
-43-3 

-30° 
-32-6 

-20° 
-21.8 

-10° 
-II.  0 

0° 

o.o 

+  10° 

+11.  1 

+  20° 
+  22.4 

+30° 
-33-9 

+40° 
-45-5 

+50° 
-57-4 

SMITHSONIAN  TABLES 


TABLES  251-252. 

SPECIFIC   HEATS   OF    MINERALS  AND  ROCKS. 

TABLE  251.— Specific  Heat  of  Minerals  and  Rocks, 


229 


Substance. 

Tempera-    ' 
ture  °  C. 

Specific 
Heat. 

Refer-1 
ence. 

Substance. 

Tempera- 
ture °  C. 

Specific 
Heat. 

Refer- 
ence. 

Andalusite 

O-IOO 

0.1684 

, 

Rock-salt 

13-45 

0.219 

6 

Anhydrite,  CaSO4 

O-IOO 

•1753 

I 

Serpentine    . 

16-98 

.2586 

2 

Apatite  .... 

15-99 

.1903 

2 

Siderite 

9-98 

•J934 

4 

Asbestos 

20-98 

•195 

3 

Spinel  . 

15-47 

.194 

6 

Augite   .... 

20-98 

3 

Talc      . 

20-98 

.2092 

3 

Barite,  BaSO4 

10-98 

.1128 

4 

Topaz  .    ;     . 

O-IOO 

.2097       i 

Beryl      .... 

X5~99 

.1979 

2 

Wollastonite 

*9~S* 

.178        6 

Borax,  Na2B4O7  fused 

16-98 

.2382 

4 

Zinc  blende,  ZnS  . 

O-IOO 

.1146 

i 

Calcite,  CaCOs      . 

0-50 

.1877 

r 

Zircon  . 

21-51 

.132 

6 

"           "            .        . 

O-IOO 

.2005 

i 

Rocks  : 

"           "            . 

0-300 

.2204 

i  ' 

Basalt,  fine,  black 

I2-IOO 

.1996 

6 

Cassiterite  SnO2    . 

16-98 

•0933 

4 

"         "        " 

20-470 

.199 

9 

Chalcopyrite 
Corundum 

!5~99 

9-98 

.1291 
.1976 

2 

4 

«         «i         « 

470-750           .243 
750-880           .626 

9 
9 

Cryolite,  Al.2F6.6NaF    . 

16-99 

.2522 

2 

«         «         « 

880-1190        .323 

9 

Fluorite,  CaF2 

•2154 

4 

Dolomite     . 

20-98             .222 

3 

Galena,  PbS  . 

O-IOO 

.0466 

5 

Gneiss 

17-99             .196 

10 

Garnet    .... 

16-100 

.1758 

2 

" 

17-213           .214 

10 

Hematite,  Fe2O3    . 

15-99 

.1645 

2 

Granite 

I2-IOO 

.192 

7 

Hornblende   . 

20-98 

.1952 

3 

Kaolin 

20-98 

.224 

3 

Hypersthene 

20-98 

.1914 

3 

Lava,  Aetna 

23-IOO 

.201 

ii 

Labradorite    . 

20-98 

3 

"           "    . 

31-776 

-259 

ii 

Magnetite 

18-45 

.156 

6 

"       Kilauea     . 

25-100 

.197 

ii 

Malachite,  Cu2CO4H2O 

*5-99 

•1763 

2 

Limestone  . 

15-100 

.216 

12 

Mica  (Mg)      . 

20-98 

.2061 

3 

Marble 

O-IOO 

.21 

— 

"     (K)        .        .        . 

20-98 

.2080 

3 

Quartz  sand 

20-98 

.191 

3 

Oligoclase 

20-98 

.2048 

3 

Sandstone  . 

— 

.22 

Orthoclase 

15-90 

.1877 

2 

Pyrolusite,  MnC>2  . 
Quartz,  SiO2 
(i           <« 

17-48 

12-100 

0 

35° 
400-1200 

•1737 
.2786 

•305 

6 

I 

8 
8 

i  Lindner.       6  Kopp.           n  Bartoli. 
2  Oeberg.        7   Joly.             12  Morano. 
3  Ulrich.          8  Pionchon. 
4  Regnault.     9  Roberts-Austen,  Riicker. 
5  Tilden.        10  R.  Weber. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
TABLE  252.— Specific  Heats  of  Silicates. 


Silicate. 

Mean  specific  heats. 
o°  Cto 

True  specific  heats, 
at 

100° 

500° 

900" 

1400* 

o'C 

100* 

500° 

1000* 

1300* 

Albite       .... 

.1948 

•2363 

.2561 

__ 

.178 

.211 

.269 

.294 

_ 

"      glass     . 

.1977 

.24IO 

.2640 

— 

— 

Amphibole,  Mg.  silicate 

.2033 

.2461 

.2661 

.2731* 

.185 

.219 

.279 

.304 

- 

glass    . 

.2040 

.2474 

— 

— 

— 

— 

— 

Andesine 

•1925 

.2330 

•2525 

_ 

- 

- 

.265 

- 

- 

"        glass 

•  1934 

.2615 

_ 

_ 

_ 

_ 

— 

Anorthite 

.1901 

.2296 

02481 

.2674 

.1/4 

.205 

.260 

.286 

.318 

glass 

.1883 

.230=1 

_ 

— 

— 

— 

Cristobal!  te    . 

.1883 

i- 
.2426 

.2568 

.2680 

_ 

- 

- 

- 

- 

Diopside  .... 

.1924 

.2314 

.2500 

.26o4t 

.176 

.207 

.262 

.284 

- 

glass        .       . 

•  1939 

•  2332 

— 

— 

— 

— 

— 

— 

— 

Microcline 

.1871 

.2262 

.2450 

_ 

.171 

.201 

.258 

.279 

— 

glass     . 

.1919 

.2321 

•  2514 

.2508* 

.176 

.206 

.264 

.299 

- 

Pyroxene 

.2039 

.2484 

— 

— 

— 

— 

Quartz      .... 

.  1868 

•  2379 

.2596 

.  2640* 

.168 

.204 

.294 

•  2~85 

- 

Silica  glass 

.1845 

.2302 

.2512 

- 

.166 

.202 

.266 

.29 

- 

Wollastonite  . 

_ 

_ 

•2344 

—       [     _ 

— 

— 

— 

glass 

.1852 

.2206 

- 

- 

_ 

- 

- 

- 

"             pseudo    . 

.1844 

.2170 

.2324 

.2448 

.171 

.197 

•243 

.262 

.272 

°;     to°-i25o°; 


Taken  from  White,  Am.  J.  Sc.  47,  i,  1919. 


230 


TABLE  253. 
SPECIFIC   HEATS  OF   GASES  AND  VAPORS. 


Substance. 

Range  of 
temp.  °  C 

Sp.  ht. 
constant 
pres- 
sure. 

Authority. 

Range 
of 
temp. 
°C 

Mean 
ratio  of 
specific 
heats. 
Cp/Cv. 

Authority. 

Acetone  QHeO 

26-IIO 
-30—  fio 

O-2OO 

20-440 

20-630 
20-800 
108-220 

101-223 
23-100 
27-200 
20-90 

34-115 
35-180 
116-218 
83-228 

-28-  +7 
15-100 
11-214 

23-99 
26-198 
86-190 

i6-343 
27-118 
28-189 
69-224 
25-111 

13-100 
22-214 
-28-  +9 
12-198 

2I-IOO 
2O-2O6 

18-208 

O-2OO 
20-440 
20-630 
2O-8OO 
13-172 
27-67 
27-150 
27-280 
I6-2O7 
26-103 
27-206 
13-207 
20-440 
20-630 
I6-2O2 
0 
IOO 

180 

0.3468 
0.2377 
0-2375 
0.2366 
0.2429 
0.2430 
0-4534 

0.4580 
0.5202 
0.5356 
0.1233 
o.  2990 

0.3325 

0-3754 
0.0555 
0.1843 
0.2025 
0.2169 
0.2425 
o.  2426 
0.1596 
0.1125 
0.1441 
0.1489 

0.4797 
0.4280 

o.  1940 

0.1867 

3  •  3996 
3  •  4090 
3  .  4100 
0.2451 

0.5929 

0.2438 
0.2419 
o.  2464 
0.2497 
0.2317 
1.625 
1.115 
0.65 
0.2262 
0.2126 
o.  2241 

0.2175 

o.  2240 

0.2300 
0.1544 
0.4655 

0.421 

0.51 

Wiedemann. 
Regnault. 

Holborn  and 

Austin. 

« 

Regnault. 

Regnault. 
Wiedemann. 

14 

Dittenberger. 

Wiedemann. 
n 

Regnault. 

it 
n 

a 

Wiedemann. 
u 

Regnault. 
Strecker. 

Wiedemann. 

ii 

Regnault. 
Wiedemann. 

Strecker. 

Regnault. 
« 

a 

Wiedemann. 
Regnault. 

Regnault. 

Regnault. 
Holborn  and 

Austin. 

a 

Regnault. 
Berthelot  and 
Olger. 

Regnault. 

Wiedemann. 
u 

Regnault. 
Holborn  and 
Austin. 
Regnault. 
Thiesen. 

« 

2O 
-79-3 
-79-3 

0 

500 
53 

IOO 
IOO 
0 
IOO 

o 
20 

60 

99-7 
20-388 
4-1  1 

0 

o 

IOO 

3-67 
o 

22-78 
99.8 
42-45 

I2-2O 
0 
2O 
IOO 
4-16 

19 
3IO 

11-30 
19 

0 
IOO 

5-14 
16-34 

78 

94 

IOO 

19 

1.4011 
1.405 

2-333 
.828 

•399 
•133 
•134 
.256 
•3172 
1.2770 
1.667 
1.403 
1.403 
1.105 
1-293 
1  •  2995 

1.3003 
1.403 

1-395 
1.205 
1-336 

I.  IO2 
I.I50 
I.O29 
I.O24 
1.64 
1.389 
I.40O 
1.4080 

I.4I9 
1.324 

1.666 
1.666 

1.316 
1.642 
1.41 
1.405 

1-394 
i-3i 

1.311 
i.  272 
i-324 
1-3977 

1.256 
1.274 
i-33 
1-305 
1.666 

Moody. 
Koch,  1907. 
"     200  atm 

Si              ii            it 

Fiirstenau. 
Jaeger. 

Stevens. 

n 

Wullner. 

a 

Niemeyer. 
Pagliani. 

(4 

Stevens. 
Strecker. 
Lummer  and 
Pringsheim. 
Moody,  1912. 
Wullner. 

Beyme. 
Martini. 
Beyme. 
Stevens. 
Miiller. 
Low,  1894. 
Mean,  Jeans. 
Strecker. 

u 

Lummer  and 
Pringsheim. 
Hartmann. 
Capstick. 
Ramsay,  '12. 
Kundt  and 
Warburg. 
Miiller. 
Ramsay,  '12 
Cazin. 
Masson. 

(i 

Natanson. 

Wullner. 

« 

Leduc,  '98. 
Lummer  and 
Pringsheim. 

Miiller. 
Beyme. 
Jaeger. 
Makower. 
Ramsay,'  12. 

Air 

« 

" 

« 

Alcohol,  'C2H6OH.! 

«               <« 

CH3OH  

Ammonia      

Benzene.  C«H| 

«            a 

«            « 

Bromine      

Carbon  dioxide,  CO2  .  .  • 

«           <«         <i 

«           «         « 

"     monoxide,  CO.. 

«             «           « 

"     disulphide,CS2". 
Chlorine  

Chloroform,  CHC13...- 

«                « 

Ether,  CJIioO 

«           « 

Helium  
Hydrochloric  acid,  HC1. 

Hydrogen  

ii 

sulphide',  H2S 
Krypton 

Mercury  

Methane,  CH4  
Xeon 

Nitrogen  .  . 

a 

« 

Xitric  oxide,  NO  

Xitrogen  tetroxide,  NO2 

«               «i           « 

«               i<           « 

Nitrous  oxide,  N2O  .  . 

.  «          «         « 

«          ««        « 
Oxygen  

« 

Sulphur  dioxide,  SO2.  .  . 
Water  vapor,  H2O  

«                  «                     (( 

«          «            « 
Xenon 

SMITHSONIAN  TABLES 


TABLE  254. 
LATENT    HEAT  OF   VAPORIZATION. 


23I 


The  temperature  of  vaporization  in  degrees  Centigrade  is  indicated  by  /,  the  latent  heat  in 
large  calories  per  kilogram  or  in  small  calories  or  therms  per  gram  by  r;  the  total  heat  from  o° 
C,  in  the  same  units  by  H.  The  pressure  is  that  due  to  the  vapor  at  the  temperature  t. 


i 
(                    Substance. 

Formula. 

t°C 

r 

H 

Authority. 

Acetic  acid  
Air  .  .                

C2H402 

118° 

84.9 

tjo.o? 

— 

Ogier. 
Fenner-Richtmyer 

Alcohol  :  Amyl  

C&Hi2O 

1^1 

1  20 



Schall. 

Et^  

C2H60 

78.1 
o 

205 

2^6 

255 
2^6 

Wirtz. 
Regnault 

u 
« 
It 

Methyl  
tt 
tt 

n 

CH40 

50 

TOO 
150 
64-S 
0 

50 

IOO 
I  <\O 

267 

289 

264 

267 
285 

307 
289 
274 

246 

206 

<« 
tt 
tt 

Wirtz. 
Ramsay  and  Young. 

tt 
tt 

it 

2OO 

I  C.2 

n 

n 

228  <; 

4.4.    2 

u 

Aniline  
Benzene  
Bromine  
Carbon  dioxide,  solid  — 
liquid  .  .  . 

<                          « 
<                          « 
<                          <« 
<                          « 

disulphide  
<                « 

C6H7N 
C6H6 
Br 

C02 

a 

tt 

n 

CS2 

u 
It 

"O"-  o 
184 
80.  i 
61 

-25 
o 

12.35 
22.04 
29.85 
30.82 
46.1 

0 
IOO 

no 

92.9 

45-6 

72.23 
57.48 
44-97 
31-8 
14.4 
3-72 
83.8 
90 

127.9 
138.7 

94.8 
90 

IOO    ^ 

Mean. 
Wirtz. 
Andrews. 
Favre. 
Cailletet  and  Mathias. 

«            a              « 

Mathias. 
« 

« 
tt 

Wirtz. 
Regnault. 

t                (t 

(I 

14.0 

IO2    4. 

it 

Chloroform 

CHC13 

60  o 

*8  <? 

72    8 

Wirtz. 

Ether           

C4Hi0O 

•74.    er 

88  4 

IO7 

« 

< 

u 

•2A.  Q 

QO     ? 

Andrews. 

< 

u 

o 

04 

04. 

Regnault. 

i 

tt 

CO 

11^.  I 

< 

« 

1  2O 

, 

140 

«< 

Ethyl  bromide  .  . 

C2H6Br 

18    2 

60  4 

Wirtz. 

'      chloride  
'      iodide  
Heptane  
Hexane 

C2H6C1 
C2H5I 
C7H16 

CcHu 

12.5 

71 
QO 
7O 

n.s 

7O    2 

98 

Regnault. 
Mean. 
Young. 

Iodine  .... 

I 

22     QC 

_ 

Favre  and  Silbermann. 

Mercury  .... 

Hg 

•2  CT7 

fo-Va 

65 



Mean. 

Nitrogen  
Octane  

N2 

-195.6 

I^O 

47-65 
70.0 

— 

Alt. 
Young. 

Oxygen 

O2 

—  182  9 

fQ     Q7 

\lt. 

Pentane 

TO 

8<;  8 

Younr. 

Sulphur  

Sulphur  dioxide  .... 
tt            K 

(i            it 
Toluene  .  .  . 

s 

SO2 

u 
11 

C7H8 

3l6 

0 

30 

65 

III 

362.0 
91.2 
80.5 
68.4 
86  o 

— 

Person. 

Cailletet  and  Mathias. 

«          «          (( 

tt          if          « 
Mean. 

Turpentine  .  . 

I  £.0    3 

74.  O4. 

.  

Brix. 

SMITHSONIAN  TABLES. 


232 


TABLES  256-257. 

LATENT   HEAT  OF  VAPORIZATION- 
TABLE  255.  —  Formulae  for  Latent  and  Total  Heats  of  Vapors. 


r  «  latent  heat  of  vaporization  at  *°  C;  B 
scale.    Same  units  as  preceding  table. 


total  heat  from  fluid  at  o°  to  vapor  at  *°  C.     T°  refers  to  Kelvin 


Acetone,  C»H«O  

B  -  140.5  +0.36644*  -0.000516** 

-3°  to  147° 

R 

=  139.9+0.23356*  +o.ooos53S8<* 

-3         H7 

W 

r    —  139-9  —  0.27287*  +  0.0001571** 

—3         147 

W 

Benzene  CeH6  

B  -  109.0  +0.24429*  —  0.0001315** 
r»  =  118.485(31  -  *)  -  0.4707(31  -  *)* 
B  =-  90.0  +0.14601*  —  0.0004123** 

H   «  89.5  +0.16993*   —  O.OOIOl6l*»  +0.05342*3 

7         215 
-25           3i 
-6         143 
-6         143 

R 
C 
R 
W 

Carbon  dioxide  
Carbon  bisulphide,  CSi  .... 

f      :B  89.5    —  O.O6530*   —  0.0010976**  +  O.05342*3 

—6         143 

W 

Carbon  tetrachloride,  CCh. 

B  =  52.0  +  0.14625*  —  0.000172** 
H  =  51.9  +0.17867*  —  0.000959Q*2  +  0.053733*3 
r    =  51.9  —  0.01931*  —  0.0010505**  +  0.053733*3 

8         163 
8         163 
8         163 

R 
W 
W 

Chloroform,  CHCU  

B  =  67.0  +  0.1375* 
B  =  67.0  +0.14716*  —  0.0000937** 

—  5         159 

-5         159 

R 
W 

r    =  67.0  —  0.08519*  —  0.0001444** 

-5         159 

W 

Ether,  CiHwO  

B  =94.0  +0.45000*  -0.0005556** 

—4         121 

R 

=  94.0  —  0.07900*  —  0.0008514** 

-4         121 

R 

Molybdenum  

=  177000  —  2.sncal/g-atom) 



L 

Nitrogen   Nj                 .      .  . 

=  68.85  -0.2736F 
J  =  131.75(36.4  —  *)  —  0.928(36.4  —  *)* 

—  20               36 

A 

Nitrous  oxide  NiO 

Oxygen,  Oi  

=  69.67  —  o.2o8or 
=  128000  —  2.sr(cal/g-atom) 



A 
L 

Platinum 

^ulphur  dioxide 

=  91.87  —  0.3842*  —  0.000340** 
=  217800  —  i.SZXcal/g-atom) 

0                20 

M 
L 

Tungsten  

Water,  HjO  ,  

B  =  638.9  +  o.3745(*  -  ioo)  -  o.ooo99(/  -  100)2 



D 

r    =  94-  210(365  -  *)°-31249     (See  Table  259) 

0             IOO 

H 

R,  Regnault;   W,  Winkelmann;    C,  Cailletet  and  Mathias;   A,  Alt.;   D,  Davis;   H,  Henning;   L,  Langmuir. 

TABLE  256.— Latent  Heat  of  Vaporization  of  Ammonia. 
CALORIES  PER  GRAM. 


°c 

o 

I 

2 

3 

F 

4 

5 

6 

7 

8 

9 

-40 

331-7 

332-3 

333-0 

333-6 

334-3 

334-9 

335-5 

336.2 

336.8 

337-5 

—  30 

324.8 

325.5 

326.2 

326.9 

327.6 

328.3 

329.0 

329-7 

330.3 

331-0 

—  20 

317.6 

3i8.3 

3I9-I 

319-8 

320.6 

321-3 

322.0 

322.7 

323-4 

324-1 

—  10 

309.9 

310.7 

3".5 

312.2 

313-0 

313-8 

314.6 

3I5-3 

316.  i 

3i6.8 

—    0 

301.8 

302.6 

303.4 

304-3 

305.1 

305-9 

306.7 

307-5 

308.3 

309.1 

+  o 

301.8 

300.9 

300.1 

299.2 

298.4 

297-5 

296.6 

295-7 

294.9 

294.0 

+  10 

293  i 

292.2 

291.3 

290.4 

289.5 

288.6 

287.6 

286.7 

285.7 

284.8 

+  20 

283.8 

282.8 

281.8 

280.9 

279-9 

278.9 

277.9 

276.9 

275-9 

274-9 

+30 

273-9 

272.8 

271.8 

270.7 

269.7 

268.6 

267.5 

266.4 

265.3 

264.  2 

+40 

263.1 

262.0 

260.8 

259-7 

258.5 

257-4 

256.  2 

255-0 

253-8 

252.6 

Osborne  and  van  Dusen,  Bui.  Bureau  Standards,  14,  p.  439,  1918. 


TABLE  257.  —  "  Latent  Heat  of  Pressure  Variation  "  of  Liquid  Ammonia. 

When  a  fluid  undergoes  a  change  of  pressure,  there  occurs  a  transformation  of  energy  into  heat  or  vice  versa,  which 
results  in  a  change  of  temperature  of  the  substance  unless  a  like  amount  of  heat  is  abstracted  or  added.  This  change 
expressed  as  the  heat  so  transformed  per  unit  change  of  pressure  is  the  "latent  heat  of  pressure  variation."  It  is  ex- 
pressed below  as  Joules  per  gram  per  kg/cm*.  Osborne  and  van  Dusen,  loc.  cit.,  p.  433,  1918. 


Temperature  c  C      —44.1 

Latent  heat  ....  1     —.055 
1 

—39-0 
—  •057 

-24.2 
-.068 

—  0.  2 
-.088 

+  16.5 
—  .107 

+  26.5 
—  .123 

+35-4 
-.140 

+40-3 
-.150 

SMITHSONIAN  TABLES. 


TABLE  258. 
LATENT  AND  TOTAL   HEATS  OF  VAPORIZATION   OF  THE  ELEMENTS. 


233 


The  following  table  of  theoretical  values  is  taken  from  J.  W.  Richards,  Tr.  Amer.  Electrcch. 
Soc.  13,  p.  447,  1908.  They  are  computed  as  follows:  8Tm  (8  =  mean  value  atomic  specific 
heat,  Dulong-Petit  constant,  o°  to  T°  K,  Tm  =  melting  point,  Kelvin  scale)  plus  2Tm  (latent 
heat  of  fusion  is  approximately  2Tm,  ].  Franklin  Inst.  1897)  plus  io(Tb  —  Tm]  (specific  heat 
of  liquid  metals  is  nearly  constant  and  equal  to  that  of  the  solid  at  Tm,  Tj,  =  boiling  point,  Kelvin 
scale)  plus  23 Tb  (23  =  Trouton  constant;  latent  heat  of 'vaporization  of  molecular  weight 
in  grams  is  approximately  23  times  T&)  =  33  T&.  Total  heat  of  vapor  when  raised  from  273°  K 
(o°  C)  equals  33^6  —  1700  (mean  value  of  Dulong-Petit  constant  between  o°  and  273°K  is 
1700).  Heats  given  in  small  calories  per  gram. 


Ele- 
ment. 

Tb 
°K 

23  Tb 

Latent 
heat  of 
vapori- 
zation. 

33^6- 
1700 

Total 
heat 
vapor 
from 
273°  K 

Ele- 
ment. 

Tb 
°K 

23  Tb 

Latent 
heat  of 
vapori- 
zation. 

33  Tb  — 

1700 

Total 
heat  of 
vapor 
from 
273°  K 

Hg 

630 

14,500 

72 

I9,IOO 

96 

Rh 

2773 

63,800 

620 

9O,OOO 

870 

K 

993 

22,800 

590 

31,100 

800 

Ru 

27QO 

64,100 

630 

90,000 

880 

Cd 

1050 

24,200 

230 

33,ooo 

3IO 

Au 

2800 

64,500 

330 

91,000 

460 

Na 

1170 

27,000 

1170 

37,000 

1610 

Pd 

28lO 

64,600 

610 

9I,OOO 

850 

I  Zn 

1  200 

27,700 

430 

38,000 

580 

Ir 

2820 

64,800 

340 

91,300 

470 

In 

1270 

29,300 

— 

40,300 

— 

Os 

2870 

66,000 

350 

93,000 

490 

Mg 

1370 

31,600 

1320 

43,600 

1820 

U 

3170 

73,000 

305 

103,000 

430 

Te 

1660 

38,200 

300 

54,900 

430 

Mo 

3470 

80,000 

830 

113,000 

1180 

Bi 

1710 

39,300 

190 

56,400 

270 

W 

3970 

91,400 

500 

129,000 

700 

Sb 

1870 

43,100 

360 

60,000 

5io 

H2 

2O 

460 

230 

— 

— 

Tl 

1970 

4S,4oo 

220 

63,400 

310 

N2 

77 

1,770 

63 

— 

— 

Pb 

2070 

47,700 

230 

66,700 

320 

02 

85 

1,960 

61 

— 

— 

Ag 

2310 

S3,ooo 

490 

74,600 

690 

C12 

251 

5,78o 

81 

— 

— 

Cu 

2370 

54,5oo 

860 

76,600 

I2IO 

Br2 

33i 

7,600 

48 

— 

— 

Sn 

2440 

56,100 

480 

78,800 

670 

Is 

447 

10,300 

27 

— 

— 

Mn 

2470 

56,500 

1030 

79,5oo 

1440 

Ps 

56o 

13,000 

138 

— 

— 

Ni 

2690 

59,800 

IOIO 

84,000 

I42O 

As3 

723 

16,600 

74 

•  — 

— 

Cr 

2640 

60,700 

1170 

85,400 

1640 

Se3 

963 

22,100 

94 

— 

— 

Fe 

2690 

62,000 

IIIO 

87,200 

1560 

B2 

3970 

91,000 

4200. 

— 

— 

Pt 

2720 

62,600 

320 

88,000 

450 

C2 

3970 

91,000 

3800 

— 

— 

Ti 

2750 

63,200 

1320 

89,000 

1850 

SMITHSONIAN  TABLES. 


234 


TABLE  259. 
PROPERTIES  OF   SATURATED  STEAM. 

Metric  and  Common  Units. 


Reprinted  by  permission  of  the  author  and  publishers  from  "  Tables  of  the  Properties  of  Steam,"  Cecil  H  Peabody, 
8th  edition,  rewritten  in  1009.  Calorie  used  is  heat  required  to  raise  i  Kg.  water  from  15°  to  16°  C.  B  1 .  U.  is  heat 
required  to  raise  i  pd.  water  from  62°  to  63°  F.  Mechanical  Equiv.  of  heat  used,  778  ft.  pds.  or  427  in.  Kg.  Specific 
heats,  see  Barnes-Regnault-Peabodv  results,  p.  227.  Heat  of  Liquid,  q.  heat  required  to  raise  i  Kg.  (i  It)  to  corre- 
sponding temperature  from  o°  C.  Heat  of  vaporization,  r-  heat  required  to  vaporize  i  Kg^  (i  Ib.)  at  corresponding  tem- 
perature to  dry  saturated  vapor  against  corresponding  pressure;  see  Hennmg,  Ann.  der  Phys.,  21,  p.  849,  1906.  lotal 


grfl 

=  'i  £ 

Pressure. 

Heat  of  the 
Liquid. 

Heat  of 
Vaporization. 

Heat  Equivalent 
of 
Internal  Work. 

||1 

z£  I 

Mm.  of 

Kg. 

1'ds. 

Calories. 

B.  T  U. 

Calories. 

B.  T.  U. 

Calories. 

B.  T.  U. 

|«2 

t. 

Mercury. 

.   P- 

per  sq.  cm. 
P- 

per  sq.  in. 
P- 

q- 

q- 

r. 

r. 

P 

p. 

t. 

0 

4-579 

0.00623 

0.0886 

0.00 

o.o 

595-4 

1071.7 

565.3 

1017.5 

32-0 

5 
10 

6.541 
9-205 

.00889 
.01252 

.1265 
.1780 

5.04 

10.06 

9.1 
18.1 

592.8 
590.2 

1067.1 
1062.3 

562.2 
559-0 

1011.9 
I  OO6.  2 

41.0 
50.0 

20 

12.779 
17.51 

•01737 
.02381 

.2471 
-3386 

15.06 
20.06 

27.1 
36.1 

587-6 
584-9 

1057.6 
1052.8 

555-9 
552-7 

IOOO.5 

994-8 

68.0 

25 

23.69 

.03221 

.4581 

25.05 

45.1 

582.3 

1048.1 

549-5 

989.1 

77.0 

3° 

.04311 

"6132 

30.04 

54.1 

579-6 

1043-3 

546.3 

983.4 

86.0 

35 

42.02 

•05713 

.8126 

35-03 

63.1 

576.9 

1038.5 

543-1 

977-6 

95-0 

40 
45 

55-13 
71.66 

-07495 
•09743 

I.  O66l 
1.3853 

40.02 

45.00 

72.0 
81.0 

574-2 
571-3 

1033-5 
1028.4 

539-9 
536.5 

971.7 
965-7 

104.0 
113.0 

5° 

92.30 

.12549 

1.7849 

49-99 

90.0 

568.4 

1023.2 

533-o 

959-6 

122.  0 

55 

117.85 

.16023 

2.279 

54-98 

99-o 

565.6 

1018.1 

529.7 

953-5 

I3I.O 

66 

149.19 

.20284 

2.885 

59-97 

1  08.0 

562.8 

1013.1 

526-4 

947-5 

140.0 

65 

187.36 

•2547 

3.623 

64.98 

117.0 

559-9 

1007.8 

523.0 

941-3 

149.0 

70 

233-53 

•3175 

4.516 

69.98 

126.0 

556.9 

1002.5 

519.5 

935-0 

158.0 

75 

289.0 

.3929 

5.589 

74-99 

^35-0 

554-o 

997-3 

516.0 

928.8 

167.0 

80 

355-1 

.4828 

6.867 

80.01 

144.0 

551-1 

991.9 

512.6 

922.6 

I76.O 

85 
90 

433-5 
525.8 

.5894 
.7149 

8.383 
10.167 

85.04 
90.07 

'53-1 
162.1 

548.1 
544-9 

986.5 
980.9 

509.1 
505-4 

916.3 
909.9 

185.0 
194.0 

9i 

546.1 

.   .7425 

10.560 

91.08 

163.9 

544-3 

979-8 

504.7 

908.5 

195.8 

92 

567-1 

.7710 

10.966 

92.08 

165.7 

543-7 

978.7 

504-0 

907.2 

197.6 

93 

588.7 

.8004 

11.384 

93-09 

167-5 

543-1 

977.6 

503-3 

906.0 

199.4 

94 

611.0 

.8307 

11.815 

94.10 

169-3 

542-5 

976.5 

502.6 

904.7 

201.2 

95 

634.0 

.8620 

12.260 

95-" 

171.2 

541-9 

975-4 

501.9 

903-4 

203.0 

96 

657-7 

.8942 

12.718 

96.12 

173.0 

541.2 

974-2 

501.1 

902.1 

204.8 

97 

682.1 

.9274 

13.190 

97.12 

174.8 

540.6 

973-1 

500.4 

900.8 

206.6 

98 

707-3 

.9616 

13.678 

98.13 

176.6 

539-9 

971.9 

499-6 

899.4 

208.4 

99 

733-3 

.9970 

14.180 

99.14 

178.5 

539-3 

970.8 

498.9 

898.2 

210.2 

IOO 

760.0 

1.0333 

14.697 

IOO.2 

180.3 

538.7 

969.7 

498.2 

896.9 

2I2.O 

IOI 

787-5 

1.0707 

15.229 

IOI.  2 

182.1 

538-1 

968.5 

497-5 

895-5 

213-8 

1  02 

815.9 

1.1093 

I5-778 

102.2 

183.9 

537-4 

967-3 

496.8 

894.1 

215.6 

103 

845-1 

1.1490 

16.342 

103.2 

185.7 

536.8 

966.2 

496.1 

892.9 

217.4 

104 

875.1 

1.1898 

16.923 

104.2 

187.6 

536.2 

965.1 

495-4 

891.6 

219.2 

105 

906.1 

1.2319 

17.522 

105.2 

189.4 

535-6 

964.0 

494-7 

890.3 

22I.O 

106 

937-9 

1.2752 

18.137 

1  06.  2 

191.2 

534-9 

962.8 

493-9 

889.0 

222.8 

107 

970.6 

1.3196 

18.769 

IO7.2 

193.0 

534-2 

961.6 

493-  i 

887.6 

224.6 

108 

1004.3 

'•3653 

19.420 

1  08.  2 

194.8 

533-6 

960.5 

492.4 

886.3 

226.4 

109 

1038.8 

1.4123 

20.089 

109.3 

196.7 

532.9 

959-3 

491.6 

885.0 

228.2 

I  10 

1074.5 

1.4608 

20.777 

I  IO.3 

198.5 

532-3 

958.1 

490-9 

883.6 

23O.O 

1  1  1 

1  1  1  1.1 

1.5106 

21.486 

III.3 

200.3 

53  i  -6 

956.9 

490.2 

882.3 

231.8 

I  12 

1148.7 

1.5617 

22.214 

II2.3 

202.1 

530-9 

955-7 

489.4 

880.9 

233-6 

"3 

1187.4 

1.6144 

22.962 

"3-3 

203.9 

530-3 

954-5 

488.7 

879-5 

235-4 

114 

1227.1 

1.6684 

23.729 

JI4-3 

205.8 

529.6 

953-3 

487.9 

878.2 

237.2 

"5 
116 

»z 

1267.9 
1309.8 
1352-8 

1.7238 
1.7808 
I-8393 

24.518 
25.328 
26.160 

II5-3 
116.4 
117.4 

2O7.6 
2094 
211.  2 

528.9 
528.2 

527-5 

952-1 
950.8 

949-5 

487.1 
486.3 
485-S 

876.8 
875.4 
873-9 

239.0 
240.8 
242.6 

118 

1  397.o 

1.8993 

27.015 

118.4 

213.0 

526.9 

948.4 

484.8 

872.6 

244-4 

IK, 

1442.4 

1.9611 

27.893 

119.4 

214.9 

526.2 

947-2 

484.0 

871-3 

246.2 

SMITHSONIAN  TABLES. 


TABLE   259  (continued}. 

PROPERTIES  OF  SATURATED  STEAM. 


235 


Metric  and  Common  Units. 

If  a  is  the  reciprocal  of  the  Mechanical  Equivalent  of  Heat,  p  the  pressure,  s  and  a  the  specific  volumes  of  the 
liquid  and  the  saturated  vapor,  s  — .<r,  the  change  of  volume,  then  the  heat  equivalent  of  the  external  work  is  Apu  =: 
Ap(s  —  <r).  Heat  equivalent  of  internal  work,  p  —  r  —  Apu.  For  experimental  sp.  vols.  see  Knoblauch  l.inde  and 
Klebe,  Mitt,  iiber  Forschungarbeiten,  21,  p.  33,  1905.  Entropy  =  S  dQ/T,  where  dQ  =  amount  of  heat  added  at  ab- 
solute temperature  T.  For  pressures  of  saturated  steam  see  Holborn  and  Henning,  Ann.  der  Phys.  26  p.  831  1008' 
for  temperatures  above  205°  C.  corrected  from  Regnault. 


0 

Heat  Equivalent 

U            -jj 

of  External 

Specific  Volume. 

Density. 

u        .J 

i|I 

Work. 

Entropy 

Entropy 
of  Evapo- 

IP 

jrl 

Calories. 

B.t.U. 

of  the 
Liquid. 

ration. 

Cubic  Meters 
per  Kilo- 

Cubic Feet 
per 

Kilograms 
per  Cubic 

Pounds 
per 

w 

gram. 

Pound. 

Meter. 

Cubic  Foot. 

t 

Apu. 

Apu. 

e 

T 

T 

s 

s 

1 

1 

t 

s 

8 

o 
5 

3O.I 
30.6 

54-2 

55-2 

o.oooo 

.0183 

2.1804 
2.1320 

206.3 
147.1 

33°4- 
2356. 

0.00485 
.00680 

O.OOO3O3 
.000424 

32.0 

41.0 

10 

31.2 

56.1 

.0361 

2.0850 

106.3 

1703. 

.00941 

.000587 

50.0 

15 

3T-7 

57-1 

•0537 

2.0396 

77-9 

1248. 

.01283 

.OOOSOI 

59-o 

20 

32.2 

58.0 

.0709 

J-9959 

57-8 

926. 

.01730 

.OOIO8O 

68.0 

25 

32.8 

59-o 

.0878 

I-9536 

43-40 

693. 

.02304 

.001439 

77-o 

30 

33-3 

59-9 

.1044 

1.9126 

32-95 

528. 

•03035 

.OOI894 

86.0 

35 

33-8 

60.9 

/-       o 

.1207 

1.8728 

25-25 

4047 

.03960 

.002471 

95-o 

40 

34-3 

61.8 

.1368 

1.8341 

'9-57 

3I3-5 

.0511 

.003190 

104.0 

45 

34-8 

62.7 

.1526 

1-7963 

'5-25 

244.4 

.0656 

.004092 

1  13.0 

50 

35-4 

63.6 

.1682 

1-7597 

I  2.  02 

192.6 

.0832 

.00519 

122.0 

55 

35-9 

64.6 

.1835 

1.7242 

9.56 

153-2 

.1046 

.00653 

131.0 

60 

36-4 

65.6 

.1986 

1.6899 

7-66 

122.8 

•I3°5 

.OOSI4 

I4O.O 

65 

36-9 

66.5 

•2135 

1-6563 

6.19 

99-2 

.1615 

.01008 

149.0 

70 

37-4 

67.4 

.2282 

1.6235 

5.04 

80.7 

.1984 

.01239 

158.0 

75 

38.0 

68.5 

.2427 

1.5918 

4.130 

66.2 

.2421 

.OI5IO 

167.0 

80 

38.5 

.2570 

1.5609 

3-404 

54-5 

.2938 

.01835 

176.0 

85 

39-o 

70.2 

.2711 

1-5307 

2.824 

45-23 

•3541 

.O22I  I 

185.0 

90 

39-5 

71.0 

.2851 

1.5010 

2.358 

37-77 

.4241 

.02648 

194.0 

91 

39-6 

71.3 

.2879 

1.4952 

2.275 

36.45 

•4395 

-02743 

195.8 

92 

39-7 

71.5 

.2906 

1.4894 

2.197 

35-19 

•4552 

.02842 

197.6 

93 

39-8 

71.6 

•2934 

1.4836 

2.122 

34.00 

-4713 

.02941 

199.4 

94 

39-9 

71.8 

.2961 

1-4779 

2.050 

32.86 

.4878 

•03043 

2OI.2 

96 

40.0 
40.1 

72.0 
72.1 

.2989 

.3016 

1.4723 
1.4666 

1.980 

3i-75 
30.67 

•505 
•523 

.03149 
.03260 

203.0 
204.8 

97 

40.2 

72-3 

•3043 

1.4609 

{$49 

29.63 

•541 

•03375 

206.6  ; 

98 

40-3 

72.5 

.3070 

M552 

1.787 

28.64 

.560 

.03492 

208.4  i 

99 

40.4 

72.6 

•3097 

1.4496 

1.728 

27.69 

•579 

.O36l  I 

2IO.2 

100 
IOI 

40-5 
40.6 

72.8 
73-o 

•3I25 

1.4441 
1.4386 

1.671 
1.617 

26.78 
25.90 

.598 
.618 

-03734 
.03861 

212.0 
213.8 

1  02 

40.6 

73-2 

•3T79 

1-433° 

1.564 

25.06 

•639 

-.   .03990 

215.6 

103 

40.7 

73-3 

•3205 

1-4275 

1.514 

24-25 

.661 

W  .04124 

2174 

104 

40.8 

73-5 

•3232 

1.4220 

1.465 

23-47 

.683 

.04261 

219.2 

105 
1  06 

40.9 
41.0 

73-7 
73-8 

•3259 
.3286 

1.4165 
1.4111 

1.419 

J-374 

22.73 

22.01 

:$ 

.04400 
•04543 

221.0 
222.8 

107 

41.1 

74.0 

•3312 

1-4057 

21.31 

•751 

.04692 

224.6 

108 

41.2 

74-2 

•3339 

1.4003 

1.289 

20.64 

.776 

.04845 

226.4 

109 

41-3 

74-3 

•3365 

'•3949 

1.248 

19.99 

.801 

.0500 

228.2 

IIO 

in 

41.4 
41.4 

74-5 
74-6 

•3392 
.3418 

I-3895 
1.3842 

1.209 
1.172 

1877 

.827 
•833 

.0516 

.0533 

230.0 
231.8 

112 

41-5 

74-8 

•3445 

1-3789 

1.136 

18.20 

.880 

.0550 

233-6 

113 

41.6 

75-o 

1.3736 

I.  IOI 

17.64 

.908 

.0567 

235-4 

114 

41.7 

75-1 

'3498 

1-3683 

i.  068 

17.10 

•936 

.0585 

237.2 

"5 
116 
117 

41.8 
41.9 
42.0 

75-3 
75-4 
75-6 

•3524 
•3550 
.3576 

1-3631 
1-3579 

1.036 
1.005 
0.9746 

16.59 

16.09 
15.61 

.965 

•995 
1.026 

.0603 
.0622 
.0641 

239.0 
240.8 

242.6  i 

118 

42.1 

75-8 

.3602 

!-3475 

0.9460 

15.16 

1-037 

.0659 

244.4 

119 

42.2 

75-9 

•3628 

1.3423 

0.9183 

14.72 

1.089 

.0679 

246.2 

SMITHSONIAN  TABLES. 


236 


TABLE  259  (continued). 
PROPERTIES  OF  SATURATED  STEAM 

Metric  and  Common  Units. 


jilt 

Pressure 

Heat  of 
the  Liquid. 

Heat  of 
Vaporization. 

tteat  Equivalent  of 
Internal  Work. 

I  ill 

Q.SC«        ' 

H&i? 

i  e°  s 

Mm. 

of 

Kg. 

persq. 

Pds. 
persq. 

Calories. 

B.  T.  U. 

Calories. 

B.  T.  U. 

Calories 

i.  T.  U. 

IQ!  i 
&  * 

H     u 

Mercury. 

cm. 

in. 

t* 

t. 

P- 

P. 

P- 

q- 

q 

r 

r. 

P 

p- 

t. 

1  2O 
121 

122 

1489 
1537 

2.024 
2.089 
2.156 

28.79 
29.72 
30.66 

I2O-4 
I2I.4 

122.5 

216.7 
218.5 
220.4 

525.6 

524.9 
524.2 

946.0 
944-8 
943-5 

tsJ.6 

481.8 

870.0 
868.6 
867.1 

248.0 

249.8 

251.6 

124 

1636 
1688 

2.224 
2.294 

31.64 
32.64 

123-5 
124.5 

222.2 
224.1 

522'J 

942.3 
941.0 

481.0 
480.2 

865.8 
864.3 

253-4 
255-2 

Si 

129 

1740 

J795 
1850 

'907 
1966 

2-366 
2.440 
2.516 

2-593 
2.673 

33-66 
34-71 

38.01 

126.5 

127-5 
128.6 
129.6 

225.9 

2277 

229-5 
231.4 

233-3 

522.1 
521.4 
520.7 
520.0 

5[9-3 

939-9 
938.6 

937-3 
936.1 

934-8 

479-4 
478.6 
477.8 
477-0 
476.3 

863.0 
861.6 
860.2 
858.8 
8574 

257.0 
258.8 
260.6 

262.4 
264.2 

!  130 

I31 
!    132 
133 

2026 
2087 
2150 
2214 

2.754 
2.837 
2.923 
3.010 

39-  i  7 
40.36 

41-57 
42.81 

130.6 
131.6 
132.6 
133-7 

235-1 
236.9 

238.7 
240.6 

518.6 
5J7-9 
5I7-3 
516.6 

933-6 
932-3 
93I-J 
929.8 

475-5 
474-7 
474-0 
473-3 

856.0 
854-6 
853-2 
851.8 

266.0 
267.8 
269.6 
271.4 

i    134 

2280 

3.100 

44.09 

134-7 

242.4 

5*5-9 

928.5 

472.5 

850.4 

273.2 

!| 

2348 
2416 
2487 

3.192 
IP* 

45-39 
46.73 
48.10 

135-7 
136.7 

244.2 
246.0 
247.9 

5I5-1 
5I4-4 
5I3-7 

927.2 
924.6 

471.6 
470.8 
470.1 

848.9 

847.5 
846.1 

275.0 
276.8 
278.6 

139 

2560 
2634 

3.480 
3-58i 

49-5° 
50-93 

139.8 

249.7 
251.6 

5J3-0 
5*2-3 

923-3 
922.1 

469-3 
468.5 

844.6 
843-3 

280.4 
282.2 

140 

2710 

3.684 

52.39 

140.8 

2534 

5«-S 

920.7 

467.6 

841.8 

284.0 

141 

2787 

53-89 

141.8 

255-3 

510.7 

9I9-3 

466.8 

840.2 

285.8 

142 

2866 

3-897 

55-43 

142.8 

257-1 

510.1 

918.1 

466.1 

838.9 

287.6 

i43 

2948 

4.008 

57-oo 

143-9 

509-3 

916.7 

465-3 

837-4 

289.4 

3030 

4.121 

58.60 

144.9 

26a8 

508.6 

9J5-4 

464.4 

835.9 

291.2 

145 

3I!5 

4-236 

60.24 

M5-9 

262.7 

507-8 

914.1 

463-6 

834-5 

293.0 

i   146 

3202 

4-354 

61.92 

146.9 

264.5 

5°7-i 

912.8 

462.8 

833-1 

294.8 

M7 

3291 

4-474 

63.64 

148.0 

266.4 

506.4 

911.5 

462.0 

831.6 

296.6 

,48 

4-597 

65-39 

149.0 

268.2 

505-6 

910.1 

461.2 

830.1 

298.4 

,    *49 

3474 

4-723 

67.18 

150.0 

270.1 

504-9 

908.8 

460.4 

828.7 

300.2 

I50 

3569 

4.852 

69.01 

I5I.O 

271.9 

504.1 

9°7-4 

459-5 

827.2 

302.0 

151 

3665 

4.984 

70.88 

152.1 

273.8 

5°3-4 

906.1 

458.7 

825-7 

303-8 

I52 

3764 

5.118 

72.79 

275.6 

502.6 

904.7 

457-9 

824.2 

305-6 

'S3 

3865 

5-255 

74-74 

I54.I 

277.4 

501.9 

903-3 

457-1 

822.7 

307-4 

•   3968 

5-395 

76.73 

279.2 

501.1 

901.9 

456.3 

821.2 

309.2 

IP 

4073 
4181 

5-538 
5.684 

78.76 
80.84 

156.2 

I57.2 

281.1 
283.0 

500.3 

%£\ 

455-4 
454-6 

819.6 
818.2 

311.0 

312.8 

^57 

4290 

5-833 

82.96 

158.2 

284.8 

498.8 

897.8 

453-8 

816.7 

314.6 

•58 

4402 

5-985 

85.12 

J59-3 

286.7 

498.1 

896.5 

453-o 

815-3 

316.4 

45'7 

6.141 

87.33 

160.3 

288.5 

497-3 

895.1 

452-1 

8i37 

318.2 

160 

4633 

6.300 

89-59 

161.3 

290.4 

496-5 

8937 

451.2 

812.2 

320.0 

161 

4752 

6.462 

91.89 

162.3 

292.2 

495-7 

892.3 

450-4 

810.7 

321.8 

162 

4874 

6.628 

94.25 

163.4 

294.1 

494-9 

890.9 

449-5 

809.2 

323.6 

163 

4998 

6.796 

96-65 

164.4 

295-9 

494-2 

889.5 

448.7 

807-7 

325-4 

164 

5124 

6.967 

99.09 

165.4 

493-4 

888.1 

447-9 

806.2 

327.2 

a 

gS 

7.142 
7.320 

101.6 
104.1 

166.5 

167.5 

299.6 
3OI-5 

492.6 
491.9 

886.7 
885.4 

447-0 
446.3 

804.7 
803-3 

329.0 
330.8 

167 

55i8 

7.502 

106.7 

168.5 

3°3-3 

491.1 

883.9 

445-4 

801.7 

332.6 

168 

5655 

7.688 

109.4 

169.5 

3°5-  ! 

49°-3 

882.5 

444-6 

800.1 

334-4 

169 

5794 

7.877 

II2.O 

170.6 

307.0 

489-5 

88  1.  o 

443-7 

798.5 

336-2 

SMITHSONIAN   TABLES. 


TABLE  259  (continued). 

PROPERTIES  OF  SATURATED  STEAM. 

Metric  and  Common  Units. 


237 


Temperature 
r*  Decrees 
Centigrade. 

Heat  Equivalent 
of  External  Work. 

Entropy 
of  the 
Liquid. 

e. 

Entropy 
of  Evapo- 
ration. 

r 
T 

Specific  Volume. 

Density. 

Temperature  1 

r*  Degrees 
Fahrenheit. 

Calories. 
Apu. 

B.  T.  U. 

Apu. 

Cubic 
Meters  per 
Kilogram. 

s. 

Cubic 
Feet  per 
Pound. 

s. 

Kilograms 
per  Cubic 
Meter. 
1. 

8 

Pounds 
per  Cubic 
Foot. 

1. 

8 

1  2O 

42.2 

76.0 

0.36W 

1-3372 

0.8914 

14.28 

1.  122 

0.0700 

248.0 

121 

42.3 

76.2 

.3680 

I-332I 

.8653 

13.86 

1.156 

.0721 

249.8 

122 

42.4 

76.4 

.3705 

1.3269 

.8401 

13.46 

I.I90 

.0743 

251.6 

123 

42.5 

76.5 

•3731 

1.3218 

.8158 

13.07 

1.226 

.0765 

2534 

124 

42.6 

76.7 

•3756 

1.3167 

.7924 

12.69 

1.262 

.0788 

255.2 

125 

42.7 

76.8 

.3782 

1.3117 

.7698 

I2-33 

1.299 

.08ll 

257.0 

I  2O 

42.8 

77.0 

.3807 

1.3067 

•7479 

11.98 

1-337 

•0835 

258.8 

127 

42.9 

f" 

1.3017 

.7267 

11.64 

1.376 

260.6 

128 

43-o 

77-3 

1.2967 

.7063 

11.32 

1.416 

.0883 

262.4 

129 

43-° 

77-4 

1.2917 

.6867 

II.OO 

1.456 

.0909 

264.2 

130 

43-  T 

77-6 

•3909 

1.2868 

.6677 

10.70 

1.498 

•°935 

266.0 

43-2 

77-7 

•3934 

I.28l8 

.6493 

10.40 

1.540 

.0961 

267.8 

132 

43-3 

77-9 

•3959 

1.2769 

•631  5 

IO.I2 

1.583 

.0988 

269.6 

i    J33 

43-3 

78.0 

.3985 

1.2720 

.6142 

9.839 

1.628 

.IOl6 

271.4 

134 

43-4 

78.1 

.4010 

1.2672 

•5974 

9-569 

1.674 

.1045 

273.2 

i    J35 

43-5 

78.3 

•4035 

1.2623 

.5812 

9.309 

1.721 

.1074 

275.0 

1    136 

43-6 

78.4 

.4060 

1-2574 

.5656 

9.060 

1.768 

.1104 

276.8 

i    137 

43-6 

78.5 

.4085 

1.2526 

8.820 

1.816 

•"34 

278.6 

138 

43-7 

78.7 

.4110 

1.2479 

•5361 

8.587 

1.865 

.1165 

280.4 

139 

43-8 

78.8 

•4135 

1.2431 

.5219 

8.360 

1.910 

.1196 

282.2 

140 

43-9 

78.9 

.4160 

I-2383 

.5081 

8.140 

1.968 

.1229 

284.0 

141 

43-9 

79.1 

.4185 

1-2335 

•4948 

7.926 

2.O2I 

.1262 

285.8 

142 

44-o 

79-2 

.4209 

.4819 

7.719 

2.075 

.1296 

287.6  i 

'43 

44-o 

79-3 

•4234 

1.2241 

.4694 

7.519 

2.130 

•I33° 

289.4 

144 

44-2 

79-5 

•4259 

I.2I94 

•4574 

7.326 

2.186 

•I365 

291.2 

M5 

44-2 

79.6 

.4283 

1.2147 

4457 

7.139 

2.244 

.1401 

293.0 

146 

44-3 

79-7 

•43°7 

1.  2100 

4343 

6-957 

2.303 

•1437 

294.8  j 

147 

44-4 

79-9 

'     -4332 

1.2054 

.4232 

6.780 

2.363 

•1475 

296.6 

148 

44.4 

80.0 

•4356 

1.2008 

.4125 

6.609 

2.424 

298.4  \ 

149 

44-5 

80.  i 

.4380 

1.1962 

.4022 

6-443 

2.486 

•1552 

300.2 

150 

44.6 
44-6 

80.2 
80.4 

•4405 
•4429 

1.1916 
1.1870 

.3824 

6.282 
6.126 

2-550 
2.615 

.1592 
.1632 

302.0 
303-8 

J52 

44-7 

80.5 

•4453 

I.I824 

.3729 

5-974 

2.682 

.1674 

305-6 

'53 

44.8 

80.6 

•4477 

I.I778 

•3637 

5.826 

2.750 

.1716 

307-4 

154 

44.8 

80.7 

.4501 

I-I733 

•3548 

5-683 

2.818 

.'759 

309.2 

155 

44-9 

80.9 

.4525 

I.I688 

•3463 

5-546 

2.888 

.1803 

311.0 

I56 

45-o 

81.0 

•4549 

1.1644 

•338o 

5413 

2-959 

.1847 

312.8 

157 
158 

45-° 

45-1 

81.1 
81.2 

•4573 
•4596 

I-I599 
I-'554 

.3298 
.3218 

5.282 
5-  '54 

3-032 
3.108 

.1893 
.1940 

3*4-6    I 
316.4 

T59 

45-2 

81.4 

.4620 

1.1509 

.3140 

5.029 

3-^5 

.1988 

318.2 

1  60 

45-3 

81.5 

.4644 

1.1465 

•3063 

4.906 

3-265 

.2038 

320.0    I 

161 

45-3 

81.6 

.4668 

1.1421 

.2989 

4.789 

3-345 

.2088 

321.8 

162 

45-4 

81.7 

.4692 

1.1377 

.2920 

4-677. 

.2138 

323-6 

163 

45-5 

81.8 

•4715 

i-I333 

-2855 

4-571 

3-503 

.2188 

164 

45-5 

81.9 

•4739 

1.1289 

.2792 

4.469 

.2238 

327-2 

165 

45-6 

82.0 

•4763 

1.1245 

.2729 

4.368 

3.664 

.2289 

329.0 

166 

45-6 

82.1 

.4786 

I.I2O2 

.2666 

4.268 

3-751 

•2343 

330-8 

167 

45-7 

82.2 

.4810 

I.II59 

.2603 

4.168 

3.842 

•2399 

332.6 

1  68 

45-7 

82.4 

4833 

I.III5 

•2540 

4.070 

3-937 

•2457 

334-4 

169 

45-8 

82.5 

.4857 

I.I072 

.2480 

3-975 

4.032 

.2516 

336.2 

SMITHSONIAN   TABLES. 


238 


TABLE  2 59  (continued). 
PROPERTIES  OF  SATURATED  STEAM 

Metric  and  Common  Units. 


ITTf 

Pressure. 

Heat  of- 
the  Liquid. 

Heat  of 
Vaporization. 

Heat  Equivalent 
of  Internal  Work. 

Z     ~ 

ill 

III 

Mm 
of 

Kg. 
persq. 

Pds. 
persq. 

Calories. 

B.  T.  U. 

Calories. 

B.T.  U. 

Calories. 

B.  T.  U. 

|l| 
fit 

H    ^ 

klercury. 

cm. 

in. 

M 

t. 

P- 

P- 

P. 

q- 

q- 

r. 

r. 

P- 

p. 

t. 

170 
171 

5937 

6o8l 

8.071 
8.268 

114.8 
117.6 

171.6 
172.6 

308.9 
3IO-7 

488.7 
487.9 

879.6 
878.3 

442-8 
441.9 

797-0 
795-6 

338-0 
339-8 

172 

'73 
174 

6229 
6379 
6533 

8.469 
8-673 
8.882 

120.4 

1234 
126.3 

173-7 
174-7 
175-7 

312-6 
3'4-5 
316-3 

487.1 
486.3 
485.5 

876.9 
875-4 
873.9 

441.1 
440.2 

439-4 

794-1 
792-5 
790.9 

341.6 
343-4 
345-2 

'75 
176 

178 
'79 

7010 

7343 

9.094 
9.310 

9-531 
9-755 

129.4 
132.4 
135-6 
138.8 
142.0 

176.8 
177.8 
178.8 
179.9 
180.9 

318.2 

323-7 
325-6 

484.7 
483.9 
483.1 
482.3 
481.4 

872.4 
871.0 
869.5 

868.1 
866.6 

438.5 
437-7 
436.8 
436-0 
435-o 

789-3 
787-8 
786.2 
784.7 
783-1 

347-0 
348.8 
350.6 

352-4    ' 
354-2 

180 

iSi 

75M 
7688 
7866 

10.216 

10.453 
10.695 

145-3 
148.7 
152.1 

181.9 
183.0 
184.0 

327-5 
329-3 
331-2 

480.6 

479-8 
479-o 

865.1 
863.6 
862.2 

434-2 
433-3 

432-5 

781-5 
779-9 
778.4 

356.0 
357-8 
3.S9-6 

183 
184 

8046 
8230 

10.940 
11.189 

159.2 

185.0 
I86.I 

333-o 
334-9 

478-2 
4774 

860.7 
859.2 

430.8 

776.9 

775-3 

361.4 
363-2 

185 

8417 

11.44 

162.8 

187.1 

336.8 

476.6 

8577 

429-9 

773-7 

365.0 

186 

8608 

11.70 

166.5 

188.1 

338.6 

4757 

856-3 

429.0 

772.2 

366.8 

187 

8802 

11.97 

I7O.2 

189.2 

340-5 

474-8 

854.7 

428.0 

770.5 

368.6 

1  88 

8999 

12.24 

174.0 

190.2 

342-4 

474-0 

853-2 

427-2 

768.9 

3/0-4 

189 

9200 

12.51 

177.9 

191.2 

344-2 

473-2 

851-7 

426.3 

767.4 

372.2 

190 

9404 

12.79 

181.8 

192.3 

346.1 

472.3 

850.2 

4254 

765-8 

374-0 

191 

s- 

9612 

13-07 

185.9 

!93-3 

347-9 

471-5 

848.7 

424.5 

764.2 

375-8 

192 

9823 

190.0 

194,4 

349-8 

470.6 

847-1 

423-6 

762.5 

377-6 

193 

10038 

13-65 

194.1 

195-4 

469.8 

845-6 

422.8 

761.0 

379-4 

194 

10256 

13.94 

198-3 

196.4 

353-5 

468.9 

844.1 

421.9 

759-4 

381.2 

195 

10480 

14-25 

202.6 

197.5 

355-4 

468.1 

842.5 

421.0 

757-7 

383-0 

196 

10700 

2O7.O 

198.5 

357-3 

467.2 

841.0 

420.1 

756.1 

384-8 

'97 

10930 

14.87 

2II.4 

199.5 

359-2 

466.4 

839-5 

419.2 

754-6 

386.6 

198 

II  170 

15.18 

216.0 

2OO.6 

361.1 

465-6 

838.0 

418.4 

753-0 

388.4 

199 

11410 

«5-5i 

220.6 

2OI.6 

362-9 

464.7 

836.4 

417.4 

75T-3 

390.2 

200 

201 

11650 
11890 

15.84 
16.17 

225.2 
223.0 

202.7 

203.7 

364.8 
366.7 

463.8 
462.9 

834.8 
833-3 

416-5 
415.6 

749-7 
748-1 

392.0 
393-8 

202 

12140 

16.51 

234.8 

204.7 

368.5 

462.1 

831.8 

414.8 

746.6 

395-6 

203 
204 

12400 
12650 

16.85 
17.20 

239-7 
244.7 

205.8 
206.8 

370.4 
372.3 

461.2 
460.3 

830.2 
828.6 

413.8 
412.9 

744-9 
743-3 

397-4 
399-2 

205 

12920 

17.56 

249.8 

207.9 

374-1 

459-4 

827.0 

412.0 

741.6 

401.0 

!     206 

13180 

17.92 

254-9 

208.9 

376.0 

458.6 

825.4 

411.1 

740.0 

402.8 

207 

13450 

18.29 

200.1 

2IO.O 

377-9 

457-7 

823.8 

410.2 

738.3 

404.6 

208 

13730 

18.66 

265.4 

21  1.  0 

379-8 

456.8 

822.2 

409-3 

736.7 

406.4 

209 

14010 

19.04 

270.8 

212.0 

381.6 

455-9 

820.6 

408.4 

735-1 

408.2 

210 

14290 

19-43 

276.3 

2I3.I 

383-5 

455-o 

819.1 

407-5 

733-6 

410.0 

211 

14580 

19.82 

281.9 

2I4.I 

385.4 

454-1 

817.4 

406.6 

731-9 

411.8 

212 
213 

14870 

20.22 
20.62 

287.6 
293-3 

215.2 
216.2 

387.3 
389-2 

453-2 

815.8 
814.3 

405-7 
404-9 

730.2 
728.7 

413.6 
4154 

!   214 

15470 

21.03 

299.2 

217-3 

39i-i 

45i-5 

812.7 

404.0 

727.1 

417-2 

215 

15780 

21.45 

305.1 

218.3 

392.9 

450.6 

811.0 

403.1 

725.4 

419.0 

216 

16090 

21.88 

3II.I 

219.3 

394-8 

449-6 

809.3 

402.1 

723-7 

420.8 

i     2I7 

16410 

22.31 

317.3 

220.4 

396.7 

448.7 

807.7 

401.2 

722.1 

422.6 

218 

16730 

22.74 

3230 

221.4 

398.5 

447-8 

806.  i 

400.3 

720.5 

424.4 

219 

17060 

23,19 

329.8 

222.5 

400.4 

446.9 

804.5 

399-4 

718-9 

4262 

2  2O 

17390 

23.64 

336.2 

223-5 

402.3 

446.0 

802.9 

398.5 

717.3 

428.0 

SMITHSONIAN   TABLES. 


TABLE  253   (continued). 

PROPERTIES  OF  SATURATED  STEAM. 

Metric  and  Common  Units. 


239 


Temperature 
r  Degrees 
Centigrade. 

Heat  Equivalent 
of  External  Work. 

Entropy 
of  the 
Liquid. 

0. 

! 

Entropy 
of  Evapo- 
ration. 

r 
T' 

Specific  Volume. 

Density. 

Temperature 
r  Depri-rs 
Fahrenheit. 

Calories. 
Apu. 

B.  T.  U. 
Apu. 

Cubic 
Meters  per 
Kilogram. 

s. 

Cubic 
Feet  per 
Pound. 

s. 

Kilograms 
per  Cubic 
Meter. 
1 

Pounds 
per  Cubic 
Foot. 
1 

170 

45-9 

82.6 

0.4880 

I.IO29 

0.2423 

3.883 

4.127 

0.2575 

338.0 

171 

46.0 

82.7 

•4903 

1.0987 

.2368 

3-794 

4.223 

.2636 

339-8 

172 

46.0 

82.8 

.4926 

1.0944 

.2314 

3.709 

4.322 

.2696 

341.6 

173 

46.1 

82.9 

•4949 

I.090I 

.2262 

3.626 

4.421 

•2758 

343-4 

174 

46.1 

83.0 

•4972 

1.0859 

.2212 

3.545 

4.521 

.2821 

345-2 

'75 
176 

46.2 
46.2 

83.I 

83.2 

-4995 
.5018 

1.0817 
1-0775 

.2164 
.2117 

3467 
3-391 

4.621 
4.724 

.2884 
-2949 

340 

177 
178 

46.3 
46.3 

83-3 
834 

.5041 
.5064 

1-0733 
1.0691 

.2072 
.2027 

3-3*8 

3-247 

4.826 

4-933 

.3014 
.3080 

350-6 
352.4 

179 

46.4 

83-5 

.5087 

1.0649 

.1983 

3-J77 

5-°4 

.3148 

354-2 

1  80 

46.4 

83.6 

.5110 

1.  0608 

.1941 

3.109 

5-T5 

•3217 

356.0 

181 
182 

183 

184 

46.  <; 
46.5 
46.6 
46.6 

83.7 
83-8 
83.8 
83.9 

•5133 
-5156 
.5^78 
.5201 

1.0567 
1.0525 
1  .0484 
1.0443 

.1899 
-1857 
.1817 
.1778 

3.041 

2-974 
2.911 

2.849 

5-27 
5-38 
5-50 
5.62 

.3288 
•3362 

•3435 

357-8 
359-6 
361.4 
363-2 

i85 

46.7 

84.0 

.5224 

1.0403 

.1740 

2.787 

5-75 

•3588 

365-0 

1  86 

46.7 

84.I 

.5246 

1.0362 

.1702 

2.727 

5-88 

•3667 

366.8 

187 

46.8 

84.2 

.5269 

I.O32I 

.1666 

2.669 

6.00 

•3746 

368.6 

1  88 

46.8 

84-3 

.5291 

1.0280 

.1632 

2.614 

6.13 

.3826 

370.4 

189 

46.9 

84-3 

•S3»4 

I.O24O 

.1598 

2.560 

6.26 

.3906 

372.2 

190 

46.9 

84.4 

•5336 

I.O2OO 

•1565 

2-507 

6-39 

•3989 

3740 

191 

47.0 

84-5 

•5358 

1.0160 

•'533 

2.456 

6.52 

.4072 

375-8 

192 

47-o 

84.6 

.538i 

I.OI20 

.1501 

2.405 

6.66 

.4158 

377-6 

47-0 

84.6 

•5403 

I.OOSO 

.1470 

2-355 

6.80 

•4246 

379-4 

194 

47-0 

84.7 

.5426 

I.OO4O 

.1440 

2.306 

6.94 

.4336 

381-2 

i95 

47.1 

84.8 

.5448 

I.OOOO 

.1411 

2.259 

7-09 

.4426 

383-0 

196 

47.1 

84.9 

•5470 

0.9961 

.1382 

2.214 

7-23 

.4516 

384.8 

'97 

47.2 

84.9 

.5492 

•1354 

2.169 

7-38 

.4610 

386.6 

198 

47.2 

85.0 

•55r4 

.9882 

2.126 

7-53 

.4704 

388.4 

199 

47-3 

85.1 

.5536 

•9843 

.1300 

2.083 

7-69 

.4801 

390.2 

200 

47-3 

85.I 

.5558 

.9804 

.1274 

2.041 

7.84 

.4900 

392.0 

20  1 

47-3 

85.2 

•9765 

.1249 

2.OOI 

8.00 

.4998 

393-8 

202 

47-3 

85.2 

.5602 

.9727 

.1225 

1.962 

8.16 

.510 

395-6 

203 

47-4 

85.3 

•5624 

.9688 

.1201 

1.923 

8-33 

.520 

397-4 

2O4 

47-4 

85-3 

.5646 

.9650 

.1177 

1.885 

8.50 

•531 

399-2 

205 

47-4 

85-4 

.5668 

.9611 

•IT53 

1.847 

8.67 

•541 

401.0 

206 
207 

47-5 
47-5 

85.4 
85.5 

.5690 

•5712 

•9572 

•9534 

.1  130 
.1108 

I.8IO 

1-774 

8.85 
9-03 

£ 

402.8 
404.6 

208 

47-5 

85.5 

-5733 

•9496 

.1086 

1-739 

9.21 

•575 

406.4 

209 

47-5 

85.5 

•5755 

•9458 

.1065 

1-705 

9-39 

.587 

408.2 

210 

47-5 

85-5 

•5777 

.9420 

.1044 

1-673 

9.58 

.598 

410.0 

211 

47-5 

85.5 

•5799 

.9382 

.1024 

1.640 

9-77 

.610 

411.8 

212 

47-5 

85.6 

.5820 

•9344 

.1004 

1.608 

9.96 

.622 

413.6 

213 

47-5 

85.6 

.5842 

•9307 

.0984 

i-577 

10.16 

.634 

4I5-4 

2I4 

47-5 

85.6 

-5863 

.9269 

.0965 

1.546 

10.36 

.647 

417-2 

«S 

47-5 

85.6 

•5885 

.9232 

•0947 

1.516 

10.56 

.660 

419.0 

2l6 

47-5 

85.6 

•59o6 

•9T95 

.0928 

1.486 

10.78 

•673 

420.8 

217 

47-5 

85.6 

•5927 

•9r57 

.0910 

1.458 

10.99 

.686 

422.6 

218 

47-5 

85.6 

•5948 

.9120 

.0893 

1.430 

11.20 

•699 

424-4 

2I9 

47-5 

85.6 

•5969 

.9084 

.0876 

1.403 

11.41 

426.2 

220 

47-5 

85.6 

•5991 

•9°47 

.0860 

1.376 

11.62 

•727 

428.0 

SMITHSONIAN   TABLES. 


240 


TABLE  260. 
LATENT    HEAT    OF    FUSION, 


This  table  contains  the  latent  heat  of  fusion  of  a  number  of  solid  substances  in  large  calories  per 
kilogram  or  small  calories  or  therms  per  gram.  It  has  been  compiled  principally  from  Landolt 
and  Bernstein's  tables.  C  indicates  the  composition,  7"  the  temperature  Centigrade,  and  H  the 
latent  heat. 


Substance. 

C 

T 

H 

Authority. 

Alloys:  3O.5Pb  +  oo^Sn    . 
36.9Pb-f63.iSn    . 
63.7  Pb  +  36.3  Sn    . 
77.81'b  +  22.2811    . 
Britannia  metal,  QSn  +  i  Pb 
Rose's  alloy, 
24Pb-f27.3Sn-f  48.76! 
Wood's  a,loyj;5.8Pb+|4.7Sn| 

Aluminum  
Ammonia    
|  Benzene      

PbSn4 
PbSn8 
PbSn 
PbaSn 

Al 
NH3 
C6H6 

183 
179 

177-5 
176.5 
236 

98.8 

75-5 
658. 

—75- 
c.4 

17- 

!5-5 
11.6 
9-54 

28.0* 

6.85 
8.40 

76.8 
1  08. 
30.6 

Spring. 

M 

Ledebur. 
Mazzotto. 

Glaser. 
Massol. 
Mean. 

Br 

—  7."? 

16.2 

Regnault. 

Bi 

268 

12.64 

Person. 

Cadmium    
Calcium  chloride 

Cd 
CaCl2  +  6H2O 
Cu 

320.7 
28.5 

1081 

13.66 
40.7 
42. 

n 

« 

Mean. 

Iron,  Gray  cast  .... 
"     White  "    . 
"     Slag   

I 

23- 
33- 

5°. 

II.  71 

Gruner. 
« 
Favre  and  Silbermann. 

Ice      

H2O 

o 

70.6"? 

(  Dickinson,  Harper, 

M 

a 

o 

7Q.  CQ 

|      Osborne.t 
Smith  J 

"     (from  sea-water)  . 
Lead    

\  H20  +  3.535  1 
j      of  solids       1 
Pb 
Hg 

-8-7 

327 
—  39 

54-0 

5-36 
282 

Petterson. 

Mean. 
Person. 

Naphthalene       .... 
Nickel         

.  C10H8 

Ni 

79.87 

14.  -?c 

35.62 

A   64. 

Pickering. 
Pionchon 

Pd 

I  54.1 

4-«4 
l6  1 

Violle 

Phosphorus         .... 
Platinum     

P 
Pt 
K 

44.2 

1755 
62 

4-97 
27.2 

I  c  7 

Petterson. 
Violle. 
Toannis 

Potassium  nitrate       .        . 
Phenol         
Paraffin       
Silver           

KNO3 
C6H60 

Ag 
Na 

333-5 

25-37 
52.40 
961 

Q7 

48.9 
24-93 

35-10 
21.07 
31  7 

Person. 
Petterson. 
Batelli. 
Person. 
Toannis 

"       nitrate    .... 
"       phosphate 
Spermaceti           .... 

NaNO3 
(  Na2HPO4  | 
i   +  I2H20  \ 

s 

yl 

305-8 

36.1 

43-9 

I  \  r 

64.87 
66.8 
36.98 

Q  17 

« 
Batelli. 

Tin      
Wax  (bees)         .... 

Sn 
Zn 

1  1  J 

232 
61.8 

4.IQ 

y.j/ 
14.0 

42.3 
28  n 

Mean. 

<« 

l| 

LJ.i  J 

*  Total  heat  from  o°  C. 

t  U.  S.  Bureau  of  Standards,  1913,  in  terms  of  15°  calorie. 
J  iq»o3,  based  on  electrical  measurements,  assuming  mechani 
international  volt  in  use  after  1911. 

SMITHSONIAN  TABLES. 


g  mechanical  equivalent  =  4.187,  and  in  terms  of  the  value  of  the 


TABLES  261-262. 
TABLE  261.  —  Heat  of  Combustion  of  Some  Carbon  Compounds. 


241 


Compound. 

Formula. 

Kg.  cal. 
per  g- 
mol. 

Kg.  cal. 
perg 

Compound. 

Formula. 

Kg.  cal. 
perg- 
mol. 

Kg.  cal. 
perg 

Paraffins: 
Methane,  g  

CH< 

C2H6 
CsHs 
CJIio 
CoHu 

C7Hl6 

C8H18 
CioHzz 

C2H4 
C3H6 
C4H8 
CsHio 
C6H12 
C2H2 
C3H6 
CsHs 
CeHe 
CioHs 
C7Hg 
CHCla 
CS2 
CHaCl 
C^sCl 

2I4P 

37tp 
52&p 
6&7P 
99SP 
H39/> 
i3i5/> 
I026p 

343P 
496^ 
651* 
&04p 
962P 
3i3/> 
S03P 
78i/> 
7&SP 
1235^ 
937  P 
70 
253P 
i69p 
332p 

13.30 

12.4V 
12.  Op 
Il.&P 

n.6v 
ii.  4P 
it.  Si 
11.45 

12.  2P 

ii.  8v 
ii.  6p 
tt.sp 
ii.  4V 

1  2.  OP 
II.  Op 
10.  Op 

10.  ip 
9.  6v 

10.  2V 
3.2&V 

3.26P 
S-io/> 

Alcohols: 
Methyl,  1 

CH4O 
C2HeO 
CaHsO 
C4HioO 
C5H120 

C2H6O 
C4H100 
CsHsO 

CH.02 
C2H402 
CsHeOz 

C4H80J 

CjHsO, 

CeHioOs 
CizHzoOio 
CaHsOa 
CeHeO 
C^HzzOn 
CeHioCH 
CioHuO 
CO(NH»)2 

nop 

32jp 
483^ 

^ 
1$. 

5o6p 

62p 
2IOP 

3(&p 
525P 
330/> 

680 
414 
397 
735 

'82 

1353 
152 

5  3i* 
7.10* 
8.00^ 
8.68» 
8.96* 

7.6o* 
8.92* 
8-43* 

i-357» 
3-49» 
4.965 

3:S 

4.S8. 

J:S 

3-9SP 
4-23 

9.02p 

2.53 

Ethane,  g  

Ethyl  1 

Propane  g 

i-Butane,  g  

n-butyl,  1  .... 
Amyl  1 

n-Hexane,  1  

n-Heptane  1 

Ethers: 
Dimethyl  g 

n-Octane,  1  

Dekane,  1  

Diethyl  v 

defines: 
Ethylene,  g  

Ethyl-methyl,  v  

Acids: 
Formic  1 

Propylene,  g  

i-Butylene,  g  
Amylene  1 

Acetic,  1  

Hexylene,  1  
Acetylene,  g  

n-butyric,  1.  < 

Lactic,  1   .... 

Trimethylene,  g  
Benzene,  1  

Cellulose  s 

Naphthalene,  1  

Toluene,  1  

Phenol,  1  

Chloroform,  v  

Sugar,  cane,  s  
Starch  s 

Carbon  disulphide  1 

Methyl-chloride,  g  
Ethyl-chloride,  v  

Thymol,  1.    . 

Urea  1 

v,  p,  following  the  heats  of  combustion,  signify  at  constant  volume  and  pressure  respectively.    When  re- 
ferred  to  constant  pressure,  the  values  are  0.58  Kg-cal.  greater  (at  about  18°  C)  for  each  condensed  gaseous 
molecule.     The  values  are  means  from  various  observers.    The  combustion  products  are  gaseous  COt,  liquid 
water,  etc.                                                                                                                                                                        I 

TABLE  262.  —  Heat  of  Combustion  —  Miscellaneous. 


Substance. 

Small 
calories 
perg 
substance. 

Reference.  1 

Substance. 

Small 
calories 
perg 
substance. 

Reference.  1 

Asphalt 

9530 
9200 
8080 
8100 
7860 
7900 
590 
1290 
5700 
8100 
9500 
5900 
33900 
1582 
6080 
9500 
9300 
9400 

i 

2 
2 
3 

3 

5 
4 

2 
2 

2 

2 

Oils:  petroleum: 
crude 

11500 

IOOOO 
IO200 

9500 

IOOOO 

11140 
10340 
8400 

22OO 
2240 

9500 
4170 
4210 
3990 
4420 

2 

2 
2 

6 

I 

6 

2 

I 

8 
8 
8 
8 

Butter 

light 

heavy  

diamond  

Copper  (to  CuO)  

Paraffin  (to  COz,  HiiO  1)  
Paraffin  (to  COz,  HizO  g)  
Pitch 

Dynamite,  75%  

Egg  white  of 

Sulphur  rhombic  

Fats,  animal  

Sulphur,  monoclinic  
Tallow  
Woods-  beech    13%  HzO  

Hydrogen  
Iron  (to  FezOs) 

birch   12%  H«O        

oak    13%  HzO  

Oils:  cotton-seed  
lard 

pine  12%  HO    

olive  

References:  (i)  Slossen,  Colburn;  (2)  Mean;   (3)  Berthellot;   (4)  Roux,  Sarran;   (5)  Thomsen;   (6)  Stoh- 
mann;    (7)  Gibson;    (8)  Gottlieb. 

SMITHSONIAN  TABLES 


242 


TABLE  263. 
HEAT  VALUES  AND  ANALYSES    OF   VARIOUS  TYPES  OF   FUEL- 


(a)  COALS. 


Coal. 


.ignite 


f  Low  grade. 
\  High  grade 
b-bitu-     Low  jzrade. 
minous  i  High  grade 
itu-         f  Low  grade, 
minous  \  High  gni.U- 
emi-bitu- (  Low  grade 
minous  \  Highgrade 

mi-anthracite   

thra-  I  Low  grade, 
cite  1  High  grade 
en  I  Low  grade, 
coke  I  High  grade 


38.81 
33  38 
22.71 
15-54 
11.44 
3-42 

I:7* 

2.07 
2.76 
3-33 
1. 92 

1.14 


I! 


25-48 
27-44 
34.78 
33-03 
33-93 
34.36 
U.5 
14-57 
9.81 
2.48 


27.29 
29.62 
36.60 
46.06 
43.92 

58.83 

75.5 
78.20 

78.82 

82.07 
84.28 
88.87 

94-66 


8.42 
9-56 
5-91 
5-37 

10.71 
3-39 
7-3 
3-97 
9-30 

12.69 
9.12 
8.99 
3-57 


0.97 
0-94 
0.29 
0.58 
4-94 
0:58 
0.99 
0.54 
1-74 
0-54 
0.60 
1.18 
o.  69 


7.09 
6.77 
6.14 
5-89 
5-39 
5-25 
4-58 
4.76 
3-62 
2.23 
3-08 


37-45 
4I-3I 
52.54 
60.08 
60.06 
77-98 
80.65 
84.62 
80.28 
79.22 
8i.35 


0.50 
0.67 
1-03 
1-05 

1.02 
1.29 
1.82 
1.02 
1.47 

0.68 
0.79 


45-57 

4°-75 

34-09 

27-03 

17.88 

11.51 

4.66 

5-09 

3-59 

4-64 

5.o6 


s, 


3526 

3994 
5"5 
5865 
6088 
7852 
7845 
8166 
7612 
6987 
7417 
7946 
8006 


6347 
7189 
9207 

10557 
10958 


14121 
14699 
13702 
12577 
I335I 
14300 
14410 


PEATS  AND  WOOD  (air  dried). 


Vol. 

hydro- 
carbon. 


Fixed 
carbon. 


Ash. 


Sul- 
phur. 


Hydro- 
gen. 


Carbon. 


Nitro- 
gen. 


Oxygen. 


Calories 

per 
gram. 


B.T.U.' 

per 
pound. 


Peats: 

Franklin  Co.,  N.  Y..  . 

Sawyer  Co.,  Wis 

Woods: 

Oak,  dry 

Birch,  dry 

Pine,  dry 


67.10 
56.54 


28.99 
27.92 


3-Qi 

15-54 

0.37 
0.29 
0.37 


0.15 
0.29 


5-93 
4.71 

6.02 
6.06 

6.  20 


57-17 
51.00 

50.16 
48.88 
50.31 


5726 
4867 

4620 
4771 
5085 


10307 
8761 


8316 
8588 
9153 


(c)  LIQUID  FUELS. 


Fuel. 


Specific  gravity 
at  15°  C. 


Calories  per  gram. 


British  thermal  units 
per  pound. 


Petroleum  ether 

Gasoline 

Kerosene 

Fuel  oils,  heavy  petroleum  or  refinery  residue 

Alcohol,  fuel  or  denatured  with  7  to  9  per 

cent  water  and  denaturing  material 


.684-. 694 
.710-. 730 
.790-. 800 
.960-. 970 

.8196-. 8202 


I22IO-I2220 
11100-11400 
IIOOO-II200 
I0200-I050O 

6440-6470 


21978-21996 
19980-20520 
I9800-20I60 
18360-18900 

II592-U646 


(d)  GASES. 


Gas. 


Natural  gas,  Cal 

Natural  gas,  Pa 

Natural  gas,  France 

Coal  gas,  low  grade 

Coal  gas,  high  grade 

Water  gas,  low  tfrade 

Water  gas,  high  grade 


34-So 
57-2 
52.88 
36.4 


28.80 
18.8 

2.16 
23.2 


C2H2 


45_8« 
9-50 


"llumi- 
i  ants. 


1.70 

0.8 

3-47 

14.05 


C02 


0.58 

O.  20 
2.00 

3-02 


CO 


10.40 

3-20 

36.8 
19.1 


O.I 

0.40 


1-15 


N2 


0.90 

0.90 

0.48 

14. 20 

18.0 

4.69 

3-08 


Cal. 
per 
m" 


8339 
12635 
9364 
6151 
3736 
2642 
6140 


B.T.U 

per 

cu.  ft. 


937 
1420 
1052 
657 
399 
283 
657 


•  CiH«.     Data  from  the  Geological  Survey,  Poole's  The  Calorific  Power  of  Fuels,  and  for  natural  gas  from  Snelline 
(Van  Nostrand  s  Chemical  Annual). 

SMITHSONIAN  TABLES. 


TABLE  264. 

CHEMICAL  AND   PHYSICAL   PROPERTIES  OF  FIVE   DIFFERENT 
CLASSES    OF    EXPLOSIVES. 


243 


Explosive. 

Specific  gravity.  i 

Number  of  large  calories  developed  1 
by  i  kilogram  of  the  explosive.  | 

Pressure  developed  in  own  volume 
after  elimination  of  surface  in- 

fluence. 

Unit  disruptive  charge  by  ballistic 
pendulum. 

Rate  of  detonation. 
Cartridges  i  J  in.  diam. 

Duration  of  flame  from  100  grams  1 
of  explosive. 

Length  of  flame  from  100  grams. 

Cartridge  ij  in.  transmitted  explo-  1 
sion  at  a  distance  of 

Products  of  combustion  from  200 
grams;  gaseous,  solid,  and  liquid, 
respectively. 

Ignition  occurred  in  4%  fire  damp  &  1 
coal  dust  mixture  with 

£§ 
3* 

s 
o 

h 

,gs 

•Js'S 
1§ 

1 

c 

i 

O 

O 

(A)  Forty-per-centnitro- 
glycerin  dynamite 

(B)  FFF  black  blasting 
powder 

(C)  Permissible      explo- 
sive; nitroglycerin 
class 

(D)  Permissible      explo- 
sive;   ammonium 
nitrate  class 

(E)  Permissible      explo- 
sive; hydrated  class 

1.22 

1.25 
I.IO 
0.97 

i-54 

I22I.4 

789.4 
760.5 
992.8 
6lO.6 

8235 
4817 

5912 
7300 

6597 

227* 

374t 
458* 

301* 
279* 
434* 

4688 
469.41 
3008 

3438§ 
2479 

-358 
925. 
.471 

-483 
-338 

24.63 

54.32 
27.79 
25.68 
17.49 

12 

4 
I 

3 

88.4 
79-7 
'4-5 

1544 
126.9 

4-i  II 

103.9 
65.1 
15-4 

89.8 

27-5 
75-5 

86,1 
56.0 
33-o 

25 
25 
IOOO 

800 

Over 

IOOO 

Chemical  Analyses. 

(A)  Moisture 

0.91 
39.68 
42.46 
13-58 
3-37 

0.80 
70.57 

17-74 
10.89 

7.89 
24.02 
36-25 

9.20 
21.31 
0.97 
0.36 

(D) 
(E) 

Moisture 
Ammon 
Sulphur 
Starch 
Wood  p 
Poisono 
Mangaru 
Sand 

VToisture 
Nitrogly 
Ammon 

SanH 

0.23 
83.10 

0.46 
2.61 

1.89 
2.54 
2.64 
6.53 

2.-U 
30-85 

9-94 

Il7$ 
11.98 

7.64 
8.96 
6.89 
19.65 

Nitroglycerin 

lum  nitrate 

Calcium  carbonate 

ulp 
js  ma 
ise  pe 

(B)  Moisture     

roxide 

Sodium  nitrate    

Charcoal    

(C)  Moisture     

cerin 
um  n 

itrate 

Nitroglycerin  

Sodium  nitrate    

Coal 

Wood  pulp  and  crude  fibre  from 
arauis 

Clay                          . 

Ammonium  sulphate 
Zinc  sulphate  (7  HO) 
Potassium  sulphate 



Starch    

Calcium  carbonate  . 
Magnesium    "    .     . 



*  One  pound  of  clay  tamping  used.  t  Two  pounds  of  clay  tamping  used.  t  Rate  of  burning. 

§  Cartridges  if  in.  diam.  ||  For  300  grammes. 

Compiled  from  U.  S.  Geological  Survey  Results,  —  "  Investigation  of  Explosives  for  use  in  Coal  Mines,  1909." 
SMITHSONIAN  TABLES. 


244 


TABLES  265-268. 
TABLE  265.  -    Additional  Data  on  Explosives. 


Explosive. 
(Ref.  Young,  Nature,  102,  216,  1918.) 

Vol.  gas 
per  gin 
cc  =  V 

Calories 
per 
g=0 

Coefficient 
=  QV 

-i-  IOOO 

Coefficient 
GP  =  i 

Calculated 
Temperature 
Q/C 
C,  sp.  ht.  gases 
=  0.24 

fiunpnwr|er 

cc 
280 

738 

207 

i 

2240°  C 

741 

1652 

1224 

6 

6880 

Nitrocellulose,  13%  Nj  

923 

931 

859 

4-3 

3876 

Cordite,  Mk.  I.  (NG,  57;  NC,  38;  Vaseline,  5) 
Cordite,  MD  (NG,  30;  NC,6s;  Vaseline,  5)..  . 
Ballistite  (NG,  50;  NC,  50;  Stabilizer,  5)  .... 
Picric  acid  (Lyddite) 

871 
888 
817 
877 

1242 
1031 
1349 
810 

1082 
915 

IIO2 
7IO 

5-2 

4-4 
5-3 
3-4 

SI7S 
4225 
5621 
3375 

Shattering  power  of  explosive  =  vol.  gas  per  g  X  cals./g   X  Vd  X  density  where  Vd  is  the  velocity  of  detonation. 

Trinitrotoluene:    Vd  =  7000  m/sec.    Shattering  effect  =  .87  picric  acid. 

Amatol  (Ammonium  nitrate  +  trinitrotoluene,  TNT):    Vd  =  4500  m/sec. 

Ammonal  (Ammonium  nitrate,  TNT,  Al):   1578  cal/g;   682  cc  gas;    Vd  =  4000  m/sec. 

Sabulite  (Ammonium  nitrate,  78,  TNT  8,  Ca  silicide  14):   about  same  as  ammonal. 

TABLE  266.  —  Ignition  Temperatures  Gaseous  Mixtures. 

Ignition  temperature  taken  as  temperature  necessary  for  hot  body  immersed  in  gas  to  cause  ignition;  slow  com- 
bination may  take  place  at  lower  temperatures.  McDavid,  J.  Ch.  Soc.  Trans,  in,  1003,  1917.  Gases  were  mixed 
with  air.  Practically  same  temperatures  as  with  Cfe  (Dixon,  Conrad,  loc.  cit.  95,  1909). 


Benzene  and  air 

1062°  C 

Ether  and  air         .    .    . 

1033°  C 

878 

Ethylene  and  air 

CO  and  air 

931 

Hydrogen  and  air  

747 

TABLE  267.  —  Time  of  Heating  for  Explosive  Decomposition. 


Temperature  °  C. 

170 

1  80 

190 

200 

220 

Ignition  temperature. 

Time. 

sec. 

cec. 

sec. 

sec. 

sec. 

°ct          °ct 

n 
600 
190 
170 
870 
160 
n 
n 

n 
iQS 

*l° 

60 

165 

100 

340 
n 

n 
130 

"67 
60 
240 
n 

n 
45 
90 

21 
56 
50 
ISO 
590 

n 
23 
25 
9 
18 
30 

00 

480 

440 
|300 

300 
590 

900 

450 

Smokeless  powder  B  

Celluloid  Pyroxylin 

Collodion  cotton  

Celluloid  *  

Safety  matches 

Parlor  matches  

Cotton  wool  . 

n,  failure  to  explode  in  twenty  minutes.  *  The  decomposition  of  nitrocellulose  in  celluloid  commences  at  about 
100°  C;  above  that  the  heat  of  decomposition  may  raise  the  mass  to  the  ignition  point  if  loss  of  heat  is  prevented. 
Above  170°,  decomposition  occurs  with  explosive  violence  as  with  nitrocellulose.  Rate  of  combustion  is  5  to  10  times 
that  of  poplar,  pine,  or  paper  of  the  same  size  and  conditions. 

t  Measured  by  contact  with  porcelain  tube  of  given  temperature.    Average. 

J  Measured  by  contact  with  molten  lead.     Average. 

Taken  from  Technologic  Paper  of  Bureau  of  Standards,  No.  98,  1917. 

TABLE  268.  —  Flame  Temperatures. 

Measures  made  with  optical  pyrometer  by  F6ry,  J.  de  Phys.  (4)  6,  1907. 


Alcohol,  with  NaCl  

I705°C 

1900°  C 

Bunsen  flame,  i  air  

1812 

2458 

Bunsen  Same,  full  air. 

1871 

Illuminating  gas-oxygen  

MOO 

Cooper-Hewuf  Hg  '.I'.'.'.'.'.'.'.'.'.'.'. 

35OO 

SMITHSONIAN  TABLES. 


TABLE  269.  245 

THERMO-CHEMISTRY.    CHEMICAL   ENERGY   DATA. 

The  total  heat  generated  in  a  chemical  reaction  is  independent  of  the  steps  from  initial  to  final 
state.  Heats  of  formation  may  therefore  be  calculated  from  steps  chemically  impracticable. 
Chemical  symbols  now  represent  the  chemical  energy  in  a  gram-molecule  or  mol{<?) ;  treat  re- 
action equations  like  algebraic  equations  :  CO  -f-  O  =  CO2  +  68  Kg-cal ;  subtract  C  -j-  2  O  =  CO2 
+  97  Kg-cal,  then  C -f  O  =  CO-|- 29  Kg-cal.  We  may  substitute  the  negative  values  of  the 
formation  heats  in  an  energy  equation  and  solve  MgCl2  +  2  Na=  2  NaCl  -f  Mg-f  x  Kg-cal; 
—  151= — 196  + x;  x  =  45  Kg-cal.  Heats  of  formation  of  organic  compounds  can  be  found 
from  the  heats  of  combustion  since  burned  to  H2O  and  CO2.  When  changes  are  at  constant 
volume,  energy  of  external  work  is  negligible ;  also  generally  for  solid  or  liquid  changes  in  vol- 
ume. When  a  gas  forms  a  solid  or  liquid  at  constant  pressure,  or  vice  versa,  it  must  be  allowed 
for.  For  N  mols  of  gas  formed  (disappearing)  at  TK°  the  energy  of  the  substance  is  decreased  (in- 
creased) by  0.002  •  N  •  TK  Kg-cal.  H2  -f  O  =  H2O  -f  67.5  Kg-cal.  at  i8°C.  at  constant  volume  ; 
\(2  H2+02  —  2  H20  =  135.0+  0.002  X  3  X  291  =  136.7)  =68.4  Kg-cal. 

The  heat  of  solution  is  the  heat,  +  or  — ,  liberated  by  the  solution  of  i  mol  of  substance  in  so 
much  water  that  the  addition  of  more  water  will  produce  no  additional  heat  effects.  Aq.  signifies 
this  amount  of  water;  H2O,  one  mol. ;  NH3-f  Aq  =  NH4OH  •  Aq. -f-8  Kg-cal. 

TABLE  269.  (a).    Heats  of  Formation  from  Elements  In  Kilogram  Calories. 
At  ordinary  temperatures. 


Compound. 

Heat  of 
Forma- 
tion. 

Compound. 

Heat  of 
Forma- 
tion. 

Compound. 

Heat  of 
Forma- 
tion. 

Compound. 

Heat  of 
Forma- 
tion. 

1  A12O3 
i  Ag20 
BaO 

380. 

6-5 
126. 

HgO 
Na2O 
Nd2O3 

21.4 
IOO. 

435- 

KC1 
LiCl 
MgCl2 

1057 

93-8 
151.0 

Li2SO4 
(NH4)2S04 
Na2SO4 

sr 

328.3 

BaO2 

142. 

NiO 

57-9 

MnCl2 

112.3 

MgS04 

301.6 

1  Bi203 

138. 

P2O5  sgs 

370- 

NaCl 

97.8 

PbSO4 

216.2 

j  CO  am 
j  COdi 

29.0 
26.1 

Pb02 

50-3 
62.4 

NdCl3 
NH4C1 

250. 
76-3 

T12SO4 
ZnSO4 

221.0 
229.6 

[  CO2  am 

97-o 

Pr203 

412. 

NiCl2 

74-5 

CaCO3 

270. 

!  C02  gr 
|  CO2  di 

94-8 
94-3 

Rb2O 
SO2  rh  sgg 

89.2 
70. 

PbCl2 
PdCl2 

83-4 
40-5 

CuCO3 
FeC03 

143- 
179. 

CaO 

152. 

SiO2 

191.0 

PtCl4 

60.4 

K2C03 

280. 

Ce02 

225. 

SnO 

66.9 

SnCl2 

80.8 

MgC03 

267. 

i  C120  g 

-16.5 

SnO2  cr 

I37-5 

SnCl4 

128. 

Na2C03 

272. 

CoO  am 
CoO  cr 

50-5 

57-5 

SrO2 
Th02 

all 

SrCl2 
ThCl4 

185. 
300. 

ZnCO3 
AgN03 

194. 
28.7 

Co304 

*93-4 

TiO2  am 

215.6 

T1C1 

48.6 

Ca(N03)2 

209. 

Cr03 

140. 

TiO2  cr 

218.4 

RbCl 

105.9 

Cu(NO3)26H2O 

92-9 

Cs2O 

91.3 

T1O2 

42.2 

ZnCl2 

97-3 

HNO8  gggl 

41.6 

Cu20 

42.3 

WO2 

HBr  gig 

8.6 

KN03 

II9.2 

CuO 

37-2 

W03 

194. 

NH4Br 

66. 

LiNO3 

112. 

FeO 

Fe203 
Fe304 
H20  ggl 

65.7 
196.5 
270.8 
68.4 

ZnO 

AgCl 
Ag2Cl 
A1C13 

85.2 
29.2 

29.5 
161.4 

HI  gsg 
HFggg 
Ag2S 
CS2sgg 

-6.2 

38- 
-26.0 

NH4NOS 
NaN03 
T1NO3 
CH4  sgg 

88.3 
III.O 
58.2 
20. 

H202  ggl 

46.8 

AuCly 

S.8l 

CaS 

90.8 

C2H6  sgg 

25- 

Hg,0 

22.2 

AuCl3  y 

22.8 

(NH4)2S 

66.2 

C2H2  sgg 

-S3- 

HgO 

21.4 

BaCl2 

197. 

Cu2S 

18.3 

HCN  di  gsgg 

-3°-5 

K20 

91. 

BiCl3 

90.6 

CuS 

1  1.6 

NH3  ggg 

I2.O 

La203 
Li02 

447- 
141.6 

CC14  am 
CaCl2 

21.0 
l87. 

H,S  gsg 
K.S 

2-73 
103.4 

Ca(OH)2 
NH4OH 

230. 

88.8 

MgO 

I43-6 

CdCl2 

93-2 

MgS 

79-4 

NaOH 

102. 

MnO 

90.8 

CoCl2 

76.5 

Na2S 

89-3 

Na     H2O  •  Aq  —  H 

44.* 

Mn02 
Mn3O4 

123. 

325- 

CuCl2 
CuCl 

PbS 
CaSO4 

19-3 
262. 

i(2Na  •  O  •  H2O) 
J(NauO  •  H2O  •  Aq) 

68.* 

30-*! 

MoO2 

143- 

FeCl2 

82.1 

CuS04 

111.5 

KOH 

103-5  | 

MoO3 

174. 

FeCl3 

96.0 

H2S04  sggg 

K  •  H2O  •  Aq-H 

45-* 

N2O  ggg 
NO  ggg 

-18.2 

-21.6 

G1C12 
HC1  ggl 

155- 

22. 

-SO3     H2O* 
Hg2S04 

21.3 
'75- 

£(2K  •  O  •  H2O) 
1(K2O  •  H2O  •  Aq) 

69.*! 

35-5*, 

N02 

-  8.1 

HgCl 

3I-3 

HgSO4 

165. 

Na204 

-  2.6 

HgCl2 

53-3 

K2S04 

344-3 

i 

am  =  amorphous ;  di  —  diamond ;  gr  =  graphite ;  cr  —  crystal ;  g  =  gas  ;  1  =  liquid ;  s  =  solid ;  y  =  yellow  (gold); 
rh  =  rhombic  (sulphur).  *  Heats  of  formation  not  from  elements  but  as  indicated. 

SMITHSONIAN   TABLES. 


246 


TABLES  270-272. 


HEATS  OF  FORMATION  OF  IONS  IN  KILOGRAM-CALORIES. 

+  and  —  signs  indicate  signs  of  ions  and  the  number  of  these  signs  the  valency.  For  the  ioni- 
tation  of  each  gram-molecule  of  an  element  divide  the  numbers  in  the  table  by  the  valency,  e.  g., 
9-°3  8r-  Al  =9.03  gr.  A1+  4-40.3  Kg.  cal.  When  a  solution  is  of  such  dilution  that  further  dilu- 
tion does  not  increase  its  conductivity,  then  the  heats  of  formation  of  substances  in  such  solutions 
may  be  found  as  follows  :  FeCljAq  —  +  22.2  +  2  X  39.1  =  100.4  Kg.  cal.  CuSO4Aq  =—  15.8 
-t-  214.0  =  198.2  Kg.  cal. 


Ag+               —25-3 
A1  +  +  +     +121.0 
Co++         +170.0 
Ca+  +          +  133.? 
Cd  +  +           +  18.4 

NH4+             +  32-7 
NH4C>  +         +37-5 
Na+               +57-3 
Ni  +  +           +  16.0 
Mg++        +  108.8 

AsO4  [-215.0 
Br—                +28.2 
BrOj—            +  II-2 
CO3  +  160.8 
Cl-                 +39-1 

10,-              +55-8 
I04-              +46.5 
OH  -             +  54.4 
PO4  h  298.0 
S203  +138-6 

Cu  +  +          —  16.0 

Mn  +  +          +  50.2 

CIO  —             +  26.0 

S208  +278.2 

Cu-f                —15-8? 

Pb  +  +             +  4-0 

C103  —           +  23.4 

S4O6  +260.8 

Fe  +  +           +22.2 
Fe  +  +  +        —9-3 

Rb  +             +  625.0 
Sn  +  +  +        +3-3 

C104  —            —38.7 
HC03  —        +163.0 

S03  +151-0 
SO4  +214.0 

H+                       o.o 

Sr  +  +          +119-6 

HP02—        +143-9 

Se  -35.6 

Hg+               —19-8 

T1+                  +1.7 

HPO,  +229.6 

SeO3  +119.6 

K+                 +61.8 

Zn++           +35-0 

HP04  +304.8 

SeO4  +144-8 

Li  +                 +  62.8 

HS—                +1.2 

Te  -34.8 

NO2  —             +  27.0 

Te03  +77.0 

N03-             +48.9 

Te04  +98.4 

I-                   +13,1 

S  —12.6 

TABLE    271.— Heats   of   Neutralization   in    Kilogram-Calories, 

The  heat  generated  by  the  neutralization  of  an  acid  by  a  base  is  equal,  for  each  gram-molecule 
of  water  formed,  to  13.7  Kg.  cal.  plus  the  heat  produced  by  the  amount  of  un-ionized  salt  formed, 
plus  the  sum  of  the  heats  produced  in  the  completion  of  the  ionizations  of  the  acid  and  the  base. 
(See  also  p.  209). 


Base. 

HCl.aq 

HNO3.aq 

H,SO4.aq 

HCN-aq 

CH3COOH.aq 

H2.C03-aq 

KOH  •  aq 

13-7 

I3.8 

15-7 

2-9 

13-3 

10.  1 

NaOH  •  aq 

13-7 

13-7 

2.9 

T3-3 

10.2 

NH4OH  •  aq 

12.4 

I2-5 

14.5 

12.0 

8. 

i  Ca(OH)2  •  aq 

14.0 

'3-9 

I5.6 

3-2 

*34 

9-5 

1  Zn(OH)2  •  aq 

9.9 

9-9 

II.7 

8.1 

8.9 

5-5 

|Cu(OH)2  •  aq 

7.5 

7-5 

9.2 

~~ 

6.2 

TABLE   272.— Heat   of  Dilution,   H2S04. 

In  Kilogram-calories  by  the  dilution  of  one  gram-molecule  of  sulphuric  acid  by  m  eram-mole- 
cules  of  water. 


m  .  .  .  . 
Kg.  Cal.  .  . 

6.38 

2 
9.42 

3 
11.14 

5 
13.11 

*9 
16.26 

49 
16.68 

?l* 

199 

17.06 

399 
17.31 

1599  o. 
17.86 

SMITHSONIAN  TABLES. 


247 


TABLES  273-275. 
RADIATION  CONSTANTS. 

TABLE  273.— Radiation  Formula  and  Constants  for  Perfect  Radiator. 

(exclusive  of  convection  losses)  at  the  tem 


J  =  ff  (  T±  —  /4)     (  Stef  an-Boltzmann)  ; 
where  <r=  I-374X  io~12  gram-calories  per  second  per  sq.  centimeter. 
=  8.26   X  lo-11     "  "        "    minute  "      " 

=  5.75   X  io~12  watts  per  sq.  centimeter. 
The  distribution  of  this  energy  in  the  spectrum  is  represented  by  Planck's  formula  : 


where  J\  is  the  intensity  of  the  energy  at  the  wave-length  A  (A,  expressed  in  microns,  /u)  and  e  it 
the  base  of  the  Napierian  logarithms. 

G  =  9.226  X  10*  for  /  in  gram'  Cal2'  =3.86  X  10'  for  /  i 

sec.  cm. 
C2=  14350  for  \in  ft 


cm.~ 


watts 


/»«  =  3.ii  X  10-  7*  for  /  in  .--  =1.30X10-"  7*  tor  /  in 

see.  cm.  cm. 

Xmax  7=2910  for  X  in  n 

h  —  Planck's  unit  =  elementary  "Wirkungs  quantum  "=6.83  X  io~27  ergs.  sec. 
k  =  constant  of  entropy  equation  =  1.42  X  IO~16  ergs./degrees. 

TABLE  274.  —  Radiation  In  Gram-Calories  per  24  Hours  per  sq.  cm.  from  a  Perfect  Radiator  at  P  C  to 
an  absolutely  Cold  Space  (—273°  0). 

Computed  from  the  Stefan-Boltzmann  formula. 


« 

/ 

« 

/ 

oc 

/ 

<oc 

/ 

«>C 

/ 

« 

/ 

—273 

0 

—  120 

6< 

10 

m 

+  12 

787 

+34 

1059 

+56 

1400 

—  220 

I 

—  110 

84 

—8 

588 

+  14 

808 

+36 

1087 

143° 

—  2IO 

2 

—  IOO 

107 

—6 

606 

+  16 

831 

+18 

I]tI5 

+60 

1470 

—  200 

3 

—90 

—4 

62  S 

+  18 

855 

+40 

H45 

+70 

1650 

—  190 

5 

—  80 

JQC 

2 

643 

+20 

879 

+42 

1174 

+80 

1850 

—  180 

9 

—70 

201 

0 

662 

+  22 

9°3 

+44 

1204 

+90 

2070 

—170 

—60 

245 

+2 

682 

+  24 

928 

+46 

1234 

+  100 

2310 

—160 

19 

—5° 

294 

+4 

701 

+  26 

953 

+48 

+2OO 

5960 

—ISO 

27 

—40 

350 

+6 

722  1 

+28 

979 

+  50 

1298 

+  IOOO 

3I3XI08 

—140 

38 

—30 

4l6 

+8 

744 

+30 

1005 

+52 

I33° 

+2OOO 

3I8XIO* 

—130 

50 

—  20 

488 

+  10 

765 

+32 

1032 

+54 

1363 

+  5OOO 

921  Xio6 

TABLE  275.— Values  of  JA  for  Various  Temperatures  Centigrade. 
Ekholm,  Met.  Z.  1902,  used  ^  =  8346  and  C2=  14349,  and  for  the  unit  of  time  the  day. 
For  100°,  the  values  for  JA  have  been  multiplied  by  10,  for  the  other  temperatures  by  TOO. 


A 

T—  100°  C 

30°  C 

15°  C 

o°C 

—  30°  C 

—  80°  C 

A 

100°  C 

30°  C 

15°  C 

o°C 

—  30°  C 

—  80°  C 

2 

I 

o 

0 

0 

0 

0 

?8 

5" 

2961 

2.SS7 

2I7S 

1491 

623 

3 

80 

41 

18 

7 

i 

o 

19 

2626 

2281 

19  S4 

1363 

594 

4 

469 

So8 

272 

*38 

27 

i 

20 

386 

2329 

2034 

17  S4 

1242 

I 

1047 
1526 

1777 
3464 

1085 
2296 

628 

M  S4 

172 
493 

8 
39 

21 

22 

337 
295 

2068 
1840 

1816 
1622 

1574 
MI3 

1129 
1026 

527 
494 

7 

1768 

4954 

348i 

2353 

93  i 

I05 

23 

2S9 

1639 

1448 

1270 

931 

460 

8 

1810 

SQ28 

4352 

3088 

1372 

203 

24 

228 

1462 

!298 

1141 

846 

428 

9 

10 
ii 

12 

1724 

1398 
1225 

6382 
6386 
6127 
S7I2 

4834 
4979 
4833 
4633 

3646 
378i 
3798 
3676 

1730 
1971 
2098 
2114 

316 
426 
520 

592 

y 

28 
30 

202 
I79 
142 
114 

1307 
1170 

947 
771 

1165 

1047 
850 

696 

1028 
926 

757 
623 

768 
698 

482 

398 
369 
317 

272 

13 

1063 

5222 

4300 

3467 

2090 

640 

40 

44 

3" 

285 

259 

209 

I3° 

14 

918 

792 

4713 
4220 

3930 
3SS6 

3215 
2944 

2004 
1889 

666 
673 

£ 

20 
10 

146 

77 

135 
72 

124 
66 

102 

55 

38 

16 

683 

3759 

2674 

1760 

663 

80 

4 

27 

25 

24 

20 

14 

17 

59° 

3340 

2862 

2417  1626 

649 

IOO     2 

12 

II 

10 

9 

7 

i 

SMITHSONIAN  TABLES. 


248 


TABLE  276. 
BLACK-BODY    SPECTRUM    INTENSITIES   (J\). 


Values  of  J\  using  for  Ci,  0.23  X  io»,  Ct,  14350.,  X  in  M-  W  the  figures  given  for  J\  are  plotted  in  cms  as  ordi- 
nates  to  a  scale  of  abscissae  of  i  cm  to  i  M.  then  the  area  in  cm'  between  the  smooth  curve  through  the  resulting  points 
and  the  axis  of  abscissae  is  equivalent  to  the  radiation  in  calories  per  sec.  from  i  cm*  of  a  black  body  at  the  correspond- 
ing temperature,  radiating  to  absolute  zero.  The  intensities  when  radiating  to  a  body  at  a  lower  temperature  may  be 
obtained  by  subtracting  the  intensities  corresponding  to  the  lower  temperature  from  those  of  the  higher.  Ihe  nature 
of  the  black-body  formula  is  such  that  when  \7'  is  small,  a  small  change  in  Ct  produces  a  great  change  in  /A;  e.g., 
when  Ci/Xr  is  100  or  10,  the  change  is  100  and  10  fold  respectively;  as  Xr  increases,  the  change  becomes  proportional; 
e.g.,  when  Ct/  Xr  is  less  than  0.05,  the  change  in  /*  is  proportional  to  the  change  in  62. 


X 

50°  K. 

100°  K 

150°  K 

200°  K. 

250°  K. 

273°  K. 

300°  K. 

373°  K. 

400°  K. 

500°  K. 

600°  K. 

I.O 

.0583 

.OJ72 

.0176 

.0201 

.O18I 

.0161 

.0112 

.01124 

.0831 

.0538 

i  .  5 

i  

.O142 

.O172 

.0133 

.0117 

.0102 

.o88 

.0749 

.0558 

.03143 

2.0 

.0191 

.0182 

.0185 

.on? 

.091 

.0911 

.O7I2 

.0513 

.0546 

.03168 

.00184 

2-5 

.O47I 

.Ottl 

.0142 

.0103 

.O7IO 

.077 

.0646 

.0419 

.0450 

.0397 

.0066 

3.0 

.O409 

.0196 

.0115 

.082 

.061  8 

.069 

•0545 

.03102 

.03242 

.00265 

.0131 

3-5 

.OJ44 

.0163 

.0102 

.072 

.0613 

.055 

.0420 

.0329 

.03620 

.00482 

.0189 

4.0 

.0306 

.0142 

.094 

.0614 

.0552 

.0418 

•  0457 

.0360 

.00115 

.00690 

.0229 

5-0 

.0143 

.0111 

.0714 

.0517 

.0430 

.048 

.0321 

.00134 

.00226 

.00952 

.0249 

6.0 

.01019 

.0105 

.0514 

.058 

.048 

.0318 

.0341 

.00195 

.  00301 

.01001 

.0224 

7-o 

.01883 

.096 

.0.6 

.0419 

.0315 

.0330 

•  0359 

.00225 

.00328 

.00925 

.0186 

8.0 

.01672 

-085 

.0518 

.0436 

.0322 

-0339 

.0371 

.00232 

.00321 

.  00801 

.0149 

9.0 

.01422 

.0718 

.0538 

•  0454 

.0327 

•  0345 

.0377 

.00220 

.00295 

.00672 

.0118 

10.  0 

-01331 

•  0754 

.0565 

.0471 

.0330 

.0348 

.0378 

.00201 

.00262 

.00554 

.00929 

12.0 

•  OllIS 

.0624 

.0413 

.0494 

.0331 

.0347 

.0370 

.00157 

.00196 

•00374 

.00585 

14.0 

.01021 

.o66i 

.0418 

.  O4IO2 

.0329 

.0341 

.0358 

.00117 

.00144 

.00254 

.00380 

16.0 

.0914 

.0611 

.0422 

.04IOO 

.0325 

.0334 

.0546 

.0387 

.00105 

.00176 

.00254 

18.0 

•  0957 

.0517 

.0424 

.0492 

.0321 

.0328 

.03368 

.03653 

.03760 

.00124 

.00176 

20.  o 

.  O8l6 

.0522 

.0424 

.0482 

.0317 

.03224 

.03200 

•  03493 

•03575 

.03902 

.00125 

25.0 

•0897 

.0530 

.0421 

•  0457 

.O3I22 

.03131 

.03164 

.03258 

-03295 

.03439 

'.03589 

30.0 

.0726 

.0532 

.0416 

.0438 

.0466 

.0479 

.0497 

.03146 

.03164 

.03237 

.03311 

40.0 

.0769 

.0526 

.059 

.0418 

.04282 

•0433 

.04391 

•04558 

.04620 

.04858 

.O3IIO 

50.0 

•  0795 

.0518 

.0551 

.0592 

.O4I50 

.04158 

.04184 

•04255 

.04281 

.04381 

.04482 

75-0 

.0787 

.0*67 

.0515 

.0524 

.05338 

.  05383 

-  05436 

.05580 

.  05634 

.05834 

.04103 

IOO.O 

•  0755 

.0629 

•  0657 

.0588 

.05119 

.05134 

.03150 

.05197 

.05214 

.05277 

.05342 

800° 

1000° 

1500° 

2000° 

3000° 

4000° 

5000° 

6000° 

8000° 

10000° 

20000° 

K. 

K. 

K. 

K. 

K. 

K. 

K. 

K. 

K. 

K. 

K. 

O.I 

_ 

_ 

_ 

0.0226 

0.01115 

0.0624 

0.0331 

0.038 

IS- 

540. 

710000. 

O.2 

— 

— 

— 

0.087 

O.OOI2 

0.46 

iS-4 

184. 

3660. 

22100. 

820000. 

0-3 

— 

— 

— 

0.0315 

0.44 

24.2 

263. 

1310. 

9640. 

31000. 

3820000. 

0.4 

— 

— 

— 

0.0145 

5-75 

US- 

690. 

2280. 

10300. 

25600. 

180000. 

0-5 

— 

— 

— 

0.172 

20.6 

226. 

952. 

2400. 

8400. 

17800. 

92300. 

0.6 

— 

.0548 

0.014 

0-757 

40.8 

301. 

1000. 

2240. 

6290. 

H950. 

51460. 

o-7 

.0540 

.0468 

0.064 

1-93 

59-2 

328. 

925. 

1860. 

4590. 

8110. 

30700. 

0.8 

.0651 

.00045 

0.180 

3-58 

321. 

800. 

1490. 

3350. 

5620. 

19400. 

0.9 

•0434 

.00183 

0.378 

5-35 

77-3 

295. 

671. 

1177. 

2470. 

3980. 

12820. 

I.O 

.00015 

.00538 

0.645 

7.06 

77.8 

262. 

554- 

928. 

1842. 

2880. 

8800. 

i-S 

•0775 

.0848 

2.07 

10.  25 

52.2 

122. 

2IO. 

309. 

527- 

758. 

1980. 

2.0 

.0367 

.221 

2.43 

8.19 

29.0 

57-6 

90.2 

125. 

198. 

275- 

668. 

2-5 

.0719 

•305 

2.IO 

5-68 

16.4 

29-5 

43-9 

58.9 

90.1 

121.9 

284. 

3-0 

.0964 

•  320 

1.64 

3.82 

9.66 

16.4 

23-7 

31-1 

46.4 

61.9 

140.7 

3.5 

.1050 

.296 

1.22 

2.60 

6.02 

9.84 

13-8 

17-9 

26.3 

34-7 

77-3 

4.0 

.1027 

.256 

0.007 

1.  80 

3.90 

6.20 

8-59 

II.  O 

15-9 

20.9 

45-9 

5-o 

.0839 

.178 

0.511 

0.923 

1.84 

2.81 

3-8i 

4.81 

6.84 

8.89 

I9-I5 

6.0 

.0629 

.119 

0.302 

0.514 

0.973 

1-45 

1-935 

2.42 

3-40 

4-39 

9-34 

7-0 

•0459 

.O8ll 

0.188 

0.307 

0.560 

0.820 

1.165 

1.348 

1.88 

2.41 

5-09 

8.0 

•0335 

.0562 

0.122 

0.194 

0.344 

0.498 

•653 

0.808 

1.20 

1-43 

3-00 

9.0 

.0247 

.0398 

0.0824 

0.128 

0.223 

0.319 

.416 

0.513 

0.709 

0.90 

1.87 

10.  0 

.0184 

.0288 

0.0575 

0.0880 

0.151 

0.214 

.278 

0.342 

0.470 

0.598 

1.24 

12.  0 

.01072 

.Ol6o 

0.0304 

0.0553 

0.0757 

0.107 

•1373 

0.168 

0.230 

0.292 

0.602 

14-0 

16.0 

.00660 
.00425 

.0096 
.00606 

0.0175 
0.0108 

0.0256 

0.0155 

0.0421 
0.0253 

0.0587 
0.0350 

•0754 
.0448 

0.0921 
0.0546 

0.125 
0.0742 

0.159 
0.0938 

0.326 
0.192 

18.0 

.00285 

.00400 

0.00697 

0.00997 

0.0160 

0.0221 

.0282 

0.0344 

o  .  0466 

0.0585 

0.120 

20.  O 

.00198 

.00275 

0.00470 

0.00668 

0.01068 

0.0147 

.01868 

0.0227 

0.0307 

0.0388 

0.0789 

25.0 

.00000 

.OOI22 

0.00203 

0.00284 

0.00448 

O.OO6I2 

.00777 

o  .  00941 

0.0127 

0.0160 

0.0325 

30.0 

.03464 

.03619 

O.OOIOI 

0.00141 

O.  00220 

0.00299 

.00378 

0.00455 

0.00616 

0.00775 

0.0157 

40.0 

.03159 

.03209 

0.03334 

0.03459 

O.O37IO 

0.03960 

.00121 

0.00146 

0.00197 

0.00247 

0.00498 

50.0 

.04684 

.04888 

0.03140 

0.03191 

0.03294 

0.03397 

.03500 

0.03603 

0.03808 

O.OOIOI 

0.00204 

75-o 

.04144 

.04184 

0.04286 

0.04387 

0.04591 

0.04794 

0.04997 

0.  03120 

o.  03161 

0.03201 

o  .  03406 

IOO.O 

.05470 

.05598 

0.05919 

0.04124 

0.04188 

0.04252 

0.04317 

0.04381 

0.04510 

0.04639 

0.03128 

See  Forsythe,  J.  Opt.  Soc.,  4,331,  1920,  relative  values,  0.4  to  0.76  ju.  (steps  o.oi  /«.),  12  temperatures,  1000  to  5000°  K. 
SMITHSONIAN  TABLES. 


TABLES  277-278. 

RADIATION    EMISSIVITIES- 

TABLE  277.  —  Relative  Emissive  Powers  for  Total  Radiation. 


249 


Emissive 
600  +  °  C.    Ka 


of  black  body  =  i.     Receiving  surface  platinum  black  at  25°  C;    oxidized   surfaces  oxidized  at 
1   and  Overholzer,  Phys.  Review,  2,  p.  144,  1913. 


Temperature,  Deg.  C. 

200 

400 

600 

Silver 

O.O20 
O.O60 

O.II3 
0.180 
O.2IO 
0.369 
0.4II 
0.521 
0.568 

0.610 
0.631 

0.643 
0.790 

I.  CO 

0.030 

0.086 

O.IIO 

0.153 
0.185 

0.424 

0-439 
0-547 
0.568 
0.600 

0.710 
0.788 

I.OO 

0.038 

O.IIO 

0.192 

0.190 

0.478 
0.463 
0.570 
0.568 
0.589 

0.777 
0.787 

I.OO 

Platinum  (i  )  

Oxidized  zinc 

Oxidized  aluminum  

Calorized  copper,  oxidized.    . 

Cast  iron 

Oxidized  nickel  

Oxidized  monel 

Calorized  steel,  oxidized  

Oxidized  copper.      .    . 

Oxidized  brass 

Oxidized  lead  

Oxidized  cast  iron 

Oxidized  steel 

Black  body  

Remark:  For  radiation  properties  of  bodies  at  temperatures  so  low  that  the  radiations  of  wave-length  greater  than 
20  n  or  thereabouts  are  important,  doubt  must  exist  because  of  the  possible  and  perhaps  probable  lack  of  blackness  of 
the  receiving  body  to  radiations  of  those  wave-lengths  or  greater.  For  instance,  see  Table  379  for  the  transparency 
of  soot. 


TABLE  278.  —  Emissivities  of  Metals  and  Oxides. 

Emissivities  for  radiation  of  wave-length  0.55  and  0.65  ft.  Burgess  and  Wallenberg,  Bui.  Bureau  of  Standards, 
n,  591,  1914. 

In  the  solid  state  practically  all  the  metals  examined  appear  to  have  a  negligible  or  very  small  temperature  coeffi- 
cient of  emission  for  X  =  0.55  and  0.65  /j,  within  the  temperature  range  20°  C  to  melting  point.  Nickel  oxide  has  a 
well-defined  negative  coefficient,  at  least  to  the  melting  point.  There  is  a  discontinuity  in  emissivity,  for  X  =  0.65  p 
at  the  melting  point  for  some  but  not  all  the  metals  and  oxides.  This  effect  is  most  marked  for  gold,  copper,  and 
silver,  and  is  appreciable  for  platinum  and  palladium.  Palladium,  in  addition,  possesses  for  radiation  a  property 
analogous  to  suffusion,  in  that  the  value  of  emissivity  (X  =  0.65  /*)  natural  to  the  liquid  state  may  persist  for  a  time 
after  solidification  of  the  metal.  The  Violle  unit  of  light  does  not  appear  to  define  a  constant  standard.  Article  con- 
tains bibliography. 


Metals. 

Cu 

Ag 

Au 

Pd 

Pt 

Ir 

Rh 

Ni 

Co 

Fe 

Mn 

Ti 

ex,  0.55  ju  solid  — 
0.55  /i  liquid.  . 

0.65  n  solid.  .  . 
liquid  .  .  . 

0.38 
0.36 

O.  IO 

0.15 

0-35 
0.35 

0.04 
0.07 

0.38 
0.38 

0.14 

0.22 

0.38 

0.33 
0.37 

0.38 

0-33 
0.38 

0.30 

0.29 

0.29 
0.30 

0-44 
0.46 

0.36 
0.37 

0.36 
0.37 

0-37 
0.37 

0.59 
0-59 

0-75 
0.75 

0.63 
0.65 

Metals 

Zr 

Th 

Y 

Er 

Be 

Cb 

V 

Cr 

Mo 

W 

U 

eX,  0.55  n  solid.... 
liquid.  .  . 

0.65  /J,  solid..  . 
liquid  

0.32 
0.30 

0.36 

0.36 
0.40 

0.35 
0.35 

0.30 

o.SS 
0.38 

o.  61 
0.81 

0.61. 
0.61 

0.61 

0.49 
0.40 

0.29 

0-35 
0.32 

0-53 

0-39 
0-39 

0.43 
0.40 

0.39 

0-77 

0.54 
0.34 

Oxides:  0.65/1 

NiO 

C03O4 

FC304 

Mn304 

TiOa 

ThOa 

YzOs 

BeO 

CbOx 

V20, 

Crrf), 

UiO« 

e\  solid. 

0.89 

o  77 

0.63 

o.  52 

o.  57 

0.61 

0.37 

0.71 

0.69 

0.60 

o.  30 

liquid  

0.68 

0.63 

0.53 

0.47 

0.51 

0.69 

0.31 

SMITHSONIAN  TABLES. 


250 


TABLES  279-281. 
RADIATION    EMISSIVITIES. 

TABLE  279.  —  Relative  Emissivities  of  Metals  and  Oxides. 
Emissivity  of  black  body  taken  as  100. 


True  temperature  C. 

500° 

600° 

700° 

800° 

900° 

1000° 

1100° 

1200° 

Ref. 

60  FeO.4o  FeiOj 
=  Fe  heated 
in  air  X  = 

Total 

=  0.65  n 

85 

85 

86 

87 
98 

87 
97 

88 
95 

88 
93 

89 

92 

i 

i 

NiO     
X  = 

..Total 
=  0.65  fji 

- 

54 

62 
98 

68 
96 

72 
94 

75 
92 

Si 
88 

86 
87 

2 
2 

Platinum: 
True  temp.  C  
App.*  temp.  C  
Total  emiss.  Pt  

o 

3-i 

100 

4-0 

200        300        4OO 

5.1      6.1      7.0 

500 
8.0 

750 
10.3 

1000 

486 
12.4 

1200 

630 
14.0 

1400 
780 
15-5 

1600 
930 
16.9 

1700 
1005 
17-5 

3 
3 
3 

Tungsten: 
True  temp.  K  (abs.)  
X  =  0.467  
X  =  0.665  

200 

Si-  8 
48.2 

600 
50.8 
47.2 

1000 

49-8 
46.3 

1400 
48.9 
45-3 

1800 
47-9 
44-3 

2200 
47.0 

43-3 

2600 
46.0 

42.4 

3000 
45-0 
41.4 

3400 
44.1 
40.4 

3800 
39  5 

4 
4 
4 

*  As  observed  with  total  radiation  pyrometer  sighted  on  the  platinum. 
References:   (i)  Burgess  and  Foote,  Bui.  Bureau  of  Standards,  12,  83,  1915;   (2)  Burgess  and  Foote,  loc.  cit. 
ii,  41,  1914;    (3)  Foote,  loc.  cit.  n,  607,  1914;    (4)  Worthing,  Phys.  Rev.  10,  377,  1917. 

TABLE  280.  —  Temperature  Scale  for  Tungsten. 

Hyde,  Cady,  Forsythe,  J.  Franklin  Inst.  181,  418, 1916.    See  also  Phys.  Rev.  10, 395,  1917.    The  color  temperature 
temperature  of  black  body  at  which  its  color  matches  the  given  radiation. 


Lumens/  watt 

Color 
temperature. 

Black-body 
temperature. 

True 
temperature. 

True 
temperature. 

True- 

color. 

True  — 
brightness. 

i 

1763°  K. 

1627°  K. 

1729°  K. 

1700° 

12° 

100° 

2 

1917 

1753 

1875 

1800 

20 

"5 

3 

2025 

1840 

1976 

1900 

26 

128 

4 

2109 

1909 

2056 

2OOO 

31 

142 

5 

2179 

1967 

2125 

2100 

36 

158 

6 

2237 

2017 

2184 

22OO 

39 

175 

7 

2290 

2062 

2238 

23OO 

41 

191 

8 

2338 

2102 

2286 

2400 

43 

208 

9 

2383 

2140 

2332 

10 

2425 

2174 

2373 

TABLE  281.  —  Color  minus  Brightness  Temperatures  for  Carbon. 

Hyde,  Cady,  Forsythe,  Phys.  Rev.  10,  395,  1917. 


Brightness  temp.  °  K  
Color  —  brightness 

1600° 

1700° 

1800° 

IQOO0 

2000° 

2100° 

,0 

2200° 

SMITHSONIAN  TABLES. 


TABLES  282,   283. 
COOLING   BY  RADIATION   AND  CONVECTION. 


251 


TABLE  282.  -  At  Ordinary  Pressures. 

According  to  McFarlane*  the  rate  of  loss  of  heat  by  a  sphere 
placed  in  the  centre  of  a  spherical  enclosure  which  has  a 
blackened  surface,  and  is  kept  at  a  constant  temperature  of 
about  14°  C,  can  be  expressed  by  the  equations 

e  —  .000238  +  3.06  X  io—6*  _  2.6  X  io— V, 
when  the  surface  of  the  sphere  is  blackened,  or 

e  =  .000168  -{-  1.98  X  io— 6t  —  1.7  X  io— s/2, 

when  the  surface  is  that  of  polished  copper.  In  these  equa- 
tions, e  is  the  amount  of  heat  lost  in  c.  g.  s.  units,  that  is, 
the  quantity  of  heat,  small  calories,  radiated  per  second  per 
square  centimeter  of  surface  of  the  sphere,  per  degree  differ- 
ence of  temperature  t,  and  t  is  the  difference  of  temperature 
between  the  sphere  and  the  enclosure.  The  medium  through 
which  the  heat  passed  was  moist  air.  The  following  table 
gives  the  results. 


Differ- 
ence of 
tempera- 
ture 
t 

Value  of  e. 

Ratio. 

Polished  surface. 

Blackened  surface. 

5 

.000178 

.000252 

.707 

IO 

.000186 

.000266 

.699 

15 

.000193 

.OOO279 

.692 

20 

.OOO2OI 

.000289 

.695 

25 

.OOO2O7 

.000298 

.694 

30 

.000212 

.000306 

.693 

35 

.000217 

.000313 

.693 

40 

.OOO22O 

.000319 

•693 

45 

.000223 

.000323 

.690 

5° 

.OOO225 

.000326 

.690 

55 

.000226 

.000328 

.690 

60 

.OOO226 

.000328 

.690 

TABLE  283.  -At  Different  Pressures. 

Experiments  made  by  J.  P.  Nicol  in  Tail's  Labo- 
ratory show  the  effect  of  pressure  of  the  en- 
closed air  on  the  rate  of  loss  of  heat.  In  this 
case  the  air  was  dry  and  the  enclosure  kept  at 
about  80  C. 


Polished  surface. 

Blackened  surface. 

I 

et 

t 

et 

PRESSURE  76  CMS.  OF  MERCURY. 

63.8 

.00987 

6l.2 

.01746 

57-1 
5°-5 

.00862 
.00736 

50.2 
41.6 

.01360 
.01078 

44.8 

.00628 

34-4 

.00860 

40.5 

.00562 

27-3 

.00640 

34-2 
29.6 

.00438 
.00378 

20.5 

•00455 

23.3 

.00278 

- 

- 

.00210 

" 

" 

PRESSURE  10.2  CMS.  OF  MERCURY. 

67.8 

.00492 

62.5 

.01298 

61.1 

•00433 

57-5 

.01158 

55 

.00383 

53-2 

.01048 

49-7 

.00340 

47-5 

.00898 

44.9 

.00302 

43-o 

.00791 

40.8 

.00268 

28.5 

.00490 

PRESSURE  i  CM.  OF  MERCURY. 

65 

.00388 

62.5 

.01182 

60 

.00355 

57-5 

.01074 

5° 

.00286 

54-2 

.01003 

40 

.00219 

41.7 

.00726 

30 

.00157 

37-5 

.00639 

23-5 

.00124 

34-o 

27-5 

.00569 
.00446 

24.2 

.00391 

SMITHSONIAN  TABLES. 


*  "  Proc.  Roy.  Soc."  1872. 
t  "  P.roc.  Roy.  Soc."  Edinb.  1869. 
See  also  Compan,  Annal.  de  chi.  et  phys.  26,  p.  526. 


252  TABLES  284,   285. 

COOLING  BY  RADIATION  AND  CONVECTION. 

TABLE   284.  —  Cooling  of  Platinum  Wire  In  Copper  Envelope. 

Bottomley  gives  for  the  radiation  of  a  bright  platinum  wire  to  a  copper  envelope  when  the  space  between  is  at  the 
highest  vacuum  attainable  the  following  numbers  :  — 

r  =  4o8°  C.,  et  —  378.8  X  ID-*,  temperature  of  enclosure  16°  C. 
^=505°  C.,  ft=  726.1  X  lo-4,          "  "  17°  C. 

It  was  found  at  this  degree  of  exhaustion  that  considerable  relative  change  of  the  vacuum  produced  very  small 
change  of  the  radiating  power.  The  curve  of  relation  between  degree  of  vacuum  and  radiation  becomes  asymp- 
totic for  high  exhaustions.  The  following  table  illustrates  the  variation  of  radiation  with  pressure  of  air  in 
enclosure. 


Temp,  of  enclosure  16°  C.,  *  =  4o8°  C. 

Temp,  of  enclosure  17°  C.,  t  —  505°  C. 

Pressure  in  mm. 

et 

Pressure  in  mm. 

et 

740. 

8137.0  X  ID-* 

0.094 

1688.0  X  io-* 

440. 

7971.0 

•053 

1255-0 

140. 

7875-° 

-034 

1  1  26.0 

42. 

4- 
0.444 

7591.0 
6036.0 
2683.0 

.013 
.0046 

.00052 

920.4 
831-4 
767.4 

.070 
•034 

.012 

1045.0 
727-3 
539-2 

.00019 
Lowest   reached    ) 
but  not  measured  ) 

746.4 
726.1     " 

.0051 

436.4 

.00007 

378.8 

TABLE  285.— Effect  of  Pressure  on  Loss  of  Heat  at  Different  Temperatures. 

The  temperature  of  the  enclosure  was  about  15°  C.     The  numbers  give  the  total  radiation  in  therms  per  square  cen- 
timeter per  second. 


Pressure  in  mm. 

Temp,  of 

wire  in  C°. 

About 

IO.O 

I.O 

0.25 

0.025 

o.i  M. 

100° 

0.14 

O.I  I 

0.05 

O.OI 

0.005 

2OO 

.31 

.24 

.11 

.02 

•0055 

300 

•50 

•38 

.18 

.04 

.OIO5 

400 

•75 

•53 

•25 

•07 

.025 

5OO 

— 

.69 

•33 

.13 

•055 

6OO 

— 

•85 

•45 

•23 

700 

— 

— 

•37 

.24 

800 

- 

- 

- 

.56 

.40 

1 

900 

~ 

— 

- 

.61 

NOTE.  —  An  interesting  example  (because  of  its  practical  importance  in  electric  light- 

ing) of  the  effect  of  difference  of  surface  condition  on  the  radiation  of  heat  is  given  on  the 

authority  of  Mr.  Evans  and  himself  in  Bottomley's  paper.     The  energy  required  to  keep 

up  a  certain  degree  of  incandescence  in  a  lamp  when  the  filament  is  dull  black  and  when 

it  is  "  flashed  "  with  coating  of  hard  bright  carbon,  was  found  to  be  as  follows  :  — 

Dull  black  filament,  57.9  watts. 

Bright  "            "         39.8  watts. 

SMITHSONIAN  TABLES. 


TABLES  286-287. 
TABLE  286.  —  Conduction  of  Heat  across  Air  Spaces  (Ordinary  Temperatures). 


253 


Loss  of  heat  by  air  from  surfaces  takes  place  by  radiation  (dependent  upon  radiating  power  of  surface;  for  small 
temperature  differences  proportional  to  temperature  difference;  follows  Stefan-Boltzmann  formula,  see  p.  247) 
conduction,  and  convection.  The  two  latter  are  generally  inextricably  mixed.  For  horizontal  air  spaces,  upper  surface' 
warm,  the  loss  is  all  radiation  and  conduction;  with  warm  lower  surface  the  loss  is  greater  than  for  similar  vertical 
space. 

Vertical  spaces:  The  following  table  shows  that  for  spaces  of  less  than  i  cm  width  the  loss  is  nearly  proportional 
to  the  space  width,  when  the  radiation  is  allowed  for;  for  greater  widths  the  increase  is  less  rapid,  then  reaches  a  maxi- 
mum, and  for  yet  greater  widths  is  slightly  less.  The  following  table  is  from  Dickinson  and  van  Dusen,  A.  S.  Refrigerat- 
ing Engineers  J.  3,  1916. 

HEAT  CONDUCTION  AND  THERMAL  RESISTANCES,  RADIATION  ELIMINATED, 
AIR  SPACE  20  CM  HIGH. 


Heat  conduction. 

Thermal  resistance. 

Cal./hour/cmV°  C. 

Same  units. 

space, 
cm. 

Temperature  difference. 

Temperature  difference. 

10° 

15° 

20° 

25° 

10° 

15° 

20° 

25° 

o.S 

0.46 

0.46 

0.46 

0.46 

2.17 

2.17 

2.17 

2.17 

I.O 

i-5 

0.24 

O.  IOO 

0.24 
o.  172 

0.24 

0.182 

0.24 

0.192 

4-25 
6.25 

4.20 
5.8o 

4-15 
5-50 

4.10 

5-20 

2.O 

0.161 

0.178 

0.200 

0.217 

6.  20 

5.6o 

5.00 

4.60 

3-0 

0.172 

0.196 

0.208 

o.  217 

5-80 

5-io 

l&o 

1.60 

Variation  with  height  of  air  space:  Max.  thermal  resistance 
20  cm  high;  8.9  at  2.5  cm,  60  cm  high. 


4.0  at  1.4  cm  air  space,  10  cm  high;   6.0  at  1.6  cm, 


TABLE  287.  —  Heat  Convection  in  Air  at  Ordinary  Temperatures. 

In  very  narrow  layers  of  air  between  vertical  surfaces  at  different  temperatures  the  convection  currents,  in  the 
main,  flow  up  one  side  and  down  the  other,  with  eddyless  (stream-line)  motion.  It  follows  that  these  currents  trans- 
port heat  to  or  from  the  surfaces  only  when  they  turn  and  flow  horizontally,  from  which  fact  it  follows,  in  turn,  that 
the  convective  heat  transfer  is  independent  of  the  height  of  the  surface.  It  is,  according  to  the  laws  of  eddyless 
flow,  proportional  to  the  square  of  the  temperature  difference,  and  to  the  cube  of  the  distance  between  the  surfaces. 
As  the  flow  becomes  more  rapid  (e.g.,  for  a  20°  difference  and  a  distance  of  1.2  cm)  turbulence  enters,  and  the  above 
relations  begin  to  change.  For  the  dimensions  tested,  convection  in  horizontal  layers  was  a  little  over  twice  that  in 
vertical. 

Taken  from  White,  Physical  Review,  10,  743,  1917. 

Heat  Transfer,  in  the  Usual  C.G.S.  Unit,  i.e.,  Calories  per  Second  per  Degree  of  Thermal  Head  per  Square  Cm  of 
Flat  Surface,  at  22.8°  Mean  Temperature. 

Where  two  values  are  given,  they  show  the  range  among  determinations  with  different  methods  of  getting  the  tem- 
perature of  the  outer  plate.  It  will  be  seen  that  the  value  of  the  convection  is  practically  unaffected  by  this  difference 
of  method. 


1  

Thermal 
head. 

8  mm  gap. 

12  mm  gap. 

24  mm  gap. 

Total. 

Convection. 

Total. 

Convection. 

Total. 

Convection. 

0.99° 

- 

— 

.  ooo  083  9  \ 
.  ooo  084  8  J 

— 

.000  065 

— 

1.98* 

/  .000  109 
\            no 

— 

.  ooo  084  o  \ 

.000    085    2  J 

.000   OOO 

ooo 

I 
4 

— 

— 

4-Q5° 

.  OOO    III 

.000    001 

/  .000  086  6 
\             88  i 

.000    002 

003 

!) 

.000  090 

over  .000  025 

9.89° 
19.76° 

f   .000    112 

I             "3 
.000  116 

.000  003 

003 

.000  007 

.000  093  7 
95  2 
/  .000  107  7 
\            109  4 

.  OOO   OIO 

.000  on 
.000  024 
026 

.000  106 
.000  126 

over  .000  040 
over  .  ooo  060 

SMITHSONIAN  TABLES. 


254  TABLE  288. 

CONVECTION    AND   CONDUCTION    OF    HEAT    BY   GASES   AT  HIGH   TEMPERATURES-' 

The  loss  of  heat  from  wires  at  high  temperatures  occurs  as  if  by  conduction  across  a  thin  film  of  stationary  gas 
adhering  to  the  wire  (vertical  and  horizontal  losses  very  similar).  Thickness  of  film  is  apparently  independent  of 
temperature  of  wire,  but  probably  increases  with  the  temperature  of  the  gas  »nd  vanes  with  the  diameter  of  the  wire 
according  to  the  formula  b-logb/a  =  28,  where  B  =  constant  for  any  gas,  b  =  diameter  of  film,  a,  of  wire.  The  rate 
of  convection  (conduction)  of  heat  is  the  product  of  two  factors,  one  the  shape  factor,  s,  involving  only  a  and  B,  the 
other  a  function  d>  of  the  heat  conductivity  of  the  gas.  If  W  =  the  energy  loss  in  watts/cm,  then  W  =  s(<£i  -  </>i). 
s  may  be  found  from  the  relation 


kdt. 


where  A  is  the  heat  conductivity  of  the  gas  at  temperature  T  in  calories/cm  °  C.  <fc  is  taken  at  the  temperature  Tz 
of  the  wire,  <f>i  at  that  of  the  atmosphere.  The  following  may  be  taken  as  the  conductivities  of  the  corresponding 
gases  at  high  temperatures: 


For  hydrogen 
air... 
mercury  vapor 


k  =    28  X 
*  =  4-6  X 


*  =  2.4  X  iQ-V;r{i/(i 


+  .ooo2T)/(i  +  77^)} 
+  .ooo2T)/(i  + 


To  obtain  the  heat  loss:  B  may  be  assumed  proportional  to  the  viscosity  of  the  gas  and  inversely  proportional  to 
the  density.  For  air  (see  Table  289(6))  B  may  be  taken  as  0.43  cm;  for  Hz,  3.05  cm;  for  Hg  vapor  as  0.078.  Obtain 
s  from  section  (a)  below  from  a/B;  then  from  section  (b)  obtain  <fc  and  <f>i  for  the  proper  temperatures;  the  loss  will 
<£i)  in  watts/cm. 

(a)  s  AS  FUNCTION  OF  a/B. 


5 

a/B 

s 

a/B 

5 

a/B 

s 

a/B 

O.O 

0.0 

S-o 

0-453 

IO 

1.696 

30 

7.738 

o-S 

I.O 

0-735  X  io~« 
0.594  X  io~s 

1:1 

0.558 
0.671 

12 
14 

2.263 
2.844 

32 
34 

8.370 
8-995 

1-5 

0.725  X  io~* 

6.5 

0.788 

16 

3.438 

36 

9.622 

2.O 

2.75  X  io~* 

7.0 

0.908 

18 

4.040 

38 

10.  25 

2-5 

0.0644 

7-5 

1.032 

20 

4-645 

40 

10.87 

3-0 

0.1176 

8.0 

1.160 

22 

5-263 

42 

11.50 

3-5 
4.0 

0.185 
0.265 

8.5 
9.0 

1.291 

1.424 

24 

26 

5.877 
6.505 

3 

12.14 
12.77 

4-5 

0-354 

9-5 

1.561 

28 

7.122 

48 

13-14 

5-o 

0-453 

IO.O 

1.696 

30 

7.738 

50 

14.03 

(6)  TABLE  OF  </>  IN  WATTS  PER  CM  AS  FUNCTION  OF  ABSOLUTE  TEMP.  (°K.). 


r°K. 

Hz 

Air 

Hg 

r°K. 

H2 

Air 

Hg 

0° 

o.oooo 

o.oooo 

_ 

1500° 

4.787 

0.744 

0.1783 

100 

0.0329 

0.0041 

— 

1700 

5-945 

0.931 

0.228 

200 

0.1294 

0.0168 

— 

1900 

7-255 

1.138 

0.284 

300 

0.278 

0.0387 

— 

2IOO 

8-655 

1-363 

0-345 

400 

0.470 

0.0669 

— 

230O 

10.  18 

i.  608 

0.411 

500 

0.700 

0.1017 

0.0165 

2500 

11.82 

1.871 

0.481 

700 

I.  261 

0.189 

0.0356 

27OO 

13-56 

— 

o.556 

900 

1.961 

0.297 

0.0621 

2900 

15-54 

— 

0.636 

I  IOO 

1300 

2.787 

3.726 

0.426 
0.576 

0.0941 
o.i333 

3IOO 
3300 

17.42 
19-50 

— 

0.719 
0.807 

1500 

4.787 

0-744 

0.1783 

3500 

21.79 

— 

0.898 

SMITHSONIAN  TABLES. 


*  Langmuir  Physical  Review,  34,  p.  401,  1912. 


TABLE  289. 
HEAT    LOSSES   FROM    INCANDESCENT    FILAMENTS- 

(a)  WIRES  OF  PLATINUM  SPONGE  SERVED  AS  RADIATORS  (TO  ROOM-TEMPERATURE  SURROUND- 
INGS).   HARTMAN,  PHYSICAL  REVIEW,  7,  p.  431,  1916. 


Diameter 
wire, 
cm. 

(A)  Observed  heat  losses  in  watts  per  cm. 

Absolute  temperatures. 

900° 

IOOO° 

1100° 

1200° 

1300° 

1400° 

1500° 

1600° 

1700° 

I800° 

I90O0 

2000° 

o  .  0690 
0.0420 
0.0275 
0.0194 

1.70 
1-35 

I.  12 
0.9-2 

2.26 
1-75 
1.40 
I-  15 

3.01 
2.26 
1.76 
i-39 

3-88 
2.84 
2.23 
1.74 

4.92 
3-53 
2-73 

2.  12 

6.18 
4.29 
3-23 
2-54 

7-70 
5-33 
3-91 
3-04 

9-63 
6.60 
4-67 
3-64 

12.15 
8.25 
5-72 
4-32 

15-33 
10.20 
7-00 
5-10 

19  25 

12.45 
8.64 
6.  10 

23-75 
14-75 
10.45 

7-35 

(B)  Heat  losses  corrected  for  radiation,  watts  per  cm  (A-C). 

o  .  0690 
0.0420 
0.0275 
0.0194 

O.QI 

0.87 
0.80 

0.70 

i.  05 

1.02 
0.92 

0.81 

1-23 
1.17 
1-05 
0.89 

1.36 
i-3i 

1.22 
1-03 

1-45 

1.42 

1-35 
i.iS 

i-Si 
1-45 
1-37 
1-23 

1-54 
1-57 
1.46 
1.31 

1.66 
1.76 
i-So 
1.40 

2.OO 
2.08 
1.67 
1.47 

2.56 

2-43 
I.9I 
I-5I 

2:g 
I'll 

4-30 
3-26 
2.70 
1.88 

(C)  Computed  radiation,  watts  per  cm,  a  =5.61  X  io~u.* 

o  .  0690 
o.  0420 
0.0275 
0.0195 

0-79 
0.48 
0.32 

0.  22 

I.  21 

0-73 
0.48 
0-34 

1.78 
1.09 
0.71 
0.50 

2.52 

i-53 

I.  01 

0.71 

3-47 

2.  II 
1.38 
0.97 

4.67 
2.84 
1.86 
1.31 

6.16 
3-74 
2-45 
1-73 

7-97 
4.84 
3-17 

2.24 

IO.I5 

6.17 

4-05 
2.85 

12.77 
7-77 
5-09 
3-59 

15-85 
9-65 
6.32 
4.46 

19-45 
11.85 
7-75 
5-47 

(D)  Conduction  loss  by  silver  leads,  watts  per  cm. 

0.0420 
0.0275 
0.0195 

0.42 

0.18 
0.06 

0.46 

O.2I 

0.08 

0.49 
0.28 
0.08 

0.61 
0.35 
0.09 

0-75 
0.43 

O.II 

0.88 
0.48 

O.  12 

I.  CO 

0.55 

0.14 

1.07 
o.S7 
0.15 

*-«J 

0.60 

O.22 

I.  22 
0.67 
0.23 

— 

— 

(E)  Convection  loss  by  air,  watts  per  cm. 

0.0420 
0.0275 
0.0195 

0.45 

O.62 
0.64 

0.56 
0.71 
0-73 

0.68 
o.77 
0.81 

o.  70 
0.87 
0.94 

0.67 
0.92 
1.04 

0.57 
0.89 
i.  ii 

0-59 
0.91 
1.17 

o.  69 
0.93 
1-25 

0-95 
1.07 
1.29 

I.  21 
1.24 
1.30 

— 

— 

*  This  value  is  lower  than  the  presently  (1919)  accepted  value  of  5.72. 

(b)  WIRES  or  BRIGHT  PLATINUM  40-50  CM  LONG  SERVED  AS  RADIATORS  TO  SURROUNDINGS 
AT  300°  K.     LANGMUIR,  PHYSICAL  REVIEW,  34,  p.  401,  1912. 


Diameter 
wire, 
cm. 


0.0510 

0.02508 

0.01262 

0.00691 

0.00404 


Observed  energy  losses  in  watts  per  cm. 


Absolute  temperatures. 


0.22 
0.17 
0.13 
0.12 
O.II 


700 


0.52 
0-39 
0.31 
0.29 
0.24 


900 


0.90 

0.68 
0-53 
0.48 
0.41 


1.42 

1.02 

0.79 
0.72 
0.61 


1300° 


2.03 
i-45 
i. ii 
o.99 
0.84 


1500° 


2.89 

2.00 
I.46 

1-33 
1.14 


1700° 


4.10 
2.68 
i-95 
1.79 

1-54 


1900 


5-65 
3-55 
2.71 
2.48 
2.13 


Energy  radiated  in  watts  per  cm.'1 


0.0510 

0.02508 

0.01262 

0.00691 

0.00404 


0.002 
o.ooi 
o.  ooi 

0.000 
0.000 


0.013 
0.007 
0.003 

0.002 
O.OOI 


0.049 

0.024 

O.OI2 

0.007 
0.004 


0.137 
0.067 
0.034 
0.019 

O.OII 


0.323 
0.159 
0.080 
0.044 

0.026 


0.67 
0-33 

0.17 
0.09 
0.05 


1.25 

0.62 

0.31 
0.17 

O.  10 


2.15 
1. 06 
0.53 

0.29 
0.17 


'  Convection  "  losses  in  watts  per  cm. 


0.0510 
0.02508 
0.01262 
0.00691 
o . 00404 


0.22 
O.I? 
0.13 
0.12 
O.II 


0.51 
0.38 
0-31 
0.29 
0.24 


0.85 

0.66 
0.52 
0.47 
0.41 


1.28 
0-95 
0-75 
0.70 
0.60 


1.71 
1.29 
1.03 
0-95 
0.81 


2.22 
1.67 
1.29 
1.24 
1.09 


2.85 
2.06 
1.64 
1.62 
1.44 


3-50 

2.49 
2.18 
2.19 
1.96 


Thickness  of  theoretical  conducting  air  film. 


0.0510 
0.02508 
0.01262 
0.00691 
0.00404 
Means. 


0.28 
0.30 
0.42 
0.31 
0.27 
0.31 


0.42 
0.32 
0.43 
0.37 


0-33 
0-37 
0.44 
0.38 
0.43 
0-39 


0.33 
0.41 
0.49 
0.40 
0.47 
0.42 


0.36 
0.45 
0.56 
0.43 
0.56 
0-49 


0.37 
0.45 
0.69 
0.47 
0.47 
0.49 


0.36 
0.56 
o.47 
0.26 
0.25 
0.38 


Means. 
0-34 
0-43 
0.54 
0-37 
0.41 

to.  43 


*  Computed  with  a  =  5.32,  black -body  efficiency  of  platinum  as  follows  (Lummer  and  Kurlbaum):  492°  K. 
0.039;  654°,  0.060;  795°,  0.075;  1108°,  0.112;  1481°,  0.154;  1761°  K.,  0.180.  For  significance  of  last  group 
of  data,  see  next  page. 


,  0.075; 
t  Weighted  mean. 


SMITHSONIAN  TABLES. 


256 


TABLES  290-291. 
THE   EYE   AND   RADIATION- 


Definitions:  A  meter-candle  is  the  intensity  of  illumination  due  to  a  standard  candle  at  a  meter  distance.  The 
millilambert  (o.ooi  lambert)  measures  the  brightness  of  a  perfectly  diffusing  (according  to  Lamberts  cosine  law) 
surface  diffusing  i  lumen  per  cmj.  A  brightness  of  10  meter-candles  equals  i  millilambert.  o.ooi  ml  corresponds 
roughly  to  night  exteriors,  o.i,  to  night  interiors,  10  ml  to  daylight  interiors  and  1000,  to  daylight  exteriors.  A  bright- 
ness of  100,000  meter-candles  Is  about  that  of  a  horizontal  plane  for  summer  day  with  sun  in  zenith,  500,  on  a  cloudy 
day,  4,  ist  magnitude  stars  just  visible,  0.2,  full  moon  in  zenith,  .001,  by  starlight;  in  winter  the  intensity  at  noon  may 
drop  about  $. 


TABLE  290.  —  Spectral  Variation  of  Sensitiveness  as  a  Function  of  Intensity. 

Radiation  is  easily  visible  to  most  eyes  from  0.330  ft  (violet)  to  0.770  M  (red).  At  low  intensities  near  threshold 
values  (gray,  rod  vision)  the  maximum  of  spectral  sensibility  lies  near  0.503  /J.  (green)  for  90%  of  all  persons.  At  higher 
intensities  after  the  establishment  of  cone  vision,  the  max.  shifts  as  far  as  0.560  u.  See  Table  297  for  more  accurate 
values  of  sensitiveness  after  this  shift  has  been  accomplished.  The  ratio  of  optical  sensation  to  the  intensity  of  energy 
increases  with  increasing  energy  more  rapidly  for  the  red  than  for  the  shorter  wave-lengths  (Purkmje  phenomenon); 
i.e.,  a  red  light  of  equal  intensity  to  the  eye  with  a  green  one  will  appear  darker  as  the  intensities  are  equally  lowered. 
This  phenomenon  disappears  above  a  certain  intensity  (above  10  millilamberts).  Table  due  to  Nutting,  Bulletin 
Bureau  of  Standards. 

The  intensity  is  given  for  the  spectrum  at  0.535/1  (green). 


Intensity 
(meter-candles)  = 
Ratio  to  preceding  step  = 

.00024 

.00225 

9.38 

.0360 

16 

-575 
16 

2.30 

4 

9.22 

4 

36.9 

4 

147.6 
4 

590-4 

4 

Wave-length,  X. 

Sensitiveness. 

0.430/11 

0.081 

0.093 

0.127 

0.128 

0.114 

0.114 







0.450 

0-33 

0.30 

0.29 

0.31 

0.23 

0.175 

0.16 

— 

—. 

0.470 

0.63 

o.SQ 

0.54 

0.58 

0.51 

0.29 

0.26 

0.23 

— 

0.400 

0.96 

(0.89) 

(0.76) 

(0.89) 

(0.83) 

0.50 

0-45 

0.38 

0-35 

0.505 

I.OO 

I.OO 

I.OO 

I.OO 

0.99 

(0.76) 

0.66 

0.61 

0.54 

0.520 

0.88 

0.86 

0.86 

0.94 

0.99 

(0.85) 

0.85 

0.85 

0.82 

0.535 

0.61 

0.62 

0.63 

0.72 

0.91 

(0.98) 

0.98 

0.99 

0.98 

0-555 

0.26 

0.30 

0-34 

0.41 

0.62 

0.84 

0-93 

0.97 

0.98 

0-575 

0.074 

O.IO2 

0.122 

0.168 

(0-39) 

(0.63) 

(0.76) 

(0.82) 

(0.84) 

0.590 

0.025 

0-034 

0.054 

0.091 

0.27 

0.49 

0.61 

0.68 

0.69 

0.605 

0.008 

0.012 

O.024 

0.056 

0.173 

0-35 

(o.45) 

0-54 

0-55 

0.625 

0.004 

0.004 

O.OII 

0.027 

0.098 

o.  20 

0.27 

0.35 

0-35 

0.650 

0.000 

0.000 

O.OO3 

0.007 

0.025 

0.060 

0.085 

O.I22 

0.133 

0.670 
X,  maximum  sensitiveness 

0.000 

0.503 

0.000 
0.504 

O.  OOI 

0.504 

0.002 
0.508 

0.007 
0.513 

0.017 
0-530 

0.025 
0.541 

0.03O 

0.543 

0.030 
0.544 

TABLE  291.  —  Threshold  Sensibility  as  Related  to  Field  Brightness. 

The  eye  perceives  with  ease  and  comfort  a  billion-fold  range  of  intensities.  The  following  data  were  obtained  with 
the  eye  fully  adapted  to  the  sensitizing  field,  B,  the  field  flashed  off,  and  immediately  the  intensity,  T,  of  a  test  spot 
(angular  size  at  eye  about  5°)  adjusted  to  be  just  visible.  This  table  gives  a  measure  of  the  brightness,  T,  necessary 
to  just  pick  up  objects  when  the  eye  is  adapted  to  a  brightness,  B.  Intensities  are  indicated  log  intensities  in  milli- 
lamberts. Blanchard,  Physical  Review,  n,  p.  81,  1918. 


Log  B  

—  7  -° 

—6.0 

—  5.0 

—4.0 

—3  .0 

—  2    O 

—  I    O 

O    O 

+  1    0 

+  ->  o 

+3  o 

/  Log  T  white 

—  5  81 

—4  87 

_LO   2o 

\T/B..'  

i  5 

o  38 

13 

068 

0018 

0018 

Log  T  blue 

6  *8 

e    82 

^    A6 

2    l8 

I  62 

Log  T  green  .     . 

—6  42 

—  5  62 

2    60 

2    O8 

I  62 

Log  T,  yellow  

—  5  47 

—  5  17 

—4  61 

I  62 

Log  T,  red  

—  4-  27 

—4  oo 

-2    96 

SMITHSONIAN  TABLES. 


TABLES  292-295. 

THE   EYE   AND   RADIATION. 

TABLE  292.  —  He  tero  chroma  tic  Threshold  Sensibility. 


257 


The  following  table  shows  the  decrease  in  sensitiveness  of  the  eye  for  comparing  intensities  of  different  colors.  The 
numbers  in  the  body  of  the  table  correspond  to  the  line  marked  T/B  of  Table  291.  The  intensity  of  the  field  was 
probably  between  10  and  100  millilamberts  (25  photons). 


Comparison  color. 

0.693  ju 

o  .  640  [i 

0-575  M 

o.SOSM 

0-475  M 

0-430M 

Standard  color:  red  
yellow  
green 

0.693  M 
0-575  M 
o.  505  /j. 

0.044 
0.174 

O.  211 

0.088 

o.  160 
o  180 

0.165 
0.032 
o  138 

0.180 
0.166 

0.197 
0.174 

0.150 
0.134 

blue  

0.475  M 

0.168 

0.180 

0.130 

0.130 

0.068 

0.142 

TABLE  293.  —  Contrast  or  Photometric  Sensibility. 

For  the  following  table  the  eye  was  adapted  to  a  field  of  o.i  millilambert  and  the  Sensitizing  field  flashed  off.  A 
neutral  gray  test  spot  (angular  size  at  eye,  5  X  2.5°)  the  two  halves  of  which  had  the  contrast  indicated  (\  transparent, 
$  covered  with  neutral  screen  of  transparency  =  contrast  indicated)  was  then  observed  and  the  brightness  of  the 
transparent  part  measured  necessary  to  just  perceive  the  contrast  after  the  lapse  of  the  various  times.  One  eye  only 
used,  natural  pupil.  Blanchard,  Physical  Review,  n,  p.  88,  1918.  Values  are  log  brightness  of  brighter  field  in 
millilamberts. 


Time  in  seconds. 

0 

I 

2 

5 

IO 

20 

40 

60 

Contrast'  o  oo 

—  80 

—  3  47 

—3  82 

—  4  3O 

—4  60 

—4  89 

0.39  
o  67 

-  .63 

—   40 

-3.36 
—  3  .00 

-3-58 
—  3.  13 

—3-74 

—  3  •  22 

-3.85 

—  3  21 

—3-97 
—  3  33 

-4-06 
—3  46 

-4-23 
—  3  48 

o  87 

—   IO 

—  2  46 

—  2  49 

—  2  48 

—  2  55 

—  2  67 

0.97  

—  .  20 

—  1.  57 

-1.67 

—  1.69 

—  1-59 

-1.63 

—  I  •  73 

TABLE  294.  —  Glare  Sensibility. 

When  an  eye  is  adapted  to  a  certain  brightness  and  is  then  exposed  suddenly  to  a  much  greater  brightness,  the 
latter  may  be  called  glaring  if  uncomfortable  and  instinctively  avoided.  Observers  naturally  differ  widely.  The  data 
are  the  means  of  three  observers,  and  are  log  brightnesses  in  millilamberts.  The  glare  intensity  may  be  taken  as  roughly 
1 700  times  the  cube  root  of  the  field  intensity  in  millilamberts.  Angle  of  glare  spot,  4°.  Blanchard,  Physical  Review, 
loc.  cit. 


Log.  field... 
Log.  glare.  .  . 

-6.0 
1-35 

—4.0 
1.90 

—  2.O 
2.60 

—  1.0 
2.00 

0.0 

3.28 

+  1.0 

3.60 

2.O 

3-00 

3-0 

4.18 

4.0 

4.48 

TABLE  295.  —  Rate  of  Adaptation  of  Sensibility. 

This  table  furnishes  a  measure  of  the  rate  of  increase  of  sensibility  after  going  from  light  into  darkness,  and  the 
values  were  obtained  immediately  from  the  instant  of  turning  off  the  sensitizing  field.  Both  eyes  were  used,  natural 
pupil,  angular  size  of  test  spot,  4.9°,  viewed  at  35  cm.  Blanchard,  loc.  cit.  Retinal  light  persists  only  10  to  20  m  when 
one  has  been  recently  in  darkness,  then  in  a  dimly  lighted  room;  it  persists  fully  an  hour  when  a  subject  has  been  in 
bright  sunlight  for  some  time.  A  person  who  has  worked  much  in  the  dark  "gets  his  eyes"  quicker  than  one  who  has 
not,  but  his  final  sensitiveness  may  be  no  greater. 


Sensitizing 
field. 

Logarithmic  thresholds  in  millilamberts  after 

osec. 

i  sec. 

2  sec. 

5  sec. 

10  sec. 

20  sec. 

40  sec. 

60  sec. 

5  min. 

3omin. 

60  min. 

White  o  i  ml 

—   .79 

—     .20 
-     .60 
-     .00 
-     .82 
-     .69 
-     .6l 
—     -32 

-3-82 
-2.99 
-2.30 
-1.66 
—3-92 
-4.08 
-3-84 
-2.69 

-4-13 
—3-27 
-  -53 

—  .00 

-  .36 

—  -39 
-  -17 
-  .98 

-4.50 
—3-79 
-3.08 
-2.46 
—4.91 
-4-82 
—4.41 
-3-37 

—4-75 
—4-15 
-3-54 
-2.64 
—5-27 
—  S-ii 
-4-65 
-3-57 

-4.96 
—4-51 
—3-94 
-2.88 
—  5-53 
-5-26 
-4.78 
-3-65 

-5-i6 
-4.82 
—4-31 

—  3-20 

-5-68 
—  5-43 

—  5-02 

-3.73 

—3-32 
-5-06 
-4.61 
-3-84 
-5.81 
-5.56 
-5-09 
-3-8o 

-5-68 

-5-52 

—  5-22 
-4.76 

-6.23 

-5.80 

-5-39 
—4.02 

-5-91 
-5-86 
-5-83 
-5-77 

-6.06 
—6.04 
—6.01 
-5-97 

10.  o  ml  

100  o  ml    .  . 

Blue      o.i  ml  
Green  o.i  ml  
Yellow  o  i  ml 

Red       o  .  i  ml  

SMITHSONIAN  TABLES. 


2^8  TABLES  296-298. 

THE  EYE  AND  RADIATION. 

TABLE  296.  —  Apparent  Diameter  of  Pupil  and  Flux  Density  at  Retina. 

Flashlight  measures  of  the  pupil  (both  eyes  open)  viewed  through  the  eye  lens  and  adapted  to  various  field  intensi- 
ties. For  eye  accommodated  to  25  cm,  ratio  apparent  to  true  pupil,  1.02,  for  the  unaccommodated  eye,  1.14.  The 
pupil  size  varies  considerably  with  the  individual.  It  is  greater  with  one  eye  dosed;  e.g.,  it  was  found  to  be  for  o.oi 
miUilambert,  6.7  and  7.2  mm;  for  0.6  ml,  5.3  and  6.5;  for  6.3  ml,  4.1  and  5.7;  for  12.6  ml,  4.1  and  5.7  mm  for  both 
and  one  eye  open  respectively  for  a  certain  individual.  At  the  extreme  intensities  the  two  values  approach  each  other. 
The  ratio  of  the  extreme  pupil  openings  is  about  A,  whereas  the  light  intensities  investigated  vary  over  i ,ooo,ooo-fold. 
(Blanchard  and  Reeves,  partly  unpublished  data.) 


FLM 

Diameter,  mm 

Effective 

millilamberts. 

Observed. 

(1.14/1.02) 
XObs. 

area,  mm2 

lumens  per  mm2 

O.OOOOI 

8 

8.96 

64 

8.4  X  io-« 

O.OOI 
O.I 

ti 

8.51 
7.28 

57 
42 

7  .  6  X  io-"> 
5-6  Xio-s 

10 

4-0 

4-48 

16 

2.1  X  io-« 

IOOO 

2.07 

2-35 

4-3 

5-8  X  io-5 

TABLE  297.  —  Relative  Visibility  of  Radiation. 

This  table  gives  the  relation  between  luminous  sensation  (light)  and  radiant  energy.  The  results  of  two  methods 
are  given:  one  from  measures  of  the  direct  equality  of  brightness,  which  some  consider  the  true  method,  as  more  direct, 
but  criticized  because  of  the  difficulty  of  judging  heterochromatic  light  (Hyde,  Forsythe,  Cady,  A.  J.  48,  87,  1918,  29 
observers);  the  other  (Coblentz,  Emerson,  Bui.  Bureau  of  Standards,  14,  219,  1917,  130  observers)  depends  on  the 
disappearance  of  flicker  when  two  lights  of  different  color  and  intensity  are  alternated  rapidly.  Color  has  a  lower 
critical  frequency  than  brightness  and  disappears  first.  Data  determined  for  intensities  above  Purkinje  effect.  See 
Table  290.  Ratio  of  light  unit  Oumen)  to  energy  unit  (watt)  at  0.5511,  0.00162  (Ives,  Coblentz,  Kingsbury). 


Visibility. 

Visibility. 

Visibility. 

Visibility. 

Visibility. 

X 

X 

X 

X 

X 

M 

M 

M 

M 

M 

HFC 

CE 

HFC 

CE 

HFC 

CE 

HFC 

CE 

HFC 

CE 

.40 

.049 

.010 

.48 

•  138 

•  125 

•  56 

•995 

-998 

.64 

•  154 

.194 

•  72 

.0374 

.0397 

.41 

.0362 

.017 

•  49 

.216 

.194 

•  57 

•944 

.968 

-65 

.094 

•  "5 

•  73 

.0336 

.0348 

•  42 

.0041 

.024 

•50 

•  328 

•  3i6 

•  58 

.855 

.898 

.66 

•  051 

.0645 

•74 

.0318 

.0328 

•43 

.0115 

.029 

-Si 

•  515 

•  503 

•59 

•735 

.800 

.67 

.026 

•  0338 

•  75 

.049 

.0320 

•  44 

.022 

•  033 

•52 

.698 

.710 

.60         .600 

.687 

.68 

.0125 

.0178 

•  76 

.045 



.036 

.041 

•53 

-847 

.862 

.61 

•464 

•  557 

.69 

.0062 

.0085 



.46 

•  055 

056 

•54 

.968 

•  954 

.62 

•341 

.427 

.70 

.0031 

.0040 

— 

— 



•47 

.087 

.083 

•  55 

.996 

•994 

-63 

.238 

.302 

•  71 

.0015 

.00203 

TABLE  298.  —  Miscellaneous  Eye  Data. 

Light  passing  to  the  retina  traverses  in  succession  (a)  front  surface  of  the  cornea  (curvature,  7.9  mm);  (b)  cornea 
(equivalent  water  path  for  energy  absorption,  .06  cm);  (c.)  back  surface  cornea|(curv.,  7.9  mm);  (d)  aqueous  humour 
(equiv.  HjO,  .34  cm,  n  =  1.337);  M  front  surface  lens  (c,  10  mm);  (/ )  lens  (equiv.  HjO,  .42  cm,  n  —  1.445);  (s)  back 
surface  lens  (c.,  6mm);  (h)  vitreous  humour  (equiv.  HjO,  1.46  cm,  n  =  1.337).  An  equivalent  simple  lens  has  its 
principal  point  2.34  mm  behind  (a),  nodal  point  0.48  mm  in  front  of  (g),  posterior  principal  focus  22.73  mm  behind 
(a),  anterior  principal  focus  12.83  mm.  in  front  of  (a),  curvature,  5.125  mm.  At  the  rear  surface  of  the  retina  (.15  mm 
thick)  are  the  rods  (30  X  2ju)  and  cones  (10  (6  outside  fovea)  fj,  long).  Rods  are  more  numerous,  2  to  3  between 
2  cones,  over  3,000,000  cones  in  eye.  Macula  lutea,  yellow  spot,  on  temporal  side,  4  mm  from  center  of  retina,  long  axis 
2  mm.  Central  depression,  fovea  centralis,  .3  mm  diameter,  7000  cones  alone  present,  6  X  2  or  3ju.  In  region  of  dis- 
tinct vision  (fovea  centralis)  smallest  angle  at  which  two  objects  are  seen  separate  is  50"  to  70"  =  5.65  to  5-I4M  at 
retina;  50  cones  in  100/1  here;  4/1  between  centers,  3^1  to  cone,  i/x  to  interval.  Distance  apart  for  separation  greater 
as  depart  from  fovea.  No  vision  in  blind  spot,  nasal  side,  2.5  mm  from  center  of  eye,  15  mm  in  diam. 

Persistence  of  vision  as  related  to  color  (Allen,  Phys.  Rev.  n,  257,  1900)  and  intensity  (Porter,  Pr.  Roy.  Soc.  70, 
313,  1912)  is  measured  by  increasing  speed  of  rotating  sector  until  flicker  disappears:  for  color,  .4/1,  .031  sec.;  .45**, 
.020  sec.;  .SM,  015  sec.;  .57^1,  .012  sec.;  .68/Lt,  .014  sec.;  .76^1,  .018  sec.;  for  intensity,  .06  meter-candle,  .028  sec.;  i  me, 
.020  sec.;  6  me,  .014  sec.;  100  me,  .010  sec;  142  me.,  .007  sec. 

Sensibility  to  small  differences  in  color  has  two  pronounced  maxima  (in  yellow  and  green)  and  two  slight  ones 
(extreme  blue,  extreme  red).  The  sensibility  to  small  differences  in  intensity  is  nearly  independent  of  the  intensity 
(Fechner's  law)  as  indicated  by  the  following  data  due  to  Konig: 


7//o 

1,000,000 

100,000 

10,000 

IOOO 

100 

50 

10 

5 

I 

O.I 

7o  in  me 

dl/I,  white  
.60  n  

.036 

.019 

.024 

.018 
.016 

.018 

.020 

.030 
.028 

.032 

.038 

.048 
.061 

•059 

.103 

.123 

.212 

•  377 

.00072 
.0056 

•  50M  

— 

.018 

.018 

.024 

.025 

.036 

.049 

.080 

.133 

.00017 



018 

040 

049 

.074 

.137 

.00012 

SMITHSONIAN  TABLES. 


TABLE  299. 

PHOTOMETRIC    DEFINITIONS    AND    UNITS. 

Luminous  flux,  F  =  radiant  power  according  to  visibility,  i.e.,  capacity  to  produce  sensation 
of  light.  Unit,  the  lumen  =  flux  emitted  in  a  unit  solid  angle  (steradian)  by  point  source  of  one 
candle  power. 

Visibility,  A\  ,  of  radiation  of  wave-length  X  =  ratio  luminous  flux  to  radiant  power  (energy) 
producing  it.  Mean  visibility,  Km,  over  any  range  of  X  or  for  whole  visible  spectrum  of  any 
source  =  ratio  total  flux  (lumens)  to  total  radiant  power  (erg/sec,  or  watts). 

Luminous  intensity,  7,  of  (approximate)  point  source  =  solid  angle  density  of  luminous  flux 
in  direction  considered  =  dF/du  or  F/u  if  intensity  is  uniform.  o>  is  the  solid  angle.  Unit, 
the  candle. 

Illumination  on  surface  is  the  flux  density  on  the  surface  =  dF/dS  or  F/S  when  uniform. 
5  is  the  area  of  the  surface.  Units,  meter-candle,  foot-candle,  phot,  lux. 

(Lux  =  one  lumen  per  m2;    phot  =>  one  lumen  per  cm2.) 

Brightness,  b,  of  element  of  surface  from  a  given  point  =  dl/dS  cos  0,  where  6  is  the  angle 
between  normal  to  surface  and  line  of  sight.  Unit,  candles  per  cm2.  Normal  brightness,  60 
=  dl/dS  =  brightness  in  direction  normal  to  surface.  Unit,  the  lambert. 

Specific  luminous  radiation,  E'  =  luminous  flux  density  emitted  by  a  surface,  or  the  flux 
emitted  per  unit  of  emissive  area,  expressed  in  lumens  per  cm2.  For  surfaces  obeying  Lam- 
bert's cosine  law,  E'  =  TT&O. 

The  lambert,  the  cgs  unit  of  brightness,  is  the  brightness  of  a  perfectly  diffusing  surface  radiat- 
ing or  reflecting  one  lumen  per  cm2.  Equivalent  to  a  perfectly  diffusing  surface  with  illumina- 
tion of  one  phot.  A  perfectly  diffusing  surface  emitting  one  lumen  per  ft2  has  a  brightness  of 
1.076  millilamberts.  Brightness  in  candles  per  cm2  is  reduced  to  lamberts  by  multiplying  by  ir. 

A  uniform  point  source  of  one  candle  emits  4?r  lumens. 

One  lumen  is  emitted  by  .07958  spherical  candle  power. 

One  lumen  emitted  per  ft2  =  1.076  millilamberts  (perfect  diffusion). 

One  spherical  candle  power  emits  12.57  lumens. 

One  lux  =  i  lumen  incident  per  m2  =  .0001  phot  =  .1  milliphot. 

One  phot  =  i  lumen  incident  per  cm2  =  10,000  lux  =  1000  milliphots. 

One  milliphot  =  .001  phot  =  .929  foot-candle. 

One  foot-candle  =  i  lumen  incident  per  ft2  =  1.076  milliphots  =  10.76  lux. 

One  lambert  =  i  lumen  emitted  per  cm2  of  a  perfectly  diffusing  surface. 

One  millilambert  =  .929  lumen  emitted  per  ft2  (perfect  diffusion). 

One  lambert  =  .3183  candle  per  cm2  =  2.054  candles  per  in2. 

One  candle  per  cm2  =  3.1416  lamberts. 

One  candle  per  in2  =  .4968  lambert  =  486.8  millilamberts. 

Adapted  from  1916  Report  of  Committee  on  Nomenclature  and  Standards  of  Illuminating 
Engineering  Society.  See  Tr.,  Vol.  u,  1916. 

SMITHSONIAN  TABLES. 


26O  TABLES  300-302. 

TABLE  300.  —  Photometric  Standards. 

No  primary  photometric  standard  has  been  generally  adopted  by  the  various  governments.  In 
Germany  the  Heiner  lamp  is  most  used ;  in  England  the  Pentane  lamp  and  sperm  candles  are 
used  ;  in  France  the  Carcel  lamp  is  preferred;  in  America  the  Pentane  and  Hefner  lamps  are  used 
to  some  extent,  but  candles  are  more  largely  employed  in  gas  photometry.  For  the  photometry 
of  electric  lamps,  and  generally  in  accurate  photometric  work,  electric  lamps,  standardized  at  a 
national  standardizing  institution,  are  commonly  employed. 

The  "  International  candle  "  is  the  name  recently  employed  to  designate  the  value  of  the  candle 
as  maintained  by  cooperative  effort  between  the  national  laboratories  of  England,  France,  and 
America;  and  the  value  of  various  photometric  units  in  terms  of  this  international  candle  is  given 
in  the  following  table  (taken  from  Circular  No.  15  of  the  Bureau  of  Standards). 

i  International  Candle  =  i  Pentane  Candle. 
i  International  Candle  =  i  Bougie  Decimale. 
i  International  Candle  =  i  American  Candle. 
I  International  Candle  =  i.n  Hefner  Unit, 
i  International  Candle  =  0.104  Carcel  Unit. 

Therefore  i  Hefner  Unit  =  0.90  International  Candle. 

The  values  of  the  flame  standards  most  commonly  used  are  as  follows : 

1.  Standard  Pentane  Lamp,  burning  pentane 10.0  candles. 

2.  Standard  Hefner  Lamp,  burning  amyl  acetate 0.9  candles. 

3.  Standard  Carcel  Lamp,  burning  colza  oil 9.6  candles. 

4.  Standard  English  Sperm  Candle,  approximately    ....  i.o  candles. 

TABLE  301.  —Intrinsic  Brightness  of  Various  Light  Sources. 


Barrows. 

Ives  &  Luckiesl 

. 

National  Electric 
Lamp 
Association. 

C.P.perSq.  In. 
of  surface 
of  light. 

C.  P.  per  Sq.  In. 

of  surface 
of  light. 

C.  P.  per  Sq. 
Mm.  of  sur- 
face of  light. 

C.  P.  per  Sq.  In. 
of  surface 
of  light. 

Sun  at  Zenith   . 

600,000 

_ 

_ 

600,000 

Crater,  carbon  arc     . 

200,000 

84,000 

130. 

200,000 

Open  carbon  arc        . 

10,000-50,000 

- 

10,000-50,000 

Flaming  arc       . 

5,000 

- 

_ 

5,000 

Magnetite  arc   . 

- 

4,000 

6.2 

- 

Nernst  Glower           . 

800-1,000 

(ii5v.6amp.  d.c.)  3,010 

4-7 

(1.5  W.p.C.)  2,200 

Tungsten  incandescent,  1.15  w.  p.  c- 

— 

_ 

1,000 

Tungsten  incandescent,  1.25  w.  p.  c- 

1,000 

1,000 

1.64 

875 

Tantalum  incandescent,  2.0  w.  p.  c. 

750 

580 

0.9 

75° 

Graphitized    carbon    filament,    2.5 

w   p   c                      • 

625 

*7CO 

1.2 

625 

UA 

Carbon  incandescent,  3.1  w.  p.  c. 

u^;> 

480 

485 

0-75 

480 

Carbon  incandescent,  3.5  w.  p.  c. 

375 

400 

0.63 

375 

Carbon  incandescent,  4.0  w.  p.  c. 

300 

325 

O.5O 

Inclosed  carbon  arc  (d.  c.) 

100-500 

_ 

100-500 

Inclosed  carbon  arc  (a.  c.) 

- 

- 

- 

75-200 

Acetylene  flame  (i  ft.  burner)  . 
Acetylene  flame  ()£  ft.  burner) 

75-100 

53-o 
33-o 

0.082 
0.057 

75-100 

Welsbach  mantle 

20-25 

3^-9 

0.048 

20-50 

Welsbach  (mesh) 

56.0 

0.067 

Cooper  Hewitt  mercury  vapor  lamp 

16.7 

14.9 

0.023 

'7 

Kerosene  flame 

4-8 

9.0 

O.OI4 

3-8 

Candle  flame     . 

3-4 

3~4 

Gas  flame  (fish  tail) 

3-8 

2.7 

0.004 

3-8 

Frosted  incandescent  lamp 

4-8 

2-5 

;irbon-dioxide  tube  lamp 

0.6 

- 

- 

0-3-I-75 

Taken  from  Data,  1911. 
TABLE   302.— Visibility  of  White  Lights. 


Range. 

Candle  Power. 

1 

2 

i  sea-rr.ile=: 

1855  meters      .... 

0.47 

0.41 
i  6 

1      5    "    "        | 

11.8 

10. 

1  Paterson  and  Dudding.  *  Deutsche  Seewarte. 

i  micro-calorie  through  i  cm.  at  i  m.  =0.034  sperm  candle  =  0.0385  Hefner  unit  (no  diaphragm)  •=.  0.043  Hefner 
unit  (diap.  14  X  50  mm.).     Coblentz  Bui.  B.  of  S.,  u,  p.  87,  1914. 

SMITHSONIAN  TABLES. 


TABLES  303-305. 

2OI 

BRIGHTNESS  OF   BLACK   BODY.   CROVA  WAVE-LENGTH.    MECHANICAL   EQUIVALENT 
OF   LIGHT.    LUMINOUS    INTENSITY  AND   EFFICIENCY  OF    BLACK   BODY- 

The   values    of    L,    the   luminous    intensity,    are    given    in    light    watts/steroradian/cm2  of  radiating  surface 
=  (I/TT)  J^  °°  V^E^dX,  where  V^  is  the  visibility  of  radiation  function. 

Mechanical  equivalent.  The  unit  of  power  is  the  watt;  of  lumininous  flux,  the  lumen.  The  ratio  of  these  two  quan- 
tities for  light  of  maximum  visibility,  X  =  0.556  »,K  the  stimulus  coefficient  Vm;  its  reciprocal  is  the  (least)  mechanical 
equivalent  of  light,  i.e.,  least  since  applicable  to  radiation  of  maximum  visibility.  A  better  term  is  »  umi 
lent  of  radiation  o  maximum  visibility."  One  lumen  =0.001496  watts  (Hyde,  Forsythe,  Cady);  or  i  w 
tion  of  maximum  visibility  (X  =  0.556  n)  =  668  lumens. 

White  light  has  sometimes  bee  i  denned  as  that  emitted  by  a  black  body  at  6000°  K. 

The  Crova  wave-length  for  a  black  body  is  that  wave-length,  X,  at  which  the  luminous  intensity  varies  bv  the 
same  fractional  part  that  the  total  luminous  intensity  varies  for  the  same  change  in  temperature 


TABLE  303.  —  Brightness,  Crova  Wave- 
length of  Black  Body,  Mechanical 
Equivalent  of  Light.* 


TABLE  304. — Luminous,    Total    Intensity    and 
Radiant  Luminous  Efficiency  of  Black  Body.* 


Tap 

Bright- 
ness, 
candles 
per  cm2 

Crova 
wave- 
length, 
M 

Mech. 
equiv. 
watts 
per/. 

T,  degrees 
absolute. 

Luminous 
intensity 
L  watt/cm2 

Total  intensity 
<ro  T*  watt/cm2 

Radiant 
luminous 
efficiency. 

1700° 
1750 
I800 
1850 
I9OO 
1950 
2OOO 
2O5O 
2100 
2150 
2200 
2250 
2300 
2350 
2400 
2450 
25OO 
2550 
2600 
2650 

w 

\l:l 

23.1 
32.2 
44-3 
60.0 
80.  i 
105.7 
137-6 
177- 
226. 
284. 
354- 
438. 
537- 
651. 
785. 
939- 

0.584 
0-583 
0.582 
0.581 
0.580 
0.579 
0.578 
0-577 
0.576 
0.576 
0-575 
0-574 
0-574 
0-573 
0.572 
0.572 
o.57i 
0.570 
0.570 
0.569 

0.001478 
0.001491 
0.001498 
0.001498 
0.001497 
0.001496 
0.001497 
0.001497 
0.001502 
0.001511 

1,200 

i,  600 
1,700 
i,  800 
1,900 

2,000 
2,100 
2,200 
2,300 
2,400 
2,500 

2,600 

3,000 
4,000 
5,000 
6,000 
7,000 
8,000 

10,000 

2.34  X  10-6 

3.45  Xio-3 
8.46  X  io~3 
1.88  X  10-2 
3.85  X  10^2 
7.34X10-2 
1.32  X  10-1 
2.26  X  i  o-i 
3.69  Xio-i 
5.79  X  10  i 
8.77  Xio-i 
1.29 
4.66 
3-85  Xio 
1.36  X  lo2 
3.26  X  xo2 
6.03  X  lo2 
9.59  X  lo2 
1.84  X  to3 

3.762 
.189 
.515  X  10 
.905  X  10 
.365  Xio 
.903  X  10 
3.529  X  10 
4.250  X  10 
5.077  X  10 
6.  020  X  10 
7.087  X  10 
8.291  X  10 
1.470  X  xo2 
4.645  X  to2 
1.134  X  to3 
2.351  X  lo3 
4.356  Xio3 
7.432  X  lo3 
1.814  Xio« 

.000006 
.000290 
.000558 
.000987 
.00163 
.00253 
•00374 
.00532 
.00727 
.00962 
.0124 
.0156 
•  0317 
.0829 

.1201 
.1386 
•1385 
.1290 
.IOI4 

Mean. 

o  001496 

1919. 


Hyde,  Forsythe,  Cady,  Phys.  Rev.  13,  p.  45, 


*  Coblentz,  Emerson,  Bui.  Bureau  of  Standards,  14,  p.  255, 
1917- 


NOTE.  —  Minimum  energy  necessary  to  produce  the  sensation  of  light:    Ives,  38  X  iQ' 
Reeves,  19.5  X  lo"10;   Buisson,  12.6  X  io~10  erg.  sec.     (Buisson,  J.  de  Phys.  7,  68,  1917.) 


Russell,  7.7  X 


TABLE  305.  —  Color  of  Light  Emitted  by  Various  Sources.* 


Source. 

Color, 
per  cent 

white. 

Hue. 

Source. 

Color, 
per  cent 
white. 

Hue. 

Sunlight 

IOO 

45 

584 

60 

53 

584 

Standard  candle  

13 

593 

Mercury  vapor  arc        

7° 

490 

Hefner  lamp       .    . 

14 

593 

32 

598 

Pentane  lamp  

15 

592 

Neon  tube  

6 

605 

Tungsten  glow  lamp,  i  .  25  wpc  
Carbon  j'low  lamp  3  8  wpc 

35 
25 

588 
5Q2 

Crater  of  carbon  arc,  i  .  8  amp  

59 
62 

585 
585 

Nernst  glower,  i  .  50  wpc  
N-filled  tungsten,  i.oo  wpc  

31 

34 

587 
586 

Crater  of  carbon  arc,  5.0  amp  
Acetylene  flame  (flat)     

67 
36 

583 
586 

*  Jones,  L.  A.,  Trans.  HI.  Eng.  Soc.,  Vol.  9  (1914). 


SMITHSONIAN  TABLES. 


TABLE  306. 
EFFICIENCY  OF  VARIOUS   ELECTRIC  LIGHTS. 


Bryant  and  Hake,  Eng.  Exp.  Station, 
Univ.  of  111. 

Amperes. 

Terminal 
Watts. 

Lumens. 

Kw-hours 
for  100,000 
Lumen- 
hours. 

Total  cost 
per  100,000 
Lumen-hours 
at  10  cts. 
per  Kw-hour. 

Regenerative  d.-c.,  series  arc 

5-5 

385 

11,670 

3-3 

0-339 

Regenerative  d.-c.,  multiple  arc 
Magnetite  d.-c.,  series  arc 
Flame  arc,  d.-c.,  inclined  electrodes 

II 

1  0.0 

605 

528 

55° 

11,670 
8^640 

5.18 
7.16 
6-37 

0.527 
0.729 
0.837 

Mercury  arc,  d.-c.,  multiple 

3.5 

385 

4,400 

15-92 

0.89 

Flame  arc,  d.-c.,  inclined  electrodes 

8.0 

440 

6,140 

7.16 

0.966 

Flame  arc,  d.-c.,  vertical  electrodes 

8.0 

440 

6,140 

7.16 

0.966 

'  Luminous  arc,  d.-c.,  multiple 

6.6 

726 

7.370 

9-85 

0.988 

Open  arc,  d.-c.,  series 

9.6 

480 

5.025 

9-55 

.079 

Magnetite  arc,  d.-c.,  series 

4.0 

320 

2,870 

11.15 

•13 

Flame  arc,  a.-c.,  vertical  electrodes 

IO.O 

467 

5*340 

8-75 

•275 

Flame  arc,  a.-c.,  inclined  electrodes 

IO.O 

467 

5>340 

8-75 

•275 

Open  arc,  d.-c.,  series 

6.6 

325 

2,920 

11.15 

•305 

Tungsten  series 

6.6 

75 

626 

12.0 

.384 

Flame  arc,  a.-c.,  inclined  electrodes 

8.0 

374 

3.9*0 

9-55 

.405 

Inclosed  arc,  d.-c.,  series 
Luminous  arc,  d.-c.,  multiple 

6.6 
4.0 

475 
440 

3.315 
2,870 

14.32 
15-32 

•459 
•547 

Tungsten,  multiple 
Nernst,  a.-c.,  3-glo\ver 

0.545 
i.  87 

60 
414 

475 
2,160 

12.6 

19.2 

i 

Nernst,  d.-c.,  3-glower 

1.87 

414 

2,160 

19.2 

.90 

Inclosed  arc,  a.-c.,  series 

7-5 

480 

2,410 

19.9 

2.05 

Inclosed  arc,  a.-c.,  series 

6.6 

425 

2,020 

21.3 

2.193 

Tantalum,  d.-c.,  multiple 

— 

40 

199 

21.  1 

2.31 

Tantalum,  a.-c.,  multiple 

— 

40 

199 

21.  1 

2.504 

Carbon,  3.1  w.  p.  c.,  multiple 

— 

49.6 

1  66 

29.9 

3-24 

Carbon,  3.5  w.  p.  c.,  series 

6.6 

2IO 

626 

33-6 

3-47 

Carbon,  3.5  w.  p.  c.,  multiple 

— 

56 

1  66 

33-7 

3-5° 

Inclosed  arc,  d.-c.,  multiple 

5-° 

55° 

i»535 

35-8 

3.66 

Inclosed  arc,  d.-c.,  multiple 

3-5 

385 

1,030 

37-4 

3-84 

Inclosed  arc,  a.-c.,  multiple 

6.0 

430 

1,124 

38.3 

3-94 

Inclosed  arc,  a.-c.,  multiple 

4.0 

285 

688 

41.4 

4.265 

Ives,  Phys.  Rev.,  V,  p.  390,  1915 
(see  also  VI,  p.  332,  19*5);  computed 
assuming  z  lumen  =  0.00159  watt. 

Commercial  Rating 

Lumens 
per 
Watt. 

Luminous 
Watts  Flux 
-f-  Watts  In- 
put or  True 
Efficiency. 

Open  flame  gas  burner 

Bray  6'  high  pressure 

0.22 

O.OOO35 

Petroleum  lamp 

.26 

.OOO4 

Acetylene 

i.o  liters  per  hour 

.67 

.0011 

Incandescent  gas  (low  pressure) 

.350  lumens  per  B.  t.  u.  per  hr. 

1.2 

.0019 

Incandescent  gas  (high  pressure) 

.578  lumens  per  B.  t.  u.  per  hr. 

2.0 

.0031 

Nernst  lamp 

4.8 

.0076 

Moore  nitrogen  vacuum  tube 
Carbon  incandescent  (treated  filament) 

22O-v.  oo-cycle,  113  ft. 
4-watts  per  mean  hor.  C.  P. 

5.21 

2.6 

.0083 
.0041 

Tungsten  incandescent  (vacuum) 

1.25  watts  per  hor.  C.  P. 

8. 

.013 

Carbon  arc,  open  arc 

9.6  amp.  clear  globe 

1  1.8 

.019 

Mazda,  type  C 

5oo-watt  multiple  .7  w.  p.  c. 

jr. 

.024 

Mazda,  type  C 

600  C.  P.  -20  amp.  .5  w.  p.  c. 

19.6 

.031 

Magnetite  arc,  series 

6.6  amp.  direct  current 

21.6 

•034 

Glass  mercury  arc 

40-70  volt;  3.5  amperes 

23. 

.036 

Quartz  mercury  arc 
Enclosed  white  flame  carbon  arc 

174-197  volt  ;  4.2  amperes 
10  ampere,  A.  C. 

267 

.067 
.042 

"         " 

6.5  ampere,  D.  C. 

35-5 

•057 

Open  arc               "      inclined 

10  ampere,  A.  C. 

29. 

.046 

Enclosed  ye  low  flame  carbon  arc 

10  ampere,  D.  C. 
10  ampere,  A.  C. 

27.7 
3M 

.044 
•050 

«                              t                         <(                       l<                   U 

6.5  ampere,  D.  C. 

34-2 

•°54 

Open  arc,                 "      ,  inclined 

10  ampere,  A.  C. 

.066 

10  ampere,  D.  C. 

44-7 

.071 

TABLES  307-309. 

PHOTOGRAPHIC   DATA. 

TABLE  307.  —  Numerical  Constants  Characteristic  of  Photographic  Plates. 


263 


Abscissae  of  figure  are  log  E  =  leg  //  (meter- 
candles-seconds); 

Ordinates  are  densities,  D  =  i/T  ; 

E  —  exposure  =  /  (illumination  in  meter-can- 
dles) X  t  seconds; 

D,  the  density  of  deposit  =  i/T,  where  T  is  the 
ratio  of  the  transmitted  to  incident  intensity  on  de- 
veloped plate. 

*  =  inertia  =  intercept  straight  line  portion  of 
curve  on  log  E  axis. 

S  =  speed  =  (some  constant)/ i;  y  —  gamma  = 
tangent  of  angle  a. 

L  =  latitude  =  projected  straight  line  portion  of 
characteristic  curve  on  log  E  axis,  expressed  in  ex- 
posure units  =  Anti  log  (b  —  a). 

The  curve  illustrates  the  characteristic  curve  of  a 
photographic  plate. 


2B- 
24 

X 

^. 

?n 

/ 

16 

/ 

1  ? 

/ 

b 

Q 

t- 

2 

-L- 

--- 

-*l 

4 

i 

i 

J7 

\ 
°^ 

0^" 

ty 

a 

-*- 

\ 
\ 

.    4 

>• 

u    0. 

6     0 

b     0 

9      1 

2      1 

i>     1 

a   2 

1     2 

4    2 

8    30 

TYPICAL  CHARACTERISTIC  CURVE  otf  PHOTOGRAPHIC  PLATE. 


TABLE  308.  —  Relative  Speeds  of  Photographic  Materials. 

The  approximate  exposure  may  be  obtained  when  the  intensity  of  the  image  on  the  plate  is  known.  Let  L  be  the 
intensity  in  meter-candles;  E,  the  exposure  in  seconds;  P,  the  speed  number  from  the  following  table;  then  E  = 
i,35o,ooo/(L  X  P)  approximately. 


Plate. 

Relative 
speed  . 

Paper. 

Relative 
speed. 

Extremely  high  speed  

100  ooo 

High  speed  

75,000 

Slow  enlarging 

Medium  speed  

60  ooo 

Rapid  high  contrast  

6  < 

Medium  speed  high  contrast 

Process,  slow  contrast  

10,000 

Rapid  gas-light  contrasty 

Lantern  plate  

3,000 

Professiona  

i  25 

TABLE  309.  —  Variation  of  Resolving  Power  with  Plate  and  Developer. 

The  resolving  power  is  expressed  as  the  number  of  lines  per  millimeter  which  is  just  resolvable,  the  lines  being 
opaque  and  separated  by  spaces  of  the  same  width.  The  developer  used  for  the  comparison  of  plates  was  Pyro-soda; 
the  plate  for  the  comparison  of  developers,  Seed  Lantern.  The  numbers  are  all  in  the  same  units.  Huse,  J.  Opt.  Soc. 
America,  July,  1917. 


Plate. 

Albumen. 

Resolution. 

Process. 

Lantern  . 

Medium 

High  speed. 

speed. 

Resolving  power  

125 

81 

67 

62 

35 

27 

Developer  . 

Resolving 
power. 

Developer. 

Resolving 
power. 

Developer. 

Resolving 
power. 

Pyro-caustic  

77 

Pyrocatechin  

62 

Amidol    

51 

Glycin 

00 

Pyro-metol  

62 

Process  hydroquinone.  . 

5° 

64 

Eikon.-hydroquinone 

61 

Ortol 

49 

Pyro 

64 

61 

Rodinal 

49 

MQ25 

64 

Caustic  hydroquinone.  . 

57 

X-ray  powders.  .  . 

49 

Metol 

6l 

Eikonogen 

57 

Edinol  

47 

Nepera  

62 

Kachin  

54 

SMITHSONIAN   TABLES. 


264 


TABLES  310-311. 

PHOTOGRAPHIC   DATA- 

TABLE  310.  —  Photographic  Efficiencies  of  Various  Lights. 


Source. 

Visual 
efficiency. 
Lumens 
per 
watt. 

Photographic  efficiency. 

(a) 

(b) 

Ordinary 
plate. 

Ortho- 
chromatic 
plate. 

Pan- 
chromatic 
plate. 

Ordinary 
plate. 

Ortho- 
chromatic 
plate. 

Pan- 
chromatic 
plate. 

Sun 

150 

0.7 
0.07 
0.045 
40 
35 
37 

12 
29 

9 
12 

18 

•1 

,n 

21.6 

8.9 
ii 
23 

100 

181 

8 

18 
600 
218 

324 
126 
257 

% 

106 
23 
25 
33 
37 
56 
64 

1  08 
316 

IOO 

155 

£ 

28 
500 
195 
275 

112 

234 
177 
1070 
"5 
32 
35 
41 
45 
62 
68 

99 
354 

IOO 

130 

8 

£ 

165 
249 
104 
"5 
165 
744 
82 
42 
45 
50 
53 
7° 
76 

106 

273 

IOO 

0.14 
0.037 
0.053 
158 
50 
79 

10 

52 
ii 
62 

12 

0.37 
o.Sl 
1.74 
2.41 
6.1 
8.9 

1:1 

47 

IOO 

0.21 
O.O4O 
0.086 
I32 
46 

68 
10 
45 
II 
86 
14 
0.52 
0.74 

2.2 

3-0 
6.8 
9.8 

5-2 

7-3 
54-2 

IOO 

0.24 
0.042 
0.13 
99 
39 
62 
8.5 

2.O 
IO 
60 
10 

0.68 
0-95 

2.7 
3-5 
7-7 

II.  0 

5-6 
7-9 

42 

Sky 

Acetylene 

(screened) 

Pentane.  .  .  . 

Mercury  arc,  quartz  

"Nultra"  glass  
"    crown  glass. 

Carbon  arc  ordinary 

"    white  name  
"    enclosed  
Carbon  arc,  "  Artisto  "  

Magnetite  arc.  .   . 

Carbon  glow-lamp 

Carbon  glow-lamp  

Tungsten  vacuum  lamp 

vacuum  lamp  

nitrogen  lamp  
nitrogen  lamp  
"         blue  bulb  
blue  bulb.  . 

Mercury  arc  (Cooper  Hewitt)..    . 

(a)  Relative  efficiencies  based  on  equal  illumination. 
(b)  Relative  efficiencies  based  on  equal  energy  density. 
Taken  from  Jones,  Hodgson,  Huse,  Tr.  111.  Eng.  Soc.  10,  p.  963,  1915. 

TABLE  311.  —  Relative  Intensification  of  Various  Intensifies. 


Bleaching  solution. 

Blackening  solution. 

Reference 

Intensi- 
fication. 

Mercuric  bromide 

Amidol  developer 
Ammonia 

Amidol  developer 
Schlippe's  salt 
Sodium  sulphide 

Sodium  stannate 
Sodium  stannate 

Sodium  sulphide 
Paraminophenol  developer 

HgBr2  solution  (Monckhoven 
sol.  A).* 
Bleach    according     to     Ben- 
nett; blackener.* 

Piper.* 
Debenham,  B.  J.,  f  p.  186,  '17. 
B.  J.  Almanac.* 
B.  J.  Almanac.* 

Desalme,  B.  J.,t  p.  215,  '12. 

Ordinary  sepia  developer. 
Hgl2  according  to  Bennett. 

i.  IS 
i.  IS 

1-45 
2.50 
2.28 
3-50 

2.05 
1-93 

1-33 
1-23 

Mercuric  chloride  .  .  . 

Potassium    bichromate  -f-  hydro- 
chloric acid  . 

Mercuric  iodide  

Lead  ferricyanide  

Uranium  formula  
Potassium     permanganate  +  hydro- 
chloric acid  

Cupric  chloride  
Potassium  ferricyanide  +  potassium 
bromide  
Mercuric  iodide  

See  Nietz  and  Huse,  J.  Franklin  Inst.  March  3   1918. 
'  B.  J.  Almanac,  see  annual  Almanac  of  British  Journal  of  Photography 
t  B.  J.  refers  to  British  Journal  of  Photography. 


SMITHSONIAN  TABLES. 


TABLE  312. 
WAVE-LENGTHS    OF    FRAUNHOFER    LINES. 


265 


For  convenience  of  reference  the  values  of  the  wave-lengths  corresponding  to  the  Fraunhofer 
lines  usually  designated  by  the  letters  in  the  column  headed  "  index  letters,"  are  here  tabulated 
separately.  The  values  are  in  ten  millionths  of  a  millimeter,  on  the  supposition  that  the  D  line 
value  is  5896.155.  The  table  is  for  the  most  part  taken  from  Rowland's  table  of  standard  wave- 
lengths. 


Index  Letter. 

Line  due  to  — 

Wave-length  in 
centimeters  X  io». 

Index  Letter. 

Line  due  to— 

Wave-length  in 
centimeters  X  io». 

A 

!o° 

7621.28* 
7594.06* 

G 

!cF: 

4308.081 
4307-907 

a 

- 

7164.725 

g 

Ca 

4226.904 

B 

o 

6870.  182  t 

h  or  Hg 

H 

4102.000 

C  or  Ha 

H 

6563.045 

H 

Ca 

3968.625 

a 

O 

6278.303  f 

K 

Ca 

3933-825 

Di 

Na 

5896.155 

L 

Fe 

3820.586 

D2 

Na 

5890.186 

M 

Fe 

3727.778 

D8 

He 

5875.985 

N 

Fe 

3581.349 

Ei 

I" 

5270.438 

0 
P 

Fe 
Fe 

344LI55 
3361.327 

E2 

Fe 

5269.723 

Q 

Fe 

3286.898 

bi 

Mg 
Mg 

5183.791 
5172.856 

R 

!" 

3181.387 

3'79-453 

bg 

£ 

iFe 

5169.220 
5169.069 
5167.678 

Si) 

sj 

Fe 
Fe 
Fe 

3100.787 
3100.430 
3100.046 

(Mg 

5  i  67.  497 

s 

Fe 

3047-725 

F  or  Hp 

H 

4861.527 

T 

Fe 

3020.76 

d 

Fe 

4383-721 

t 

Fe 

2994-53 

G'  or  Hy 

H 

4340.634 

U 

Fe 

2947.99 

f 

Fe 

4325-939 

*  The  two  lines  here  given  for  A  are  stated  by  Rowland  to  be:  the  first,  a  line  "  beginning  at  the 
head  of  A,  outside  edge";  the  second,  a  "single  line  beginning  at  the  tail  of  A." 

t  The  principal  line  in  the  head  of  B. 

$  Chief  line  in  the  a  group. 

See  Table  321,  Rowland's  Solar  Wave-lengths  (foot  of  page)  for  correction  to  reduce  these  values 
to  standard  system  of  wave-lengths,  Table  314. 


SMITHSONIAN  TABLCB. 


266  TABLES  313-316. 

STANDARD  WAVE-LENGTHS. 

TABLE  313.— Absolute  Wave-length  *  of  Red  Cadmium  Line  in  Air,  760  mm.     Pressure,   15*    C. 

6438.4722     Michelson,  Travaux  et  Mem.  du  Bur.  intern,  des  Poids  et  Mesures,  1 1,  1895. 
6438.4700    Michelson,  corrected  by  Benoit,  Fabry,  Perot,  C.  R.  144,  1082,  1907. 
6438.4696    (accepted  primary  standard)  Benoit,  Fabry,  Perot,  C.  R.  144,  1082,  1907. 

*  ID  Angstroms.     10  Angstroms  =  i  MM  =  io~*  mm. 

TABLE  314.— International  Secondary  Standards.     Iron  Arc  Lines  in  Angstrdms, 

Adopted  as  secondary  standards  at  the  International  Union  for  Cooperation  in  Solar  Research 
(transactions,  1910).  Means  of  measures  of  Fabry-Buisson  (i),  Pfund  (2),  and  Eversheim  (3).  Re- 
ferred to  primary  standard  =  Cd.  line,  A.  =  6438.4696  Angstroms  (serving  to  define  an  Angstrom). 
76o  mm.,  I5°C.  Iron  rods,  7  mm.  diam.  length  of  arc,  6  mm.;  6  amp.  for  \  greater  than  4000 
Angstroms,  4  amp.  for  lesser  wave-lengths ;  continuous  current,  -{-  pole  above  the  — ,  220  volts ; 
source  of  light,  2  mm.  at  arc's  center.  Lines  adopted  in  1910. 


Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

4282.408 

4547.853 

4789.657 

5083.344 

5405.780 

5615.661 

6230.734 

4315.089 
4375-934 

4592.658 
4602.947 

4878.225 
4903-325 

5110.415 
5167.492 

5434.527 
5455-614 

5658.836 
5763.013 

6265.145 
6318.028 

4427.314 
4466.556 

4647-439 
4691.417 

4919.007 
5OOI.88I 

5192.363 
5232-957 

5497-522 
5506.784 

6027.059 
6065.492 

6335-34I 
6393.612 

4494-572 
453I-I55 

4707.288 
4736.786 

5012.073 
5049.827 

5266.569 
5371-495 

5569-633 
5586.772 

6137.701 
6191.568 

6430.859 
6494.993 

TABLE  315. — International  Secondary  Standards.     Iron  Arc  Lines  in  Angstroms. 
Adopted  in  1913.    (4)  Means  of  measures  of  Fabry-Buisson,  Pfund,  Burns  and  Eversheim. 


Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

3370.789 

3399-337 

3606.682 
3640.392 

3753.615 
3805.346 

3906.482 
3907.937 

4076.642 
4118.552 

4233-6I5 
5709.396 

6750.250 
58577  59  Ni 

3485-345 
35I3-82i 

3676.313 
3677.629 

3843.261 
3850.820 

3935.818 
3977746 

4134.685 
4147.676 

6546.250 
6592.928 

5892.882  Ni 

3556.881 

3724.380 

3865.527 

4021.872 

4191.443 

6678.004 

(i)  Astrophysical  Journal,  28,  p.  169,  1908;  (2)  Ditto,  28,  p.  197,  1908;  (3)  Annalen  der  Physik,  30, 
p.  815, 1909.  See  also  Eversheim,  ibid.  36,  p,  1071,  1911 ;  Buisson  et  Fabry,  ibid,  38,  p.  245,  1912 ; 
(4)  Astrophysical  Journal,  39,  p,  93,  1914, 


TABLE  316. — Neon  "Wave-Lengths. 


In- 
tensity. 

Wave 
length. 

In- 
tensity. 

Wave 
length. 

In- 
tensity. 

Wave 
length. 

In- 
tensity. 

Wave 

length. 

In- 
tensity. 

Wave 
length. 

5 

3369.004 

5 

3515.192 

2 

5820.155 

4 

6217.280 

5 

6717.043 

6       34I/.906 

8 

3520.474 

10 

5852.488 

7 

6266.495 

8 

6929  .  468 

6       3447.705 

4 

3593-526 

6 

5881.895 

4 

6304.789 

3 

7024.049 

6       3454.197 

4 

3593.634 

8 

5944-834 

8 

6334.428 

9 

7032.413 

5 

3400.526 

5 

3000.170 

4 

5975-534 

8 

6382.991 

3 

7059.III 

4 
5 

3464.340 
3466.581 

5 
8 

3633.664 
5330.779 

4 

7 

6029.997 
6374.338 

10 
9 

6402.245 
6506.528 

5 
8 

7I73.939 
7245.167 

6      3472.578 

7 

534L096 

g 

6096.163 

4 

6532.883 

6 

7438.902 

4    |  3498.067        6       5400.562 

9 

6143.062 

5 

6598.953 

5 

7488.885 

4 

3501.218          4        5764.419 

5 

6163.594 

8 

6678.276 

5 

7535.784 

International  Units  (Angstroms).     Burns,  Meggers,  Merrill,  Bull.  Bur.  Stds.  14,  765,  1918. 
SMITHSONIAN  TABLES. 


TABLE  317. 
TERTIARY  STANDARD  WAVE-LENGTHS.     IRON  ARC  LINES. 

For  arc  conditions  see  Table  314,  p.  266.  For  lines  of  group  c  class  5  for  best 
results  the  slit  should  be  at  right  angles  to  the  arc  at  its  middle  point  and  the  current 
should  be  reversed  several  times  during  the  exposure. 


Wave-lengths. 

Class. 

Inten- 
sity. 

Wave-lengths. 

Class. 

Inten- 
sity. 

Wave-lengths. 

Class. 

Inten-   ! 
sity. 

#2781.840 

4 

4337-052 

b3 

5 

5332.909 

M 

2 

#2806.985 

7 

4369-777 

b3 

3 

534L032 

34 

5 

*283I-559 

3 

4415.128 

bi 

8r 

5365.404 

ai 

2 

#2858.341 

3 

4443.198 

b3 

3 

5405.780 

a 

6 

#2901.382 

4 

4461.658 

a3 

4 

5434.528 

a 

6 

#2926.584 

5 

4489.746 

*3 

3 

5473-9I3 

a 

4 

#2986.460 
#3000.453 

3 
4 

4528.620 
4619.297 

C4 

7 
4 

5497-52  ! 
5501.471 

a 
a 

4 
4 

4 

4786.811 

C4 

3 

5506.784 

a 

3 

#3100.838 

2 

487i-33i 

C5 

8 

J5535-4I9 

a 

2 

#3154.202 

4 

4890.769 

C5 

7 

5563.612 

b 

3 

#3217.389 

A.               "        >? 

4 
4 

4924.773 
4939-685 

a 
a 

3 
3 

5975-352 
6027.059 

b 
b 

2 

3 

#3307.238 
*3347-932 

4 
4 

4973-  "3 
4994.133 

a 
a 

2 

3 

6065.495 
6136.624 

b 

b 

4 

5 

#3389.748 

3 

5041.076 

a 

3 

6I57-734 

b 

4 

#3476.705 

5 

5041.760 

a 

4 

6165.370 

b 

3 

#3506.502 
*3553-74i 

5 

5051.641 
5079.227 

a 
a 

4 
3 

6I73-345 
6200.323 

b 
b 

4 
4 

#3617.789 

6 

5079-743 

a 

3 

6213.44! 

b 

5 

#3659.521 

5 

5098.702 

a 

4 

6219.290 

b 

#3705.567 

6R  j 

5I23-729 

a 

4 

6252.567       ,    b 

6 

#3749.487 

8R 

5127.366 

a 

3 

6254.269           b 

4 

#3820.430 

8R 

5150.846 

a 

4 

6265.145 

b 

5 

*3859-9*3 

7R 

5151.917 

a 

3 

6297.802 

b 

4 

#3922.917 

6R  l 

5194.950 

a 

5 

6335-342 

b 

6 

#3956-682 

6 

5202.341 

a 

5 

6430.859 

b 

5 

#4009.718 

5 

5216.279 

a 

6494.992 

b 

6 

#4062.451 

4     • 

5227.191 

a4 

8 

14132.063 

bi 

7 

5242.495 

a 

3 

t4  1  7  5-639 

b 

4 

5270.356 

34 

8 

14202.031 

bi 

7r 

5328-043 

ai 

7 

14250.791 

7 

S328-  537 

34 

4 

*  Measures  of  Burns.  f  Means  of  St.  John  and  Burns. 

t  Means  of  St.  John  and  Goos.  Others  are  means  of  measures  by  all  three.  References  :  St.  John  and  Ware, 
Astrophysical  Journal,  36,  1912;  38,  1913;  Burns,  Z.  f.  wissen.  Photogj.  12,  p.  207,  1913,  J.  de  Phys.  1913,  and  unpub- 
lished data;  Goos,  Astrophysical  Journal,  35,  1912;  37,  1913.  The  lines  in  the  table  have  been  selected  from  the 
many  given  in  these  references  with  a  view  to  equal  distribution  and  where  possible  of  classes  a  and  b. 

For  class  and  pressure  shifts  see  Gale  and  Adams,  Astrophysical  Journal,  35,  p.  10,  1912. 
Class  a:  "This  involves  the  well-known  flame  lines  (de  Watteville,  Phil.  Trans.  A  204,  p.  139. 
1904),  i.e.  the  lines  relatively  strengthened  in  low-temperature  sources,  such  as  the  flame  of  the  arc, 
the  low-current  arc,  and  the  electric  furnace.  (Astrophysical  Journal,  24,  p.  185,  1906,  30,  p.  86, 
1909,  34,  p.  37,  1911,  35,  p.  185,  1912.)  The  lines  of  this  group  in  the  yellow-green  show  small  but 
definite  pressure  displacements,  the  mean  being  0.0036  Angstrom  per  atmosphere  in  the  arc." 
Class  b:  "To  this  group  many  lines  belong;  in  fact  all  the  lines  of  moderate  displacement  under 
pressure  are  assigned  to  it  for  the  present.  These  are  bright  and  symmetrically  widened  under 
pressure,  and  show  mean  pressure  displacements  of  0.009  Angstrom  per  atmosphere  for  the  lines 
in  the  region  \  5975-6678  according  to  Gale  and  Adams.  Group  c  contains  lines  showing  much 
larger  displacements.  The  numbers  in  the  class  column  have  the  following  meaning :  I,  synv 
metrically  reversed  ;  2,  unsymmetrically  reversed  ;  3,  remain  bright  and  fairly  narrow  under  pres- 
sure ;  4,  remain  bright  and  symmetrical  under  pressure  but  become  wide  and  diffuse  ;  5,  remain 
bright  and  are  widened  very  unsymmetrically  toward  the  red  under  pressure." 

For  further  measures  in  International  units  see  Kayser,  Bericht  iiber  den  gegenwartigen 
Stand  der  Wellenlangenmessungen,  International  Union  for  Cooperation  in  Solar  Research,  1913. 
For  further  spectroscopic  data  see  Kayser's  Handbuch  der  Spectroscopie. 

SMITHSONIAN   TABLES, 


268  TABLE  318. 

REDUCTION   OF  WAVE-LENGTH   MEASURES  TO  STANDARD  CONDITIONS- 

The  international  wave-length  standards  are  measured  in  dry  air  at  15°  C,  76  cm  pressure.  Density  variations  of 
the  air  appreciably  affect  the  absolute  wave-lengths  when  obtained  at  other  temperatures  and  pressures.  The  follow- 
ing tables  give  the  corrections  for  reducing  measures  to  standard  conditions,  viz.:  o  =  Xo(no  —  no')  (d  —  do)/do  in 
ten-thousandths  of  an  Angstrom,  when  the  temperature  t°  C,  the  pressure  B  in  cm  of  Hg,  and  the  wave-length  X  in 
Angstroms  are  given;  n  and  d  are  the  indices  of  refraction  and  densities,  respectively;  the  subscript  o  refers  to  standard 
conditions,  none,  to  the  observed;  the  prime  '  to  the  standard  wave-length,  none,  to  the  new  wave-length.  The  tables 
were  constructed  for  the  correction  of  wave-length  measures  in  terms  of  the  fundamental  standard  6438.4696  A  of  the 
cadmium  red  radiation  in  dry  air,  15°  C,  76  cm  pressure.  The  density  factor  is,  therefore,  zero  for  15°  C  and 
76  cm,  and  the  correction  always  zero  for  A  =  6438  A.  As  an  example,  find  the  correction  required  for  X  when  meas- 
ured as  3000.0000  A  in  air  at  25°  C  and  72  cm.  Section  (a)  of  table  gives  (d  —  do)/do  =  —.085  and  for  this  value  of 
the  density  factor  section  (b)  gives  the  correction  to  X  of  —.0038  A.  Again,  if  X,  under  the  same  atmospheric  condi- 
tions, is  measured  as  8000.0000  A  in  terms  of  a  standard  X'  of  wave-length  4000.000  A,  say,  the  measurement  will 
reauire  a  correction  of  (0.0020  +  0.0008)  =  +.0028  A.  Taken  from  Meggers  and  Peters,  Bulletin  Bureau  of  Stand- 
ards, 14,  p.  728,  1918. 


TABLE  318  (a).  — 1000  X  (d-do)/do. 


Bern 

60.0 

62.S 

65.0 

67.5 

70 

71 

72 

73 

74 

75 

76 

77 

78 

9°C 

—  192 

-160 

-126 

-92 

-59 

-46 

-32 

-19 

-s 

+8 

+  22 

+35 

+48 

n 

—  200 

-167 

—  133 

—  100 

-67 

-53 

-40 

-27 

-13 

0 

+  13 

+27 

+40 

13 

-206 

—172 

-139 

-106 

-73 

-60 

-46 

-33 

—  20 

—  7 

+6 

+  20 

+33 

IS 

—  211 

-178 

—  145 

—  112 

-79 

-66 

-S3 

-39 

-26 

-13 

0 

+13 

+26 

17 

-216 

-184 

-ISI 

-118 

-86 

-73 

-60 

-47 

—34 

—  21 

-8 

+5 

+19  i 

19 

—  222 

-189 

-156 

-124 

-92 

-79 

-66 

-53 

-40 

—  27 

-14 

-j 

+12 

21 

—  227 

-iQS 

-I63 

-130 

-98 

-85 

-72 

-59 

-46 

-33 

—  21 

-8 

+5 

23 

—  232 

—  200 

-168 

-136 

—  104 

—91 

-78 

-65 

—52 

—40 

—  27 

-14 

—  I 

25 

-238 

-206 

-174 

-143 

—  in 

-98 

-85 

-72 

-60 

-47 

-34 

—  22 

-9 

27 

-243 

—  211 

-179 

-148 

-116 

—104 

-91 

-78 

-66 

—  53 

—40 

-28 

-15 

2Q 

-248 

-216 

-185 

-154 

—  122 

-109 

—97 

-84 

—  72 

—  59 

-46 

-34 

—  21 

31 

-253 

—  222 

-100 

-159 

-128 

-116 

-103 

-91 

-78 

-66 

-54 

—41 

-29 

33 

-258 

-227 

-196 

.-165 

-134 

—  121 

-109 

-97 

-84 

-72 

-59 

—47 

—34 

35 

-262 

—  231 

—  200 

—  170 

—  139 

—  127 

—114 

—  IO2 

—90 

—  77 

-65 

—  53 

—  41 

TABLE  318  (b).  —  8  =  Xo(no-no')(d-do)/c?o,  in  Ten-thousandth  Angstroms. 


Wave-lengths  in  Angstroms. 

iooo  X 

d  -do 

2000 

2500 

3000 

3500 

4000 

4500 

5000 

SSoo 

6000 

6500 

7000 

7500 

8000 

9000 

1  0000 

do 

Corrections  in  ten-thousandth  Angstroms. 

-260 

-259 

-166     -116     -8 

4     —  61      —44     —30     —  18     —8 

+1 

+Q 

+17 

+  24 

+37 

+50 

-240 

-239 

—154 

\.     -io 

7      -7 

8      -S 

7      -4 

c      -25 

5      -17 

—  7 

+1 

+9 

+16 

+  22 

+35 

+46 

—  220 

-219 

-141 

-9 

8      -7 

i      —5 

2      —3' 

-2t 

—  IS 

+1 

+8 

+14 

+  20 

+42 

—  200 

-199 

-128        -89      -65      -47      -34      -23      -14 

-6 

+1 

+7 

+13 

+19 

+29 

+38 

-180 

-179 

—  115        —80      —58      —42      —30     —21 

-13 

-6 

+1 

+6 

+  12 

+17 

+26 

+34 

—  160 

-159 

—  10 

!        -7 

i      -S 

2      -3 

i        -2 

7    —ic 

—  ii 

—5 

+1 

+6 

+  10 

+15 

+  23 

+31 

-140 

—  120 

-139 
-119 

—90        —62      —45      —3 
—  77        —54      —39      —2 

3      —24      —  16     —io 
3     —20     —14      —8 

—4 

—4 

±0 

C 

+9 
+8 

+13 
+n 

+  20 

+17 

+27 
+23 

—  100 

—  100 

—64        —45      —32      —24      —17      —12       —7 

—3 

+0 

+4 

+7 

+9 

+14 

+19 

-80 

-80 

—  Si        —36      —26      -19      —14        —9        —6      —2 

+0 

+3 

+s 

+7 

+  12 

+  15 

-60 

-60 

-31 

I        -i 

7      —i 

9      —i 

i      —  K 

n      — 

r       —4 

—  2 

+0 

+  2 

+4 

+6 

+9 

—  40 

-40 

-26        -18      -13        -9        -7        -5        -3 

—  I 

+0 

+i 

+3 

+4 

+6 

+8 

—  CD 

—  20 

-13          -9        -6        -5        -3         -2        -i 

—  I 

0 

+i 

+1 

+  2 

+3 

+4 

0 

0 

0 

o           o           o           o           o           o 

0 

—o 

o 

0 

o 

o 

0 

+  20 

+  20 

+13          +9        +6        +S        +3        +2        +i 

+1 

—  o 

—  I 

—  2 

—  2 

—3 

—4 

+40 

+40 

+26        +18     +13        +9        +7        +5 

'      +3 

+1 

—  0 

-I 

—3 

—4 

-6 

-8 

SMITHSONIAN  TABLES. 


TABLE  319. 
SPECTRA  OF  THE  ELEMENTS- 


269 


The  following  figure  gives  graphically  the  positions  of  some  of  the  more  prominent  lines  in  the  spectra  of  some  of 
the  elements.    Flame  spectra  are  indicated  by  lines  in  the  lower  parts  of  the  panels,  arc  spectra  in  the  upper  parts,  and 


spark  spectra  by  dotted  lines. 


Na 


K 


CS] 


Rti 


T1 


In 


I          I 


Hg 


lamp 


Co 


Ni 


Cu 


vacuo  arc 


Ag 


I     I 


Zn 


M§ 


arc 


Sn 


H 


He 


•violet — X-blue*r8reen-*yellowX-,orange* red 

i    I    i    i    i    i    I    i    i    i    i    IV    i    i    i    I    I    i    i    i    I    i    i    ii    I    i    i    i    i    I    i 


The  following  wave-lengths  are  in  Angstroms. 


Na 

5889.965 

Rb 

4202 

Cu 

4023 

Mg 

5168 

5895.932 

4216 

4063 

5173 

K 

4044 

5648 

5105.543* 

5184 

4047 

5724 

5153-251* 

5529 

5802 

6207 

5218.202* 

Sn 

4525 

7668 

6299 

5700 

5563 

7702 

Tl 

5351 

5782.090* 

5589 

Li 

4132 

In 

4102 

5782.159* 

5799 

4602 

45" 

Ag 

4055 

6453 

6104 

Hg 

4046.8 

4212 

H 

3970 

6707.846* 

4078.1 

4669 

4102 

Cs 

4555 

4358.3 

5209.081* 

4340 

4593 

4916.4 

5465.489* 

4861 

5664 

4959-7 

5472 

6563 

5945 

5460.742* 

5623 

He 

3I87.743' 

6011 

5769.598* 

Zn 

4680.  138* 

3888.646' 

6213 

5790.659* 

4722.164* 

4026.189' 

6724 

6152 

4810.535* 

4471.477' 

6974 

6232 

4912 

47x4.1431 

4925 

4921.929- 

6103 

5015.675" 

For  other  elements,  see  Kayser's  Handbuch  der 
Spectroscopie. 
*  Fabry  and  Perot.        t  Merrill. 

6362.345* 

5875-  6i8f 
6678.  I49t 
7065.  i  88f 

SMITHSONIAN  TABLES. 


270 


TABLE  320. 
SPECTRUM    LINES   OF  THE   ELEMENTS- 

Table  of  brighter  lines  only  abridged  from  more  extensive  table  compiled  from  Kayser  and  containing  10,000  lines 
(Kayser's  Handbuch  der  Spectroscopie,  Vol.  6,  1912). 


Wave- 
lengths, 
inter- 

Ele- 

Intensities. 

Wave- 
lengths, 
inter- 

Ele- 

Intensities. 

Wave- 
lengths, 
inter- 

Ele- 

Intensities 

national 

ment. 

national 

ment. 

national 

ment. 

Ang- 
stroms. 

Arc. 

Spark. 

Tube. 

Ang- 
stroms. 

Arc. 

Spark 

Tube. 

Ang- 
stroms. 

Arc. 

Spark. 

Tube. 

3802.98 

Nb 

15 

4 

_ 

3968.48 

Ca 

30 

40 

_ 

4116.50 

V 

IS 

S 

_ 

08.21 

I 

10 

72.01 

Eu 

20 

20 

— 

18.48 

Pr 

IS 

10 

— 

10.73 

Nh 

10 

20 

— 

74-71 

Er 

IS 

5 

— 

23.24 

La 

10 

IS 

— 

14-45 

Ra 

20 

2O 

— 

76.85 

Tb 

20 

IO 

— 

z8.  3 

Y 

IS 

8 

— 

Eu 

20 

2O 



80.43 

Br 

,^_ 



10 

28.70 

I 

L- 

10 

22.15 

Rh 

12 

15 



81.68 

Em 



— 

15 

28.91 

Rh 

15 

10 

28.47 

Rh 

12 

IO 

— 

81.89 

Tb 

IS 

10 

29-75 

Eu 

So 

So 

— 

29-35 

Mg 

IS 

8 

— 

82.60 

Y 

12 

12 

— 

30.42 

Gd 

IS 

10 

— 

32.30 

Mg 

2O 

IO 

— 

88.00 

Ny 

50 

2O 

— 

35-29 

Rh 

12 

10 

— 

36-83 

Zr 



15 

_ 

88.52 

La 

10 

IS 

— 

35-80 

Os 

IS 

S 

— 

38.29 

S 



8 

10 

91.13 

Zr 

8 

12 

— 

37-13 

Nb 

12 

4 

— 

38.29 

Mg 

2O 

10 

98.96 

Zr 

8 

12 

— 

39-74 

Nb 

IS 

4 

— 

45-45 
47.98 

Co 
Tm 

10 

IS 

IS 

10 

— 

4000.47 
05-50 

Tb 

15 
15 

12 
IO 

~ 

42.86 
43-14 

Y 
Pr 

IS 

15 

8 

10, 

~ 

48-75 

Tb 

IS 

IS 

— 

05-73 

V 

20 

— 

45-12 

S 

IO 

51.02 

Cl 

10 

08.73 

Pr 

12 

8 

— 

49-20 

Zr 

10 

15 



56.50 

Rh 

IO 

12 

19.62 

Pb 

12 

10 

— 

51-12 

Er 

15 

4 

— 

58.29 

Ni 

20 

8 

— 

22.70 

Cu 

IS 

10 

— 

52.63 

Nb 

IS 

5 

— 

60.86 

Cl 



S 

10 

23-35 

V 

20 

— 

53-11 

S 

IO 

64.11 

Mo 

20 

IO 

— 

23-71 

Se 

12 

8 

— 

58.62 

A 

— 

— 

IO 

71-65 

La 

8 

15 

— 

25.1 

F 



— 

10 

61.83 

Ar 

10 

20 



73-07 

Co 

10 

12 

— 

30.80 

Mn 

18 

8 

62.  70 

S 

10 

74.16 

Tb 

15 

IS 

— 

31.70 

La   - 

8 

IS 

— 

63.64 

Nb 

IS 

10 

— 

76.66 

Lu 

IS 

10 

— 

33-03 

Ga 

IO 

30 

— 

64.66 

Nb 

12 

5 

— 

88.64 

He 

_ 

10 

33.06 

Mn 

15 

8 

— 

66.43 

Em 



20 

88.96 

Nh 

IS 

10 

— 

34-48 

Mn 

IS 

8 

— 

68.14 

Nb 

15 

S 

91.01 

Nh 

20 

15 

— 

35-62 

V 

20 

— 

69.0 

Se 

10 

10 

94-09 

Co 

IO 

IS 

— 

41-43 

Mn 

12 

8 

— 

72.05 

Ga 

IS 

20 

— 

94-22 

Pd 

IS 

15 

— 

42-92 

La 

8 

15 

— 

77-53 

Y 

12 

20 

— 

96.36 

Er 

IS 

6 

— 

44-iS 

K 

20 

10 

— 

79.04 

Ge 

— 

20 

— 

97.63 

I 

— 

— 

10 

45-45 

Nh 

20 

10 

— 

79-43 

Pr 

15 

10 

— 

3900.53 

Ti 

15 

10 

— 

45.82 

Fe 

6 

15- 

— 

80.04 

X 



20 

02.95 

Mo 

IS 

8 

— 

46.00 

Dy 

12 

4 

— 

84.25 

Lu 

20 

15 



05.5 

Si 

IS 

4 

— 

46.6 

Se 



4 

10 

89.52 

Pr 

IS 

10 



06.34 

Er 

IS 

10 

— 

17.21 

K 

20 

10 

— 

90.91 

Nb 

IS 

9 



07.14 

Eu 

30 

20 

— 

48.73 

Mn 

II 

6 

— 

4200.65 

A 

10 

07.52 

Sc 

12 

6 

— 

55-53 

Ag 

50 

6 

— 

01.82 

Rb 

20 

IS 

— 

11.85 

Sc 

IS 

6 



57-84 

Pb 

30 

20 

—  . 

03-23 

Em 



10 

14.26 

Br 

— 

10 

58-97 

Nb 

IS 

10 

— 

05.04 

Eu 

50 

30 

— 

14.94 
22.52 

Sc 
X 

12 

__ 

10 

62.75 
62.83 

Cu 
Pr 

IS 

12 

IO 

8 

~ 

05-32 
06.72 

Nb 
Pr 

IS 
15 

4 

12 

— 

25-43 

Tb 

IS 

10 

— 

63-47 

Gd 

20 

— 

08.96 

Zr 

0 

12 

— 

30.51 

Eu 

So 

So 

— 

77-3/4 

La 

IO 

12 

— 

11.14 

Rh 

15 

IO 

— 

31.  10 

33.67 

I 
Ca 

40 

So 

10 

77-37 
77-75 

Y 

Sr 

IS 

So 

S 

50 

— 

11.69 
14-74 

Dy 
Nb 

12 
12 

S 

- 

39-55 

Tb 

IS 

10 

— 

77-97 

Dy 

12 

II 

— 

IS-S2 

Sr 

30 

30 

— 

40.07 

I 

— 

__ 

10 

78.79 

^£ 

. 

^,_ 

10 

15.56 

Rb 

20 

10 

_  __ 

40.47 

Rb 

— 

IS 

79-73 

Nb 

IS 

6 

17-95 

Nb 

IS 

— 

44-68 

Dy 

12 

10 



80.62 

Ra 

12 

10 

_ 

21.  08 

I 

__ 

10 

45-33 

0 



— 

10 

86.70 

La 

10 

15 

— 

23.OO 

Pr 

IS 

12 

49.10 

La 

12 

20 

— 

92.68 

V 

IS 

— 

25.34 

Pr 

IS 

12 

— 

50.35 

Y 

12 

12 

— 

99-80 

V 

20 

— 

— 

26.56 

Ge 

7 

So 

— 

51.01 

X 



— 

10 

4100.74 

Pr 

IS 

12 

— 

26.72 

Ca 

20 

10 

— 

51-95 

V 



IS 

— 

00.97 

Nb 

20 

6 

— 

38.21 

X 



— 

10 

58.22 

Zr 

8 

15 

— 

01.82 

In 

20 

12 

— 

41.04 

IT 

12 

IO 

— 

58.66 

Pd 

15 

10 

— 

02.40 

Y 

12 

8 



44.34 

Rb 



15 



58.85 

Rh 

15 

12 

— 

03-4 

F 

10 

45-2 

Pb 



20 

— 

66.23 
67.59 

Nb 
X 

12 

— 

10 

09.78 
11.80 

V 
V 

IS 

20 

10 

45.38 
46.3 

X 

F 





10 

30 

3968.40 

Dy 

IS 

12 

4112-03 

Os 

12 

4 

4246.85 

Sc 

IS 

2O 

SMITHSONIAN  TABLES. 


TABLE  320  (continued). 
SPECTRUM    LINES    OF    THE    ELEMENTS- 


271 


Wave- 
lengths, 

Intensity. 

Wave- 
lengths, 

Intensity. 

Wave- 
lengths, 

Intensity. 

inter- 

Ele- 

inter- 

Ele- 

inter- 

Ele- 

national 

ment. 

national 

ment. 

national 

ment. 

Ang- 
stroms. 

Arc. 

park. 

Tube. 

Ang- 
stroms, l 

Arc 

Spark. 

Tube. 

Ang- 
stroms. 

Arc. 

park. 

'ube. 

4253-61 

54-34 

S 
Cr 

12 

12 

10 

4477-77 
81.17 

Br 
Mg 

— 

20 

10 

4994-13 
5035-36 

Lu 

Ni 

20 
12 

10 

— 

54.42 

Nh 

15 

8 



96.43 

Pr 

15 

10 

— 

53-30 

W 

12 

12 

— 

59-69 

Bi 

20 

— 

98.76 

Pt 

12 

10 

— 

5135.08 

Lu 

IS 

— 

— 

60.84 

Ob 

IS 

5 

— 

4510-15 

Pr 

12 

IO 

— 

56.  20 

Sr 

20 

— 

— 

7  "*    06 

Kr 

10 

22-59 

Eu 

20 

20 

— 

i  I.  19 

I 

— 

—  . 

10 

74.80 

Cr 

12 

10 

24.74 

Sn 

10 

20 

— 

63.78 

Pd 

IS 

— 

— 

86.97 

La 

10 

12 



54-97 

Cr 

15 



— 

72.68 

Mg 

15 

IS 

— 

4301.11 

Nb 

12 

5 

— 

55-52 

Ru 

10 

12 

— 

83.60 

Mg 

20 

20 

— 

O2.  12 

Bi 



15 



72-74 

H 





10 

64.51 

Cr 

12 

8 

— 

02.28 

Y 

12 

— 

73-09 

Nb 

12 

5 

— 

5206.05 

Cr 

12 

9 

— 

O3.6l 

Nd 

20 

10 

— 

74-26 

I 



IO 

08.42 

Cr 

12 

10 

— 

05-49 

Sr 

10 

20 

— 

85.47 

X 



— 

10 

09.08 

Ag 

30 

20 

— 

05.78 

Pr 

15 

10 

— 

89.35 

Dy 

IS 

5 

— 

24.70 

W 

12 

12 

— 

07.92 

Fe 

6 

15 

— 

94-09 

Eu 

30 

20 

— 

56.95 

Sr 

20 

6 

— 

08.  I 

Em 



10 

4603  .  03 

X 





10 

92.23 

X 



^— 

IO 

09  .  63 

Y 

12 

12 

06.77 

Nb 

12 

10 

— 

95-62 

Pd 

IS 

— 

— 

14.11 

Sc 

12 

12 

— 

07-34 

Sr 

30 

20 

— 

5330.65 

O 

— 

— 

10 

19.60 

Kr 





IO 

09.  22 

Em 



10 

32.01 

Br 

— 

— 

IO 

25-77 

25.78 

Nd 
Fe 

'i 

5 
15 

— 

24.28 
35.40 

X 

Em 

— 



IS 
15 

32.8 
35-14 

Sn 

s 

20 
2O 

— 

26.36 
30.47 

Nb 
X 

12 

15 

27.29 
27.98 

Eu 
H 

20 

IS 

IO 

50.49 
52.86 

Ny 

20 

IO 

20 

— 

33-77 

La 

12 

12 

33-86 

H 



— 

10 

60.59 

Mo 

IS 

12 

— 

40.67 

Ra 

IS 

10 

— 

34-02 

H 



— 

10 

69.85 

Se 

— 



IO 

43-  69 

Cl 

s 

10 

44-11 

Sm 



— 

15 

74-08 

Se 

-^— 

— 

IO 

48.01 

A 



IO 

46.16 

Cr 

12 

10 

95-27 

Pd 

12 

— 

— 

49-  65 

Em 





15 

48.66 

Ni 

15 

— 

— 

54I9.I9 

X 

— 

— 

IO 

55.  47 

•  Kr 





IO 

61.92 

Eu 

20 

IS 

— 

64-5 

I 

— 

— 

IO 

65.58 

Br 



4 

10 

66.65 

I 



10 

65-49 

Ag 

30 

2O 

— 

68.30 

O 



10 

71.24 

X 



— 

10 

76.69 

Lu 

20 

IO 

— 

74-51 

Sc 

10 

12 

72.12 

Nb 

12 

10 

— 

76.91 

.  Ni 

12 

IO 

— 

74.81 

Rh 

15 

12 

— 

75-36 

Nb 

12 

8 

— 

80.95 

Sr 

20 

IO 

— 

74-94 

Y 

15 

20 



80.138 

Zn 

10 

20 

.    — 

96.78 

I 



— 

IO 

79-  24 

V 

30 

30 

— 

80.74 

Em 





10 

5504-26 

Sr 

20 

— 

— 

79-77 

Zr 

IO 

12 

— 

82.18 

Ra 

20 

IS 

— 

06.51 

Mo 

20 

IS 

— 

81.66 

Mo 

12 

6 

—  . 

87.80 

Zr 

7 

12 

— 

14-71 

W 

20 

20 

— 

82.8 

Se 



8 

10 

4704-93 

Br 

— 

IS 

10 

21.80 

Sr 

20 



— 

83.55 

Fe 

10 

20 

. 

08.26 

I 

— 

10 

33-01 

Mo 

IS 

12 

— 

84.73 

V 

20 

30 

— 

14.42 

Ni 

IS 

8 

— 

42.78 

Pd 

12 



— 

86.9 

Pb 

20 

— 

22.164 

Zn 

10 

20 

— 

56.49 

Ny 

IS 



— 

89.98 

V 

2O 

20 



22.54 

Bi 

10 

2O 

— 

62.5 

Sn 

— 

30 

— 

93-17 

X 

10 

30.86 

Se 

— 



10 

70.46 

Mo 

IS 

IO 

— 

95-  24 

V 

15 

10 

— 

38.12 

Tl 

— 

IS 

— 

89.2 

Sa 

— 

2O 

— 

95-74 
98.03 

X 

Y 

10 

15 

10 

85-49 
94.48 

Br 
Cl 

~ 

10 
20 

10 
10 

5608.9 
20.64 

Pb 
As 

— 

12 

IO 

4401  .  54 

Ni 

IS 

IS 

— 

4806.68 

I 

— 



10 

25-64 

I 

— 



10 

04.75 

Fe 

8 

15 

— 

08.23 

I 

— 



10 

51-34 

As 

— 



IO 

08.50 

V 

15 

20 

— 

09-97 

Cl 

— 

9 

10 

62.93 

Y 

— 

12 

— 

08.83 

Pr 

12 

10 

__ 

10.534 

Zn 

10 

20 



70.05 

Pd 

IS 

« 

™~- 

10.09 

I 

10 

11.83 

Sr 

IS 

8 

— 

98.54 

V 

IS 

IS 

— 

11.71 

Mo 

12 

6 

19.28 

Mo 

12 

— 

— 

S75I.40 

Mo 

IS 

— 

— 

20.46 
24.36 

Os 

Sm 

IS 

2O 

IO 
10 

— 

25-93 
32.07 

Ra 

Sr 

IS 
IS 

10 

6 



99-4 
5813-63 

Sa 
Ra 

— 

20 

IS 

— 

29.23 

Pr 

IS 

12 

— 

40.6 

Se 

4 

10 

52.49 

Ne 

— 

— 

IS 

34.26 
35-58 
37.23 

I 

Eu 
Nb 

20 
12 

2O 

8 

10 

44-32 
44-8 
50-49 

X 

Se 

I 

— 

6 

IO 
10 
10 

57-76 
58.27 
7S-64 

Ni 
Mo 
He 

IS 

12 

8 

10 

42.56 
46.6 

Pt 
F 

12 

5 

20 

54-89 
83-71 

Y 
Y 

IO 
12 

IS 

20 

~ 

88.33 
89-96 

Mo 

Na 

IS 

20 

IO 
20 

— 

48.11 

X 



_ 

10 

4900.13 

Y 

IO 

20 

— 

95  93 

Mo 

IS 

10 

— 

5I-56 
53-00 
59-8 
4462.21 

Nd 

Em 
X 

10 

IS 

10 

10 

20 

ii-7 
24.0 
57-41 
4962.27 

Zn 
Zn 

10 
10 

IS 
15 

20 
20 

- 

95-93 
5928.82 

6090.  22 

6121.80 

Na 
Mo 
V 
H 

20 

15 

IS 

2O 

IS 

IS 

10 

NOTE.  — This  table,  somewhat  unsatisfactory  in  its  abridged  form,  is  included  with  the  hope  to  occupy  its  space 
later  with  a  better  table;  e.g.,  no  mercury  lines  appear  since  the  scale  of  intensity  used  in  the  original  tabl< 
in  the  intensity  of  all  mercury  lines  falling  below  the  critical  value  used  m  this  table. 

SMITHSONIAN  TABLES. 


272  TABLE  321. 

STANDARD    SOLAR    WAVE-LENGTHS.     ROWLAND'S    VALUES. 

Wave-lengths  are  in  Angstrom  units  (io~7  mm.),  in  air  at  20°  C  and  76  cm.  of  mercury  pressure. 
The  intensities  run  from  I,  just  clearly  visible  on  the  map,  to  1000  for  the  H  and  K  lines;  below 
I  in  order  of  faintness  to  oooo  as  the  lines  are  more  and  more  difficult  to  see.  This  table  contains 
only  the  lines  above  5. 

N  indicates  a  line  not  clearly  defined,  probably  an  undissolved  multiple  line ;  s,  a  faded  appear- 
ing line;  d,  a  double.  In  the  "substance"  column,  where  two  or  more  elements  are  given,  the 
line  is  compound  ;  the  order  in  which  they  are  given  indicates  the  portion  of  the  line  due  to  each 
element ;  when  the  solar  line  is  too  strong  to  be  due  wholly  to  the  element  given,  it  is  represented, 
Fe,  for  example;  when  commas  separate  the  elements  instead  of  a  dash,  the  metallic  lines  coin- 
cide with  the  same  part  of  the  solar  line,  Fe,  Cr,  for  example. 

Capital  letters  next  the  wave-length  numbers  are  the  ordinary  designations  of  the  lines.  A  indi- 
cates atmospheric  lines,  (wv),  due  to  water  vapor,  (O),  due  to  Oxygen. 


Wave- 
length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave- 
length. 

Sub- 
stance. 

Inten- 
sity. 

3037.5103 
3047.7255 

Fe 
Fe 

10  N 

20  N 

3372-947 
3380.722 

Ti-Pd 

Ni 

10  d? 

6N 

3533-345 
3536-709 

Fe 
Fe 

6 

7 

3053-530S 

— 

7d? 

3414.911 

Ni 

15 

354I-237 

Fe 

7 

Mn,  Ni 

IO 

3423.848 

Ni 

3542.232 

Fe 

6 

3057-552S 
3059.2125 

Ti,  Fe 
Fe 

20 

20 

3433-7I5 
3440.7623  )  Q 

Ni,  Cr 
Fe 

8d? 

20 

3555-079 
3558.6725 

Fe 
Fe 

I 

3067.3693 

Fe 

8 

3441.1555  j 

Fe 

15 

3565-535S 

Fe 

20 

3073.091 

Ti,- 

6Nd? 

3442.118 

Mn 

6 

3566-522 

Ni 

IO 

3078.7695 

Ti,  - 

8d? 

3444.0203 

Fe 

8N 

3570.2735 

Fe 

20 

3088.1453 

Ti 

7d? 

3446.406 

Ni 

*S 

3572-014 

Ni 

6 

3134.2305 

Ni,  Fe 

8 

3449-583 

Co 

6d? 

3572-712 

Se,  - 

6 

3188.656 

-  Fe 

6d? 

3453-039 

Ni 

6d? 

3578.832 

Cr 

IO 

3236.7033 

Ti 

79 

3458.601 

Ni 

8 

3581.3495 

Fe 

3° 

3239.170 

Ti 

7 

3461.801 

Ni 

8 

3584.800 

Fe   ' 

6 

3242.125 

Ti,  - 

8 

3462.950 

Co 

6 

3585-105 

Fe 

6 

3243.189 

-,  Ni 

.    6 

3466.0155 

Fe 

6 

3585-479 

Fe 

7 

3247-6885 

Cu 

10 

3475-5945 

Fe 

IO 

Fe 

6 

3256.021 
3267.8348 

Fe? 
V 

6 
6 

3476.8495 
3483.923 

Fe 
Ni 

8 
6d? 

3587-130 
3587-370 

Fe 
Co 

8 
7 

3271.129 

Fe 

6 

3485493 

FeCo 

6 

3588.084 

Ni 

6 

3271.791 
3274.0965 

Ti,  Fe 
Cu 

6d? 

IO 

3490.7335 
3493.H4 

Fe 

Ni 

10  N 
10  N 

3593-636 
3594.784 

Cr 
Fe 

I 

3277.482 

Co-Fe 

7d? 

3497-9825 

Fe 

8 

3597-854 

Ni 

8 

3286.898 
3295.9513 

Fe 
Fe,Mn 

7N 
6 

3500.9965 
3510.466 

Ni 
Ni 

6d? 
8 

3605.4795 
3606.8385 

Cr 
Fe 

6 

3302.5108 

Na 

6 

3512.785 

Co 

6 

3609.0085 

Fe 

20 

3315.807 
3318.1603 

Ni 
Ti 

76d? 

35I3-965S 
3515-206 

Fe 
Ni 

7 

12 

3612.882 

Ni 
Fe 

6d? 
6 

3320.391 

Ni 

7 

3519.904 

N 

7 

3618.9193 

Fe 

20 

3336.820 

Mg 

8N 

352i.4ios 

Fe 

8 

36I9-539 

Ni 

8 

3349-597 

Ti 

7 

3524-677 

Ni 

20 

3621.6125 

Fe 

6 

3361.327 

Ti 

8 

3526.183 

Fe 

6 

3622.1475 

Fe 

6 

3365-908 

Ni 

6 

3526.988 

Co 

6 

3631.6053 

Fe 

15 

3366.311 

Ti,  Ni 

6d? 

3529.964 

Fe-Co 

6 

3640.5353 

Cr-Fe 

6 

3369-7I3 

Fe,  Ni 

6 

3533-I56 

Fe 

6 

3642.820 

Ti 

7 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  314  (the  accepted  standards,  1913).   Temperature 
15°  C,  pressure  760  mm. 

"  The  differences  "(Fabry-Buisson-arc-iron)  —  (Rowland-solar-iron)"  lines  were  plotted,  a  smooth  curve  drawn,  and 
the  following  values  obtained  : 

Wave-length        3000.        3100.         3200.        3300.        3400.         3500.         3600.        3700. 

Correction         — .106      — .115      — .124      — .137      — .148      — .154      — .155     — .140 

H.  A.  Rowland,  "  A  preliminary  table  of  solar-spectrum  wave-lengths,"  Astrophysical  Journal,  1-6,  1895-1897. 
SMITHSONIAN  TABLES. 


TABLE  321  (continued).  273 

STANDARD  SOLAR  WAVE-LENGTHS.     ROWLAND'S    VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length.    Substance. 

Inten- 
sity. 

3647-9885 

Fe 

12 

3826.0278 

Fe 

20 

4045-975S 

Fe 

3° 

365I-247 

Fe,- 

6 

3827.980 

Fe 

8 

4055.7015 

Mn 

6 

3651.614 

Fe 

7 

3829.5015 

Mg 

IO 

4057.668 

— 

7 

3676.457 

Fe,  Cr 

6 

383I-837 

Ni 

6 

4063.7595 

Fe 

20 

3680.0695 

Fe 

9 

3832.4505 

Mg 

15 

4068.137           Fe-Mn 

6 

3684.2585 

Fe 

7d? 

3834.364 

Fe 

10 

4071.9085             Fe 

15 

3685-339 

Ti 

lod? 

3838.4355 

Mg-C 

25 

4077.8855             Sr 

g 

3686.141 

Ti-Fe 

6 

3840.5805 

Fe-C 

8 

4i02.oooH5       H,  In 

4oN 

3687.6105 

Fe 

6 

384LI95 

Fe-Mn 

IO 

4121.4775          Cr-Co 

6d? 

3689.614 

Fe 

6 

3845.606 

C-Co 

8d? 

4128.251           Ce-V,- 

6d 

3701.234 

Fe 

8 

3850.118 

Fe-Cr 

10 

4132.235           Fe-Co 

10 

3705.7085 

Fe 

9 

3856.5245 

Fe 

8 

4137.156              Fe 

6 

3706.175 

Ca,  Mn 

6d  ? 

3857.805 

Cr-C 

6d? 

4140.089 

Fe 

6 

3709.3895 

Fe 

8 

3858.442 

Ni 

7 

4144.038 

Fe 

1C 

3716.5915 

Fe 

7 

3860.0555 

Fe-C 

20 

4167.438 

— 

g 

3720.0845 

Fe 

40 

3865.674 

Fe-C 

7 

4187.204 

Fe 

6 

3722.6925 

Ni 

10 

3872.639 

Fe 

6 

4i9I-595 

Fe 

6 

3724.526 

Fe             6 

3878.152 

Fe-C 

8 

4202.1985 

Fe 

8 

3732.5455 

Co-Fe 

6 

3878.720 

Fe 

7Nd? 

4226.9O4sg 

Ca 

20  d? 

3733-469S 

Fe- 

7d? 

3886.4345 

Fe 

'5 

4233.772 

Fe 

6 

3735.0145 

Fe 

40 

3887.196 

Fe 

7 

4236.112 

Fe 

8 

3737.2815 

Fe 

3° 

3894.211 

- 

8d 

4250.2875 

Fe 

8 

3738.466 

— 

6 

3895-803 

Fe 

7 

4250.9455 

Fe 

8 

3743-508 
3745-7I7S 

Fe-Ti 
Fe 

6 

8 

3899-850 
3903.090 

Fe 
Cr,  Fe,  Mo 

10 

4254.5055 
4260.6405 

Cr 
Fe 

8 

IO 

3746.0585 

Fe 

6 

3904.023 

— 

8d 

4271.9345 

Fe 

15 

3748.4085 

Fe 

IO 

3905.6605 

Si 

12 

4274.9585 

Cr 

7d? 

3749.6315 

Fe 

20 

3906.628 

Fe 

10 

4308.08  1  sG 

Fe 

6 

3753-732 

Fe-Ti 

6d? 

3920.410 

Fe 

10 

4325-939S 

Fe 

8 

3758.3755 
3759.447 

Fe 
Ti 

i2d? 

3923.054 
3928.0755 

Fe 
Fe 

I2d? 
8 

4376.1075 

H 

Fe 

20N 

6 

3760.196 

Fe 

5 

393045° 

Fe 

8 

4383.7205 

Fe 

15 

3761.464 

Ti 

7 

3933-523 

— 

8N 

4404.9275 

Fe 

10 

3763.9455 
3765.689 

Fe 
Fe 

10 

6 

3933-825SK 
3934.108 

Ca 
Co,  V-Cr 

IOOO 

8N 

4442.510 

Fe 
Fe 

8 
6 

3767.3415 
3775.717 

Fe 

Ni 

8 
7 

3944.1605 
3956.819 

Al 
Fe 

T| 

4447.8925 
4494.7385 

Fe 
Fe 

6 
6 

3783.6745 

Ni 

6 

3957-I77S 

Fe-Ca 

7d? 

4528.798 

Fe 

8 

3788.0465 

Fe 

9 

3961.6745 

Al 

20 

4534.139 

Ti-Co 

6 

3795-  M7S 
3798.6555 

Fe 
Fe 

6 

3968.350 
3968.625sH 

-  Zr 
Ca 

6N 

700 

4549.808 
4554.21  is 

Ti-Co 
Ba 

6d? 
8 

3799-693S 
3805.4865 

Fe 
Fe 

6 

3968.886 
3969.413 

Fe 

6N 

10 

4572.1565 
4603.  1  26 

Ti- 
Fe 

6 
6 

3806.865     !  Mn-Fe 

8d? 

3974.904 

Co-Fe 

6d? 

4629.5215 

Ti-Co 

6 

3807.293 

Ni 

6 

3977.8915 

Fe 

6 

4679.0275 

Fe 

6 

3807.681 

V-Fe 

6 

3986.9035 

— 

6 

4703.1775 

Mg 

IO 

3814.698 

_ 

8 

4005.408 

Fe 

7 

4714.5995 

Ni 

6 

3815.9875 

Fe 

15 

4030.9185 

Mn 

lod? 

4736-963 

Fe 

6 

3820.5865!, 
3824.591 

Fe-C 
Fe 

2I 

4033.2245 
4034.6445 

Mn 
Mn 

8d? 
6d 

4754.2255 
4783.6135 

Mn 
Mn 

I 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  314  (the  accepted  standards,  1913).    Temperature 
15°  C,  pressure  760  mm. : 

Wave-length      3600.      3700.      3800.      3900.      4000.      4100.      4200.      4300-      44°o.      4S°°-      4600.      4700.      4800. 
Correction       —.155  —.140  —.141   —.144  —.148  —.15*  —.156  —.161  —  167  —.172  —.176    ".179  —.179. 

SMITHSONIAN  TABLES. 


274  TABLE  321  (continued). 

STANDARD   SOLAR    WAVE-LENGTHS.    ROWLAND'S    VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length 

Substance 

Inten- 
sity. 

Wave-length. 

Sub- 
stance. 

Inten- 
sity. 

486l.527sF 
4890.9483 

"I  T 

Fe 

30 

I   5948-7653 
5985.0403 

Si 
Fe 

6 
6 

6593.1613 

H 
Fe 

40 

4891.683 

Fe 

8 

6003.2393 

Fe 

6 

6867.45736 

A(0) 

6d? 

4919.1743 

Fe 

6 

6008.7853 

Fe 

6 

6868.336  ) 

A(0) 

6 

4920.685 
4957-785S 

Fe 

Fe 

10 

8 

6013.7153 

6oi6.86is 

Mn 
Mn 

6 
6 

6868.478  JS 
6869.1423 

A(0) 
A(0) 

6 

7 

5050.0083 

Fe 

6 

6022.0163 

Mn 

6 

6869.3533 

A(0) 

6 

ci67.497sb4 

Mg 

15 

6024.2813 

Fe 

7 

6870.1  1  6  I 

A(0) 

7   1  A 

5171.7783 

Fe 

6 

6065.7093 

Fe 

7 

6870.249  J  s 

A(0) 

7  ) 

5172.8563^2 

Mg 

20 

6102.3923 

Fe 

6 

6871.1803 

A(0) 

8 

5183.7913^ 

Mg 

30 

6102.9373 

Ca 

9 

6871.5323 

A(0) 

10 

5233.1223 

Fe 

7 

6108.3343 

Ni 

6 

6872.4863 

A(0) 

ii 

5266.7383 

Fe 

6 

6122.4343 

Ca 

10 

6873.0803 

A(0) 

12 

5269-723SE     !        Fe 
5283.8023                Fe 

8d? 
6 

6136.8293 
6137.915 

Fe 

Fe 

8 
7 

6874.0373 
6874.8993 

A(0) 
A(0) 

12 

5324.3733 

Fe 

7 

6141.9383 

Fe,Ba 

7 

6875.8303 

A(0) 

*3 

5328.236 

Fe 

8d? 

6i55-35o 

— 

7 

6876.9583 

A(0) 

*3 

5340.121 

Fe 

6 

6162.3903 

Ca 

6877.8823 

A(0) 

12 

534I-2I3 

Fe 

7 

6169.2493 

Ca 

6 

6879.2883 

A(0) 

12 

5367.6693 

Fe 

6 

6169.7783 

Ca 

7 

6880.1723 

A(0) 

6 

5370.1663 

Fe 

6 

6170.730 

Fe-Ni 

6 

6884.0763 

A(0) 

10 

5383-578s 

Fe 

6 

6i9T-393s 

Ni 

6 

6886.000s 

A(0) 

II 

5397-344S 

Fe 

7d? 

6191.7793 

Fe 

9 

6886.9903 

A(0) 

12 

5405.9893 

Fe 

6 

6200.5273 

Fe 

6 

6889.1923 

A(0) 

13 

5424.2903 

Fe 

6 

6213.6443 

Fe 

6 

6890.1513 

A(0) 

14 

5429.911 

Fe 

6d? 

6219.4943 

Fe 

6 

6892.6183 

A(0) 

14 

5447.1303 

Fe 

6d? 

6230.9433 

V-Fe 

8 

6893.5603 

A(0) 

15 

5528.6413 

Mg 

8 

6246.5353 

Fe 

8 

6896.2893 

A(0) 

14 

5569-848 

Fe 

6 

6252.7733 

-Fe 

7 

6897.2083 

A(0) 

15 

5573-075 

Fe 

6 

6256.5723 

Ni-Fe 

6 

6900.1993 

A(0) 

14 

5586.991 

Fe 

7 

6301.718 

Fe 

7 

6901.1173 

A(0) 

15 

5588.985s 

Ca 

6 

6318.239 

Fe 

6 

6904.3623 

A(0) 

14 

5613.8773 
5688.4363 

Fe 
Na 

6 
6 

6335-554 
6337048 

Fe 
Fe 

6 

7 

6905.2713 
6908.7833 

A(0) 
A(0) 

14 

571  1.3133 

Mg 

6 

6358.898 

Fe 

6 

6909.6763 

A(0) 

13 

5763.2183 

Fe 

6 

6393.8203 

Fe 

7 

6913.4483 

A(0) 

ii 

5857.6743 

Ca 

8 

6400.2173 

Fe 

8 

69I4-337S 

A(0) 

ii 

5862.5823 

Fe 

6 

6411.8653 

Fe 

7 

6918.3703 

A(0) 

9 

5890.18630-2 

Na 

3° 

6421.5703 

Fe 

7 

6919.2503 

A(0) 

9 

5896-155  DI 

Na 

20 

6439.2933 

Ca 

8 

6923-553s 

A(0) 

9 

5901.6823 

A(wv) 

6 

6450.0333 

Ca 

6 

6924.4273 

A(0) 

9 

5914.4303 

-,A(wv) 

6 

6494.0043 

Ca 

6 

7I9I-755 

A,- 

6N 

5919.8603 

A(wv) 

7 

6495-2I3 

Fe 

8 

7206.692 

-  A 

6 

5930.4063 

Fe 

6 

6546.4793 

Ti-Fe 

6 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  314  (the  accepted  standards,  1913).    Temperature 
15°  C,  pressure  760  mm. : 

Wave-length        4800.        4900.        5000.        5100.        5200.        5300.        5400.         550°.         5600.        5700.        5800. 
Correction        — .179     — .176     — .173      — .170     — .166     — .171     — .212     — .217     — .218     — .213     — .209 


Wave-length        5800.        5900.        6000.        6100.        6200.        6300.        6400.        6500. 
Correction        — .209     — .209     — .213     — .214     — .213      — .210      — .209    — .210. 

SMITHSONIAN  TABLES. 


6600.       6700.       6800. 


TABLE  322 
SPECTRUM  SERIES 


275 


In  the  spectra  of  many  elements  and  compounds  certain  lines  or  groups  of  lines  (doublets,  triplets,  etc.)  occur  in 
orderly  sequence,  each  series  with  definite  order  of  intensity  (generally  decreasing  with  decreasing  wave-length),  pres- 
sure effect,  Zeeman  effect,  etc.  Such  series  generally  obey  approximately  a  law  of  the  form 

I  -  /  _        N 
=  X  (m  +  RP  ' 

where  v  is  the  wave-number  in  vacuo  (reciprocal  of  the  wave-length  X)  generally  expressed  in  waves  per  on;  m  is  a 
variable  integer,  each  integer  giving  a  line  of  the  series;  L  is  the  wave  number  of  the  limit  of  the  series  (m  =  °° );  N, 
the  "Universal  Series  Constant";  and  R  is  a  function  of  m,  or  a  constant  in  some  simple  cases. 

Balmer's  formula  (1885)  results  if  L  =  N/n*,  where  n  is  another  variable  integer  and  R  =  o.  Rydberg's  formula 
(1889)  makes  R  a  constant,  and  L  is  not  known  to  be  connected  with  N.  Other  formulae  have  been  used  with  more 
success.  Mogendorff  (1906)  requires  R  =  constant/^,  while  Ritz  (1003)  has  R  =  constant/wt*.  Often  no  simple 
formula  fits  the  case;  either  R  must  be  a  more  complex  function  of  m,  or  the  shape  of  the  formula  is  incorrect. 

Bohr's  theory  (see  also  Table  515)  gives  for  Hydrogen 

If  =  {2ir*me*(M  +  m)}/MA», 

where  e  and  m  are  the  charge  and  mass  of  an  electron,  M  the  atomic  weight,  and  h,  Planck's  constant.  The  best  value 
for  N  is  109678.7  international  units  (Curtis,  Birge,  Astrophys.  J.  32,  1910).  The  theory  has  been  elaborated  by  Som- 
merfeld  (Ann.  der  Phys.  1916),  and  the  present  indications  are  that  N  is  a  complex  function  varying  somewhat  from 
element  to  element. 

Among  the  series  (of  singles,  doublets,  etc.),  there  is  apt  to  be  one  more  prominent,  its  lines  easily  reversible,  called 
the  principal  series,  P(m).  With  certain  relationships  to  this  there  may  be  two  subordinate  series,  the  first  generally 
diffuse,  D(m),  and  another,  S(m).  Related  to  these  there  is  at  times  another,  the  Bergmann  series  B(m).  m  is  the 
variable  integer  first  used  above  and  indicates  the  order  of  the  line. 

The  following  laws  are  in  general  true  among  these  series:  (i)  In  the  P(m)  the  components  of  the  lines,  if  double, 
triple,  etc.,  are  closer  with  increasing  order;  in  the  subordinate  series  the  distance  of  the  components  (in  vibration 
number)  remains  constant.  (2)  Further,  in  two  related  D(m)  and  S(m),  Av  (vibration  number  difference)  remains 
the  same.  (3)  The  limits  (L)  of  the  subordinate  series,  D(m)  and  S(m),  are  the  same.  (4)  Av  of  the  subordinate  series 
is  the  same  Av  as  for  the  first  pair  of  the  corresponding  P(m).  (5)  The  limits  (L)  of  the  components  of  the  doublets 
(triplets,  etc.)  of  the  P(m)  are  the  same.  (6)  The  difference  between  the  vibration  numbers  of  the  end  of  the  P(m) 
and  of  the  two  corresponding  subordinate  series  gives  the  vibration  number  of  the  first  term  of  the  P(m).  The  first 
line  of  the  S(m)  coincides  with  the  first  line  of  the  P(m)  (Rydberg-Schuster  law). 


ther  inform  i 

the  following  tables,  based  greatly  upon  L>unz's  Die  benengesetze  der  JLimenspeiura,  IJiss.,  Tubingen,  1911,  wmcn 
has  also  appeared  in  book  form,  Hirzel,  Leipzig.  The  following  gives  a  schematic  arrangement  of  the  various  series  of 
a  family  in  accordance  with  some  of  the  above  laws: 

Let  {m,  a,  a}  =  N/(m  +  a  +  a/m2)2;  VP(m)  =  \m,  p,  IT);  VD(m)  =  \m,  d,  d)'  VS(m)  =  \mt  s,  ff)  and 
VB(m)  =  {m,  b,  /3);  V  originally  referred  to  the  variable  part  of  the  formula;  when  m  takes  a  specific  value, 
it  becomes  a  constant  term,  viz.  FS(i). 

Then  a  single  line  system  is  represented  as  follows: 

P'(m)  =  FS'(i)  -  VP'(mY,  Vfa)  =  FP'(i)  -  FZX(f«); 

S'(m)  =  FP'(i)  -  VS'(mY,  [B'(m)  =  VD'(i)  -  VB'(m)}. 

A  system  of  double  lines  would  be  represented  as  follows: 

P\"(m)  =  VS"(i)  —  VPi"(mY,  Di"(m)  =  FP"(i)  —  VD"(mY, 

P2"(m)  =  F5"(i)  -  VP2"(mY,  D2"(m)  =  FP"(i)  -  VD"(mY, 

Si"(m)  =  FP!"(i)  -  VS"(mY,  {Bi"(m)  =  FZ>"(i)  -  VB"(m)}; 

S2"(m}  =  FP2"(i)  -  VS"(mY,  \B2"(m)  =  VD"(i)  -  F-B"(m)). 

And  similarly  for  a  series  of  triplets,  etc. 

Series  Spectra  of  the  Elements.  —  The  ordinary  spectrum  of  H  contains  3  series  of  the  same  kind:  one  in  the;  Schu- 
mann region,  v  =  N(*/i2  —  l/n?),n,  2,  3  .  .  .;  one  in  the  visible,  v  =  N(l/2*  —  V«2),  n,  3,  4,  5-  •  •',  and  one  in  the  infra- 
red, v  =  N^/Z?  —  V«2),  n,4,s,6.  .  .He  has  three  systems  of  series,  one  "  enhanced,"  including  the  Pickering  series 
formerly  supposed  to  be  due  to  H.  The  next  two  tables  give  some  of  the  data  for  other  elements. 


2,66 


1 


0.5>u 


0.3^    A 


1 


GUI      3|45  oo 


2|     3|4|5||oo 


21         3l4l5||oo| 


D(m) 


5000    10000 


20'000 


30t)00 


SEHIES  SYSTEM  or  POTASSIUM. 


SMITHSONIAN  TABLES. 


276 


TABLES  323-324. 

SPECTRUM   SERIES. 

TABLE  323.  —  Limits  of  Some  of  the  Series. 


Pi  (0°) 

-&<*) 

Bl(€0) 

*-, 

=  Si  (oo  ) 

«», 

P|(00) 

Z>,(oo) 
=  S,(oo) 

*., 

W 

H 

48,764 

27,429 

12,186 

48,764 

27,419 

12,186 

48,744 

27,429 

12,186 



He 

32,031 

27,173 

12,204 

38,453 

1  29,221 
\  29,222 

12,208 

— 

- 

— 

— 

Li 

— 

— 

— 

43,484 

28,581 

12,202 

— 

— 

— 

— 

Na 

— 

— 

— 

*4i,445 

24,472 
24,489 

12,274 

— 

— 

- 

- 

K 

— 

— 

— 

35,oo6 

21,963 
22,020 

13,471 

— 

- 

— 

— 

Rb 

— 

— 

— 

33,685 

20,868 
21,106 

14,330 

- 

— 

— 

— 

Cs 

— 

— 

— 

31,407 

19,674 
20,228 

16,809 
16,907 

— 

- 

- 

— 

Cu 

— 

— 

— 

62,306 

3i,523 
3i,77i 

12,372 
12,366 

— 

— 

— 

- 

Ag 

- 

— 

- 

61,093 

30,621 
31,542 

12,351 

- 

— 

— 

— 

39,752 

Mg 

— 

26,613 

— 

? 

? 

? 

20,467 

39,793 

13,707 

— 

39,8i3 

Ca 

— 

27,5io 

— 

? 

60,423 
60,646 

28,929 

17,761 

33,983 
<  34,089 

28,929 
28,950 

49,353 

34,142 

28,964 

Sr 

— 

25,745 

— 

- 

55,029 
55,830 





31,026 
31,420 

27,605 
27,705 

45,895 

31,607 

27,766 

Ba 

— 

— 

— 

— 

\  51,616 



? 

? 

? 

48,318 

For  the  series  of  Zn,  Cd,  Hg,  Al,  Sn,  Tl,  O,  S,  Sn,  see  original  reference. 

*48  lines  have  been  measured  in  this  series  from  16,956  to  41,417. 

TABLE  324.  —  First  Terms  of  Some  of  the  Series.    Vibration  Number  Differences  of 
Pairs  A**,  and  Triplets  A^i,  A*>2. 

For  the  P(m)  and  the  S  (m)  is  given  only  the  first  or  second  term,  since  the  term  with  index  o  may  be  omitted  as 
coinciding  with  the  first  term  of  the  S(m)  or  P(m)  respectively.  Consequently  the  numbers  always  proceed  from 
greater  to  smaller  wave-lengths.  Which  is  the  common  line  can  always  be  recognized  from  the  vibration  numbers. 
See  figure  on  the  preceding  page.  The  vibration  differences  can  be  obtained  from  Table  323. 


w 

BH 

«o 

«., 

*» 

«<„ 

sw 

B(i) 

A, 

An 

A, 

H 

21,334 

15,233 

9,871 

5332 

(6654 

26,106 

19,346 

He 

I 

He 

4,857 

,  13,970 

13,729 

5348 

Mg 

6650 

26,086 

19,326 

6,720 

Na 

17 

— 



9,231 

I  I7,"4 
I  17,  "8 

14,149 
14,148 

5351 

Ca 

[6650 

26,045 
20,495 

19,285 
19,828 

_ 

K 
Rb 

58 
237 

~ 

— 

Li 

14,903 

16,379 

12,301 

5347 

",763 

25,414 

22,153 

Cs 

552 

— 



Ma 

16,973 

12,215 

7  782 

25,191 

Cu 

249 





16,956 

12,198 

7,766 

54 

(  5036 

5,oi9 

16,381 

21,834 

921 

— 



K 
Rb 
Cs 
Cu 

Ag 

13,043 
12,985 
12,817 
12,579 
",733 
11,178 
30,783 
30,535 
30,472 
30.551 

8,552 
8,493 
6,776 
6,538 
3,32i 
2,767 
19,158 

19,191 
18,271 

8,040 
7,983 
7,552 
7,315 
7,357 
6,803 
12,601 
12,352 
13,003 
12,083 

6592 

7437 
9972 
9875 
5495 

5439 

Sr 
Ba 

5020 
[5012 

5,125 
5,177 

19,390 
9,959 
9,159 
3,842 
3,655 
3,260 
12,176 
io,493 

16,329 
16,223 

23,715 

14,721 
14,533 
14,139 
21,952 
20,261 

21,820 
21,799 

20,591 
20,533 
20,435 

Sr 
Ba 
Zn 
Cd 

In 
Tl 

223 

801 
1690 
872? 
2484? 

112 
2213 

7793 

106 

394 
878 
389 
1171 
4632 

20 
52 

187 
370 
190 
542 
1769 

Mg 

35,760 
35,668 

35,831 
35,739 

34,135 
34,043 

— 

— 

13,894 
13,523 

O 

S 

3-7 
18.2 

2.1 
II.  I 

12,645 

Se 

45 

SMITHSONIAN  TABLES. 


TABLES  325-326. 

TABLE  325.  —  Index  of  Refraction  of  Glass. 

Indices  of  refraction  of  optical  glass  made  at  the  Bureau  of  Standards. 


277 


nces  o  reraction  of  optical  glass  made  at  the  Bureau  of  Standards.  Correct  probably  to  o  ooooi  The  com 
position  given  refers  to  the  raw  material  which  went  into  the  melts  and  does  not  therefore  refer  to  the  comoosition  of 
the  finished  glass. 


Melt. 

123 

241 

135 

116 

188 

151 


163 

76 

Wave-length. 

Ordinary 
crown. 

Borosili- 
cate 
crown. 

Barium 
flint. 

Light 
barium 
crown. 

Light 
flint. 

Dense 
barium 
crown. 

Medium 
flint. 

Dense 

flint. 

Hg     4046  .  8 
Hg     4078.1 
H       4340-7 

-53189 
•53147 
.52818 

-53817 
-53775 
-53468 

.58851 
•58791 
•58327 

I-5QI37 
i  .  59084 
i  .  58698 

i  .  60507 
i  .  60430 
i  .  59860 

•63675 
.63619 
.63189 

-65788 
-65692 
•64973 

•69005 
.68894 
.68079 

Hg     4358.6 
H       4861.5 
Hg     4916.4 

.52798 
.52326 
.52283 

•  53450 
.53008 
•52967 

.  58299 
.  57646 
.57587 

1.58674 
1.58121 
1.58071 

1.59826 
i  .  59029 
i  -  58958 

.63163 
.  62548 
.62492 

.64931 
•63941 
•63854 

.68030 
.66911 
.66814 

Hg     5461  .  o 

.51929 

•52633 

•57105 

1.57657 

i  .  58380 

-  62033 

•63143 

.66016 

Hg     5769.6 
Hg      5790-5 

•51771 
.51760 

.  52484 
•52475 

•  56894 
.56881 

1-57473 
i  •  5746o 

1.58128 
1.581*2 

.61829 
.61817 

•62834 
.62815 

.65671 
.  65650 

Na     5893  .  2 
Hg     6234-6 

•5I7I4 
-51573 

-52430 
.52297 

.56819 
•  56634 

1.57406 

1.57242 

1.58038 
1.57818 

.61756 
.61576 

•62725 
.62458 

•65548 
.65250 

H       6563.0 

.51458 

.52188 

.  56482 

1.57107 

1-57638 

.61427 

.62241 

.65007 

Li       6708.2 
K        7682.0 

.51412 
.51160 

-52145 
.51908 

•56423 
.  56100 

1.57054 
1.56762 

1-57567 
1.57183 

.61369 
.  61047 

•62157 
.61701 

•64913 
.64405 

(Percentage  composition) 

SiOz 

67.0 

64.  2 

53-7 

48.0 

53-9 

37-0 

45-6 

39-0 

Na2O 

12.0 

9.4 

i-7 

2.0 

I.O 

3-4 

3-0 

K20 

5-0 

8.3 

8.3 

6.1 

7-6 

2.7 

4-1 

4.0 

BzOs 

3-5 

II.  0 

2.7 

4.0 

5-o 

BaO 

10.6 

6.1 

14-3 

29-5 

— 

47-0 

— 

— 

ZnO 

i-5 



2-5 

IO.O 



7-7 

— 

— 

As203 

0.4 

0.4 

i-4 

0.3 

— 

— 

CaO 

i  .0 



2.O 

^_ 

3-0 

4-o 

PbO 

— 

— 

16.7 

— 

35-2 

— 

44-0 

49.0 

Sb203 

I.O 

TABLE  326.  —  Dispersion  of  Glasses  of  Table  325. 


Melt. 

123 

241 

135 

116 

188 

151 

163 

76 

«D 

1-51714 

1.52430 

1.56819 

i.574o6 

i  .  58038 

1.61756 

1.62725 

1.65548 

»r-*c 

0.00868 

0.00820 

0.01164 

0.01014 

0.01391 

O.OII2I 

0.01700 

0.01904 

WjT)    —    I 

48  8 

56  6 

55  * 

36.9 

34-  4 

»*-«c 

«D  —  nf 

0.00612 

0.00578 

0.00827 

0.00715 

0.00991 

0.00792 

0.01216 

0.01363 

nF  —  nGr 

0.00492 

o  .  00460 

0.00681 

0.00577 

o  .  0083  i 

0.00641 

0.01032 

0.01168 

nD-nc 

0.00256 

0.00242 

0.00337 

o  .  00299 

0.00400 

0.00329 

0.00484 

0.00541 

i 

SMITHSONIAN  TABLES. 


278  TABLES  327-329.  INDEX  OF  REFRACTION  FOR  GLASS. 

TABLE  327.  -  Glasses  Made  by  Schott  and  Gen,  Jena. 

The  following  constants  are  for  glasses  made  by  Schott  and  Gen,  Jena :  «A,  «c»  «D,  «F,  «o,  are 
the  indices  of  refraction  in  air  for  A=o.76S2/i,  0=0.6563/1,  D=o.5S93,  F=o.486i,  G/= 0.4341. 
z/=(«D — I)/(«F  —  «c).  Ultra-violet  indices:  Simon,  Wied.  Ann.  53,  1894.  Infra-red:  Rubens, 
Wied.  Ann.  45,  1892.  Table  is  revised  from  Landolt,  Bornstein  and  Meyerhoffer,  Kayser,  Hand- 
buch  der  Spectroscopie,  and  Schott  and  Gen's  list  No.  751,  1909.  See  also  Hovestadt's  "Jena 
Glass." 


Catalogue  Type  = 

0546 

0381 

Oi84 

Ol02 

Oi65 

S57 

Designation     = 

Zinc-Crown. 

Higher  Dis- 
persion Crown. 

Light  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heaviest  Sili- 
cate Flint. 

Melting  Number:= 

1092 

1151 

45' 

469 

500 

163 

v             = 

60.7 

51.8 

41.1 

33-7 

27.6 

22.2 

.   f     Cd  0.2763^ 

•56759 

_ 

_ 

_ 

_ 

_ 

•S 

Cd    .2837 

•56372 

- 

- 

- 

— 

— 

i 

Cd     .2980 

•55723 

•57°93 

.65397 

— 

- 

- 

M 

Cd    .3403 

•54369 

.55262 

.63320 

.71968 

•85487 

- 

* 

Cd    .3610 

•53897 

.54664 

.61388 

•70536 

.83263 

~ 

rt 

£ 

H       .4340^. 

.52788 

•53312 

•59355 

.67561 

.78800 

1-94493 

*O 

H       .4861 

.52299 

•52715 

•56515 

.66367 

.77091 

1.91890 

1  • 

Na    .5893 

.51698 

.52002 

•57524 

.64985 

•75'30 

1.88995 

H       .6563 

.51446 

•  S^JZ 

•57II9 

.64440 

.74368 

1.87893 

.£ 

M 

K      .7682 

•5"43 

.51368 

.56669 

.63820 

•73530 

1.86702 

'_J 

.8oo/m 

•5'°3 

•S'31 

•5659 

•6373 

•7339 

1.8650 

*0 

1.200 

.5048 

.5069 

•5585 

.6277 

•7215 

1.8481 

•§ 

1.  600 

.5008 

.5024 

•5535 

.6217 

•7l5l 

1.8396 

S 

2.000 

.4967 

•4973 

•5487 

.6171 

.7104 

1.8316 

2.400 

- 

•544° 

.6131 

" 

1.8286 

Percentage  composition  of  the  above  glasses  : 
O  546,  SiO2,  65.4;  K2O,  15.0;  Na2O,  5.0;  BaO,  9.6;  ZnO,  2.0;  Mn2O3,  o.i  ;  As2O3,  0.4; 

B203,  2.5. 

0381,  SiO2,  68.7;  PbO,  13.3;  Na2O,  15.7;  ZnO,  2.0;  MnO2,  o.i  ;  As2O5,  0.2. 

O  184,  SiO2,  53.7  ;  PbO,  36.0;  K2O,  8.3;  Na2O,  i.o;  Mn2O3,  0.06;  As2O3,  0.3. 

O  102,  SiO2,  40.0;  PbO,  52.6;  K2O,  6.5;  Na2O,  0.5;  Mn2O3,  0.09;  As2O5,  0.3. 

O  165,  SiO2,  29.26;  PbO,  67.5;  K2O,  3.0;  Mn2O3,  0.04;  As2O3,  0.2. 

S  57,     SiO2,  21.9;  PbO,  78.0;  As2O5,  o.i. 

TABLE  328.— Jena  Glasses. 


No.  and  Type  of  Jena  Glass. 

«D  for  D 

*D—  I 

Specific 
Weight. 

O  225  Light  phosphate  crown     .     . 
O  802  Boro-silicate  crown  .... 
UV  3  199  Ultra-violet  crown    .     .     . 
0227  Barium-silicate  crown   .     .     . 
O  114  Soft-silicate  crown    .... 
O  608  High-dispersion  crown      .     . 
UV  3248  Ultra-violet  flint  .     .     .     . 
O  381  High-dispersion  crown      .     . 
O  602  Baryt  light  flint     

•5*59 
.4967 

•5035 
•5399 
•5151 
•5149 
•5332 
.5262 
.5676 
.5686 
•5398 
•5710 
.5900 
•6235 
.6489 
•7174 
•7541 
.9170 
i  .9626 

.00737 
0765 
0781 
0909 
0910 
0943 
0964 
1026 
1072 

1  IO2 
1142 
1327 
1438 
1599 
1919 

2434 
2743 
4289 
4882 

70.0 
64-9 
64-4 

59-4 
56.6 
54-6 
55-4 
5'-3 
53-° 
51.6 
47-3 
43-0 
41.1 
39-1 
33-8 
29.5 
27-5 
21.4 
19.7 

.00485 
0504 
0514 
0582 
0577 

°595 
0611 
0644 
0675 
0712 
0711 
0819 
0882 
9965 
1152 
1439 
1607 

245i 
2767 

•00515 
0534 
0546 
0639 
0642 
0666 
0680 
0727 
0759 
0775 
0810 
0943 

IO22 
1142 
1372 
1749 
1974 
3109 

3547 

.00407 
0423 
0432 
05'4 
0521 
0543 
0553 
0596 
0618 
0629 
0669 
0791 
0861 
0965 
1180 
IS*1 
i73o 
2808 
3252 

2.58 
2.38 
2.41 

2.73 
2-55 
2.60 

2-75 
2.70 
3-12 
2.83 
2.87 
3.r6 
3-28 
3.67 
3.87 
4-49 
4-78 
6.or 
6-33 

S  389  Borate  flint      

O  154  Ordinary  light  flint   .... 
Oi84        "            "".... 
O  748  Baryt  flint   

O  41               "             " 

O  165                 "   . 

S  386  Heavy  flint  

TABLE  329.— Change  ol  Indices  of  Refraction  for  1°  C  in  Units  of  the  Fifth  Decimal  Place. 


No.  and  Designation. 

Mean 
Temp. 

C 

D 

F 

G' 

—  AH 

100 

n 

S  57  Heavy  silicate  flint      .     .     . 
O  154  Light  silicate  flint     .     .     . 

58.8° 
58.4 

1.204 
0.225 

1.447 
0.261 

2.090 
0-334 

2.810 
0.407 

0.0166 
0.0078 

0327  Baryt  flint  light     .... 
O  225  Light  phosphate  crown 

58.3 
58.1 

—  0.008 

—  0.202 

0.014 
—  0.190 

0.080 
—o.i  68 

0-137 
—  0.142 

0.0079 
0.0049 

SMITHSONIAN  TABLES. 


Pulfrich,  Wied.  Ann.  45,  p.  609,  1892. 


TABLES  330-332.  INDEX  OF  REFRACTION, 

TABLE  330.  —  Index  of  Refraction  of  Rock  Salt  In  Air. 


279 


44 

«. 

Obser- 
ver. 

«* 

n. 

Obser- 
ver. 

4* 

n. 

Obser- 
ver. 

0.185409 

1.89348 

M 

0.88396 

.534011 

L 

5-8932 

.516014 

P 

.204470 
.291368 

1.76964 
1.61325 

.. 

.972298 
.98220 

•532532 
•532435 

ii 
P 

6.4825 

•5^5553 
.513628 

L 

P 

.358702 

1-57932 

" 

1.036758 

.531762 

L 

u 

•5  '3467 

L 

.441587 

1.55962 

" 

1.1786 

.530372 

P 

7.0718 

.51  1062 

P 

.486149 

1.55338 

<i 

" 

•530374 

L 

7.6611 

•508318 

«* 

" 

1.553406 

L 

1.555137 

.528211 

u 

7-9558 

.506804 

«« 

" 

1  -553399 

P 

1.7680 

.527440 

P 

8.8398 

.502035 

• 

.58902 

1-544340 

L 

" 

•527441 

L 

10.0184 

-494722 

«' 

•58932 

i-5443I3 

P 

2.073516 

•526554 

" 

11.7864 

.481816 

* 

,656304 

1.540672 

P 

2.35728 

.525863 

P 

12.9650 

.471720 

" 

" 

1.540702 

L 

.525849 

L 

14.1436 

•460547 

" 

.706548 

I-538633 

P 

2.9466 

.524534 

P 

14-7330 

.454404 

" 

.766529 

1.536712 

P 

3-5359 

.523I73 

" 

15.3223 

.447494 

" 

.76824 

1.53666 

M 

4.1252 

.521648 

P 

15.9116 

.441032 

" 

•78576 

1-536138 

P 

" 

1.521625 

L 

20.57 

•3735 

RN 

.88396 

1.534011 

P 

5.0092 

1.518978 

P 

22.3 

-340 

where  a2=_.^_._J 
^1=0.01278685 
Ai2  =  0.0148  500 
M2  =  0.005343924 


A22  =  0.02  5474  14 
/£  =0.0009285837 
/&=  0.000000286086 


^=5.680137 
MS=  12059.95 
A32=36oo.  (P) 


TABLE  331.-  -  Change  of  Index  of  Refraction  for  1°  C  In  Units  of  the  5th  Decimal  Place 


O.2O2/4 

+3-134 

Mi 

0-441/t 

—3425 

Mi 

Cline 

—3-749 

PI 

0.760/1 

—3-73 

L 

.210 

.224 

+  !-570 
—0.187 

M 

II 

.508 
•643 

-3-5I7 
—3-636 

M 

D    " 
F    " 

—3-739 
—3.648 

n 

1.368 
1.88 

—3.88 
-3-85 

L 
L 

.298 

—2.727 

G'  " 

-3-585 

4-3 

-3.82 

L 

L    Annals  of  the  Astrophysical   Observatory 
of  the  Smithsonian  Institution,  Vol.  I,  1900. 
M    Martens,  Ann.  d.  Phys.  6,  1901,  8,  1902. 
Mi  Micheli,  Ann.  d.  Phys.  7,  1902. 


P  Paschen,  Wied.  Ann.  26,  1908. 
PI  Pulfrich,  Wied.  Ann.  45,  1892. 
RN  Rubens  and  Nichols,  Wied.  Ann.  60, 1897. 


TABLE  332.  —Index  of  Refraction  of  Sylvlte  (Potassium  Chloride)  In  Air. 


AU). 

n 

Obser- 
ver. 

A(M). 

n. 

Obser- 
ver. 

A(M). 

n. 

Obser- 
ver. 

0.185409 
.200090 

1.82710 
1.71870 

M 

1.1786 

i« 

1.478311 
1.47824 

P 

w 

8.2505 
ii 

1.462726 
1.46276 

P 
W 

.21946 

1.64745 

ii 

1.7680 

1.475890 

P 

8.8398 

1.460858 

P 

•2573T7 
.281640 
.308227 

1.58125 
I-55836 
L54I36 

M 

2.35728 
2.9466 

1.47589 

I-474751 
1.473834 

w 
P 

10.0184 

1.46092 
1.45672 
L45673 

W 
P 
W 

.358702 

I-52II5 

M 

" 

1-47394 

w 

11.786 

1.44919 

P 

.394415 
.467832 
.508606 

1.51219 
1.50044 
1.49620 

II 
II 

3-5359 
4.7146 

1.473049 
1.47304 
1.471122 

P 
w 
P 

12.965 

1.44941 
1.44346 
1.44385 

w 
P 
w 

.58933 

1.49044 

P 

n 

1.47129 

w 

14.144 

1.43722 

P 

.67082 

1  .48669 

M 

5-3039 

1.470013 

P 

15.912 

1.42617 

" 

-78576 

1.483282 

P 

1.47001 

w 

17.680 

I.4I403 

.88398 

1.481422 

P 

5-8932 

1.468804 

P 

20.60 

1.3882 

RN 

.98220 

1.480084 

1.46880 

w 

22.5 

1.369 

Ml 


i+ 


Afl 


^=0.0255550 
£=0.000513495 
^=0.000000167587 


(P) 


MI = 0.008344206 

Ai2  =  O.OI  19082 

MZ = 0.00698382 
W  Weller,  see  Paschen's  article.     Other  references  as  under  Table  33*> above. 


#2=3.866619 
Ms=  5569.7 1 5 
A32= 3292-47 


SMITHSONIAN  TABLES. 


280 


TABLES  333-336. 
INDEX  OF  REFRACTION. 

TABLE  333. -Index  of  Refraction  of  Fluorite  in  Air. 


MM) 

n 

Obser- 
ver 

MM) 

• 

Obser- 
ver 

MM) 

M 

Obser- 
ver. 

0.1856 

1.50940 

S 

I-4733 

1.42641 

P 

4.1252 

1.40855 

P 

.19881 
.21441 

1.49629 
1.48462 

u 

1.6206 

1.42596 
1.42582 

M 

4.4199 
4.7146 

L40559 
.40238 

« 

.22645 

1.47762 

M 

1.7680 

1.42507 

M 

5.0092 

.39898 

u 

•25713 

1.46476 

" 

I-9I53 

1-42437 

" 

5-3036 

•39529 

•32525 
•34555 
.39681 

1.44987 
1.44697 
1.44214 

M 

1.9644 
2.0626 
2.1608 

1.42413 

1-42359 
1.42308 

5-5985 
5-8932 
6.4823 

.39142 
.38719 
•37819 

.48607 

I-437I3 

P 

2.2IOO 

1.42288 

" 

7.0718 

.36805 

" 

•58930 
.65618 
.68671 

1-43393 
1.43257 
1.43200 

P 

S 

2-3573 
2.5537 
2.6519 

1.42199 
1.42088 
1.42016 

,, 

7.6612 
8.2505 
8.8398 

•35680 

•34444 
•33079 

M 
M 

.71836 

i.  43  T  57 

M 

2.7502 

1.41971 

9.4291 

.31612 

" 

.76040 

1.43101 

" 

2.9466 

1.41826 

" 

51.2 

3.47 

RA 

.8840 

1.42982 

P 

3-  '430 

1.41707 

" 

OI.I 

2.66 

" 

1.1786 

1.42787 

" 

3-2413 

1.41612 

" 

00 

2.63 

S 

1.3756 

1.42690 

'. 

3-5359 

I.4I379 

M733 

1.42641 

3-8306 

1.41120 

References  under  Table  331. 

where  a'2  =  2.03882 


Ai'2  =  0.007  706 
*  =  0.003 1 999 


/==  0.0000029 1 6 
^  =  6.c 


6.09651 
J/2=o.oo6i3 
A,2  =  0.00884 


71/3=5114.65 

Ar2=  1260.56 

Aj,  =  0.0940;* 


(P) 


TABLE  334.  —Change  of  Index  of  Refraction  for  1C  in  Units  of  the  5th  Decimal  Place. 
C  line, — 1.220;  D,  — 1.206;  F,  — 1.170;  G,  — 1.142.      (PI) 


TABLE  335. -Index  of  Refraction  of  Iceland  Spar  (CaCO:t)  in  Air. 


*GO 

»o 

»« 

Obser- 
ver. 

A  (^) 

»0 

ne 

Obser- 
ver. 

A  (/a) 

»0 

* 

Obser- 
ver. 

0.198 

_ 

1.5780 

M 

0.508 

1.6653 

1.4896 

M 

0.991 

1.6438 

1.4802 

C 

.200 

1.9028 

'•5765 

" 

•533 

1.6628 

1.4884 

« 

.229 

J.6393 

1.4787 

.208 

1.8673 

IJ664 

« 

1.6584 

1.4864 

u 

•307 

1.6379 

1.4783 

.226 

I.8l3O 

1.5492 

— 

•643 

1.6550 

1.4849 

" 

•497 

1.6346 

1-4774 

.298 

1.7230 

LS'Si 

C 

.6S6 

1.6544 

1.4846 

" 

.682 

1-6313 

- 

-340 
.361 

I./008 
1.6932 

1.5056 
1.5022 

M 
C 

.670 
.760 

1.6537 

1.6500 

1.4843 
1.4826 

«< 

-749 
.849 

1.6280 

1.4764 

.4IO 

1.6802 

1.4964 

— 

.768 

1.6497 

1.4826 

M 

.908 

_ 

M757 

432 

I.6755 

1-4943 

M    ! 

.801 

1.6487 

1.4822 

Q 

2.172 

1.6210 

.486 

1.6678 

1.4907 

-905 

1.6458 

1.4810 

2.324 

1-4739 

C     Carvallo,  J.  de  Phys.  (3),  g,  1900. 

M    Martens,  Ann.  der  Phys.  (4)  6,  1901,  8,  1902. 

P    Paschen,  Wied.  Ann.  56,  1895. 


PI      Pulfrich,  Wied.  Ann   45,  1892. 

RA   Rubens-Aschkinass,  Wied.  Ann.  67,  1899. 

S       Starke,  Wied.  Ann.  60,  1897. 


TABLE  336.  —Index  of  Refraction  of  Nltroso-dimethyl  aniline.    (Wood.) 


A 

n 

A 

n 

A 

n 

A 

n 

A 

n 

0.497 

2.140 

1     0.525 

J-945 

0.584 

•8l5 

0.636 

1.647 

0.713 

I.7I8 

.50° 

2.II4 

•536 

1.909 

.602 

.796 

.647 

I-758 

•73° 

L7I3 

.506 
.508 
.516 

2.074 
2.025 
1.985 

•546 

|  :g 

1.879 
1.857 
1.834 

.611 
.620 
.627 

'.778 
.769 

.659 
.669 
.696 

1-75° 

1-743 
1-723 

•749 
•763 

1.709 
1.697 

Nitroso-dimethyl-aniline  has  enormous  dispersion  in  yellow  and  green,  metallic  absorption  in  violet.     See  Wood. 

Phil.  Mag.  1903. 

SMITHSONIAN    TABLES. 


TABLES  337-338. 
INDEX  OF  REFRACTION. 

TABLE  337.  —  Index  of  Refraction  of  Quartz  (S102). 


281 


Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
ture °  C. 

Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
ture °  C. 

fk 

M 

0.185 
•193 

1.67582 
.65997 

1.68999 
•67343 

18 

0.656 

.686 

1.54189 
.54099 

1.55091 
.S4998 

18 

<« 

.198 
.206 

.65090 
.64038 

.66397 
.65300 

« 

.760 
1.160 

•53917 

•5329 

.54811 

H 

.214 

.63041 

.64264 

« 

.969 

.5216 

_ 

.219 

.62494 

•63698 

" 

2.327 

•5!56 

_ 

.231 

.61399 

.62560 

.84 

•5°39 

_ 

•257 

.59622 

.60712 

" 

3.18 

•4944 

_ 

.274 
•340 

•58752 
.56748 

.59811 
•57738 

M 

« 

3 

•4799 
•4679 

Rubens. 

- 

.396 

.55815 

•56771 

4.20 

•4569 

_ 

.410 

•55650 

.56600 

" 

5.0 

.417 

_ 

.486 

.54968 

.55896 

« 

6.45 

.274 

_ 

0.589 

1.54424 

1-55334 

U 

7.0 

1.167 

~ 

Except  Rubens'  values,  —  means  from  various  authorities. 


TABLE  338.  —  Indices  of  Refraction  for  various  Alums.* 


r> 

£ 

u 

Index  of  refraction  for  the  Fraunhofer  lines. 

i 

Q 

EH 

a 

B 

c 

D 

E 

i 

F 

Q 

Aluminium  Alums.     -ffAl(SO4)2+i2H2O.t 

Na 

NH3(CH3) 
K 

1.667 
1.568 
J-735 

17-28 
7-17 
14-15 

1.43492 

•45or3 
.45226 

143563 
.45062 

•45303 

I-43653 

•45177 
•45398 

1.43884 
.45410 
•45645 

1.44185 
.45691 
•45934 

1.44231 

•45749 
.45996 

1.44412 
.45941 
.46181 

1.44804 
•46363 

Rb 
Cs 
NH4 

1.852 
1.961 
1.631 

7-21 

15-25 
15-20 

•45232 
•45437 
.45509 

.45328 
•45517 
•45599 

•45417 
.45618 

•45693 

.45660 
.45856 
•45939 

•45955 
.46141 
.46234 

-45999 
.46203 
.46288 

.46192 
.46386 
.46481 

.46618 
.46821 
•46923 

Tl 

2.329 

10-23 

.49226 

•493  1  7 

•49443 

.49748 

.50128 

.50209 

•50463 

.51076 

Chrome  Alums.     J?Cr(SO4)2+i2H,O.t 

Cs 
K 

2.043 
1.817 

6-12 

6-17 

1.47627 
.47642 

1-47732 
•4773s 

1-47836 
.47865 

1.48100 
•48137 

1.48434 
.48459 

1.48491 
•48513 

1.48723 
•48753 

1.49280 
.49309 

Rb 

1.946 

12-17 

.47660 

•47756 

.47868 

.48151 

.48486 

.48522 

•48775 

•49323 

NH4 

1.719 

7-18 

.47911 

.48014 

.48125 

.48418 

.48744 

.48794 

.49040 

•49594 

Tl 

2.386 

9-25 

.51692 

•51798 

•5I923 

.52280 

.52704 

•52787 

•53082 

•53808 

Iron  Alums.     /?Fe(SO4)2+i2H2O.t 

K 

i.  806 

7-1  1 

1.47639 

1.47706 

1.47837 

1.48169 

1.48580 

1.48670 

1.48939 

1.49605 

Rb 

1.916 

7-20 

.47700 

•47770 

.47894 

.48234 

.48654 

.48712 

.49003 

.49700 

Cs 

2.061 

20-24 

.47825 

.47921 

.48042 

.48378 

.48797 

.48867 

.49136 

49818 

NH4 

1.713 

7-20 

47927 

.48029 

.48150 

.48482 

.48921 

.48993 

.49286 

.49980 

Tl 

2-385 

*S~*7 

.51674 

.51790 

•5J943 

•52365 

•52859 

•52946 

.53284 

.54112 

*  According  to  the  experiments  of  Soret  (Arch.  d.  Sc.  Phys.  Nat.  Geneve,  1884,  1888,  and  Comptes  Rendus,  1885). 

t  JR  stands  for  the  different  bases  given  in  the  first  column. 

For  cither  alums  see  reference  on  Landolt-Bornstein-Roth  Tabellen. 

SMITHSONIAN  TABLES. 


282 


TABLE  339. 

INDEX  OF   REFRACTION. 
Selected  Monorefringent  or  Isotropic  Minerals. 


The  values  are  for  the  sodium  D  line  unless  otherwise  stated  and  are  arranged  in  the  order  of  increasing  indices. 
Selected  by  Dr.  Edgar  T.  Wherry  from  a  private  compilation  of  Dr.  E.  S.  Larsen  of  the  U.  S.  Geological  Survey. 


Mineral. 

Formula. 

Index  of 
refraction, 
X  =  0.589^. 

Villiaumite  

NaF 
3NaF.3LSF.2AlFi 
SiOi-nHiO 
CaF, 
KjO.Al203.4SO3.24HiO 
3Na20.3AljOv6Si02.2NaCl 
SiO2 
Na2O.Al203.4SiO2.2H2O 

5Na20.3Al203.6Si02.2S03 
Like  preceding  +  CaO 
4Na20.3Al.,03.6Si02.Na2S6 
K1O.Al2Os.4Si02 
2Cs20.  2  Al2O3.9SiO2  .  H2O 
NaCl 
Al,0,.nH,0 
3FeA.2As206.3K20.sH2O 
MgO.AliOs 
3(Ca,  Mg,  MnJO.AszOs 
MgO 
3CaO.Al2O3.3SiO2 
3(Mn,  Fe)O.3BeO.3SiO2.MnS 
3MgO.A«)3.3SiOj 

3Ca03.(Al,  Fe)203.3Si02 
(Mg,  Fe)O.Al20« 
3FeO.Al2O3.3SiO2 
FeO.AlzOs 
ZnO.AlzOs 
3MnO.Al2O3.3SiOj 
CaO 
3CaO.Cr2O3.3SiO2 
3CaO.Fe2O3.3SiO2 
6CaO.3Ta2O5.CbOF3 
CuCl 
Contains  CaO,  Ce2Os,  TiO2,  etc. 
3CaO.(Fe,  Ti)2O3.3(Si,  Ti)O2 
PbO.CuCl2.H20 
(Mg,  Fe)0.(Al,  Cr)^ 
2Bi2Os.3SiO2 
AgCl 
Contains  Hg,  NH«,  Cl,  etc. 
FeO.CrzOs 
SbzOs 
Ag(Br,  Cl) 
MnO 
NiO 
sCaO^TiO^SbsOs 
CuI.4AgI 
AgBr 
Contains  CaO,  FeO,  TiO^  etc. 
Cul 
(Zn,  Fe,  Mn)O.(Fe,  Mn)sOa 
(Zn,  Fe)S 
CaO.TiOz 
C 
HgO.2HgCl 
MnS2 
MnS 
CuzO 

.328 
-339 
.  406-1  .  440 
•434 
•456 
•483 
.486 
.487 
.400 
•495 
.496 
.500  ± 
•  500 
•  S2S 
•544 
•  570  ± 
.676 

.723  ± 

•  727 

.736 
.736 

•  739 
•  745 
•  755 
.763 
•  770  ± 
.778 
.800  =*= 
.800  =*= 
.811 
.830 
.838 
.857 
•925 
•  930 
.960-2.000 
.980 
.050 
.050  ± 
.050 
.061 
.065 
.070 
.087 
.i|o* 
.160 
.  18  (Li  light) 

.200 
.  2CO 
•253 
-330 
•346 

.360  (Li  light) 
.370-2.470 
.380 
.419 
.  490  (Li  light) 
.690  (Li  light) 
.  700  (Li  light) 
.849 

Cryolithionite 

Opal 

Fluorite  
Alum 

Sodalite  

Cristobalite  
Analcite 

Sylvite  
Noselite 

Hauynite  

Lazurite     .    .    . 

Leucite  

Pollucite  

Halite 

Bauxite  

Pharmacosiderite  
Spinel  
Berzeliite  

Periclasite 

Grossularite  
Helvite. 

Pyrope  

Arsenolite 

Hessonite 

Pleonaste  

Almandite  
Hercynite  
Gahnite 

Spessartite  .  .  . 

Lime          .   . 

Uvarovite  

Andradite  

Microlite  
Nantokite  
Pyrochlore    . 

Schorlomite  

Percy  lite  

Picotite 

Eulytite  

Cerargyrite  
Mosesite  .  

Chromite..    . 

Senarmontite  
Embolite  
Manganosite  
Bunsenite  

Lewisite 

Miersite  
Bromyrite  . 

Dysanalite  
Marshite  
Franklinite 

Sphalerite  

Perovskite  
Diamond  . 

tglcstonite. 

Hauerite  

Alabandite      .  . 

Cuprite 

SMITHSONIAN  TABLEC- 


TABLE  340. 

INDEX    OF    REFRACTION. 
Miscellaneous  Monorefringent  or  Isotropic  Solids. 


283 


Substance. 

Spectrum 
line. 

Index  of 
refraction. 

;  — 

Authority. 

Albite  glass 

D 

Amber  
Ammonium  chloride 

D 
D 

.546 

Mtihlheim 
Grailich 

Anorthite  glass  

D 

t;7cc 

Asphalt  .                    

D 

635 

E  L  Nichols 

o  6?ou 

621 

Bell  metal  

D 

0052 

Beer 

Boric  Acid  melted 

c 

D 

«       <«         « 

F 

„ 

Borax  melted 

c 

,, 

D 

4630 

« 

<«           « 

F 

<4 

Camphor  

D 

•  532 

Kohlrausch 

D 

5462 

Mtihlheim 

Canada  balsam  

D 

•  53O 

Mean 

Ebonite  . 

red 

.66 

Ayrton  Perry 

Fuchsin 

A 

03 

B 

•  *9 

ii 

c 

33 

« 

<« 

G 

•97 

<« 

ii 

H 

•32 

« 

Gelatin,  Nelson  no.  i  
"        various 

D 
D 

•530 
1.5  6-1.534 

Jones,  1911 

Gum  Arabic  

red 

.480 

Jamin 

red 

.514 

Wollaston 

Obsidian 

D 

i  .  482—1  .  496 

Various 

Phosphorus  

D 

.1442 

Gladstone,  Dale 

Pitch    .      . 

red 

.531 

Wollaston 

Potassium  bromide  

D 

•S593 

Topsoe,  Christiansen 

"          chlorstannate.  .  .  . 

D 

•  6574 

iodide  

D 

.6666 

«                 « 

Resins:  Aloes  
Canada  balsam 

red 
red 

.619 
.528 

Jamin 
Wollaston 

Colophony  .  .  . 

red 

•  548 

Jamin 

Copal....    
Mastic 

red 
red 

.528 
535 

Wollaston 

Peru  balsam  
Selenium  .  .           .           

D 
A 

593 
61 

Baden  Powell 
Wood 

B 

68 

« 

C 

73 

« 

« 

D 

93 

ft 

Sodium  chlorate  

D 

5150 

Dussaud 

Strontium  nitrate  

D 

5667 

Fock 

SMITHSONIAN  TABLES. 


284 


TABLE  341. 

INDEX    OF    REFRACTION. 
Selected  Uniaxial  Minerals. 


The  values  are  arranged  in  the  order  of  increasing  indices  for  the  ordinary  ray  and  are  for  the  sodium  D  line  unless 
otherwise  indicated.  Selected  by  Dr.  Edgar  T.  Wherry  from  a  private  compilation  of  Dr.  Esper  S.  Larsen  of  the  U.  S. 
Geological  Survey. 


Mineral. 

Formula. 

Index  of  refraction. 

Ordinary 
ray. 

Extraordinary 

ray. 

(a)    UNIAXIAL  POSITIVE  MINERALS. 

Ice 

HzO 

MgFj 
CuO.SiO2.2H2O 
2CaO.Al2O3.sSiO2.6H2O 
(Ca,  Na2)O.Al203.4Si02.6H2O 
2KCl.FeCl2.2H20 
2Na2O.3AlsO3.6SiO2.7H2O 
KzO.SCaO.ieSiO^^H^ 
Si02 
FeTOs.sSOa.gHzO 
MgO.HiKD 
KXX3AlzO3.4SO3.6H20 
S(Mg,  Fe)O.Al203.3SiO2.4H2O 
2Fe2O3.P2O5.i2H2O 
6Na2O.6(Ca,  Fe)O.2o(Si,  Zr)O2.NaCl 
CuO.SiO^H^ 
2BeO.Si02 
2CeOF.Ca0.3CO2 
2ZnO.SiO2 
2(Ca,  Mn,  Fe)O.(Al,  Fe)(OH,  F)O.2SiO2 

Y203.P.05 

2oCuO.SO3.2CuCl2.2oH2O 
BaO.TiO2.3SiO2 
6PbO.4(Ca,  Mn)O.6SiO2.H2O 
CaO.WOs 
ZrO2.Si02 
CaO.MoOs 
HgCl 
SnOa 
ZnO 
PbO.PbCh.COz 
Pb0.2PbCl2 
Agl 
FeO.(Ta,  CbJzOs 
ZnS 
6¥eO.S\xtO3.5TiOi 
CdS 
TiOz 
CSi 
HgS 

•  309 

•  378 
.460  ± 
•475 
.480  ± 
.488 
.490 
•  535  * 
•5-44 
•550 
•  559 
•  572 
•  576 
•  582 
.606 
•  654 
•  654 
.676 
.694 
.716  ± 
.721 
.724 
•  757 
.910 
.918 
.923  ± 
.967 
•973 
•997 
.008 
.114 
.130 

.210 
.270 
.356 
•450 
.506 
.6l6 
•654 
•854 

•  313 
•39° 

•570  =t 
.486 
.482  ± 
-500 
•  502 
•537  =*= 
•553 
•556 
•  580 
•  592 
-579 
•645 
.611 
.707 
.670 
•  757 
•  723 

'.816 
•  746 
.804 
•945 
•934 
.968  ± 
.978 
.650 
•093 
.029 
.140 

.210 
.220 

.  420  (Li  light) 
•  378 
.510  (Li  light) 
•  529 
•  903 
•  697 

3-201 

Sellaite 

Chrysocolla  

Laubanite 

Chabazite 

Douglasite              

Hydronephelite                  . 

Apophyllite  

Quartz                 .         

Brucite  

Alunite  ...      .                

Cacoxenite  

Eudialite 

Phenacite  

Parisite 

Willemite  

Vesuvianite    

Connellite  

Benitoite      

Scheelite  
Zircon 

Powellite 

Calomel          

Cassiterite 

Z  incite 

Phosgenite         

Penfieldite 

lodyrite    

Tapiolite                     

Wurtzite 

Derbylite     

Greenockite                

Rutile 

Moissanite       

(b)    UNIAXIAL  NEGATIVE  MINERALS. 

Chiolite  
Hanksite 

2NaF.AlF3 
iiNa2O.gSO3.2CO2.KCl 
3CaO.C02.Si02.S03.isH20 
eMgO.Ali-Os.CCk.isHiiO 
4Na2O.Ca0.4Al203.2C02.9Si02.3H2O 
K2O.4CaO.2Al2O3.24Si02.H2O 
KaO.AliO».2SiOi 
AhOs.C^Og.iSHzO 
"Ma"  =  sNa^.sAhOs.iSSiO^NaCl 
Na2O.Al203.2Si02 

•349 
.481 
•507 
•  512 
•524 
•532 
•537 
•539 
•539 
•  542 

.342 
.461 
.468 
.498 
.496 
•529 
•533 
•5ii 
•537 
•538 

Thaumasite  

Hydrotalcite    .  . 

Milarite    

Kaliophilite 

Mellite  

Marialite 

Nephelite  

SMITHSONIAN  TABLES. 


TABLES  341-342. 

INDEX    OF    REFRACTION. 

TABLE  341  (Continued).  —  Selected  Uniaxial  Minerals. 


285 


Mineral. 

Formula. 

—                                   .  . 

Index  of  refraction. 

Ordinary 
ray. 

Extraordinary 
ray. 

(6)    UNIAXIAL  NEGATIVE  MINERALS  (continued). 

Wernerite  
Beryl 

MeiMai  ± 
3BeO.Al2O3.6SiO2 
CuO.2UO3.P2O6.8H2O 
"Me"  =  4CaO.3Al203.6SiO2 
Contains  NazO,  CaO,  AhOs,  SiO2.  etc. 
9Ca0.3P2O5.Ca(F,  Cl)2 
CaO.C02 
2CaO.Al2O3.SiO2 
Contains  Na2O,  FeO,  AbOa,  B2O3,  SiC%  etc. 
CaO.MgO.2CO2 
MgO.CO2 
MnO.H2O 
A12O3 
ZnO.CO2 
MnO.CO2 
K2O.3Fe2O3.4SO3.6H2O 
FeO.C02 
9Pb0.3P2O5.PbCl2 
3PbO.2Si02 
9Pb0.3As205.PbCl2 
PbO.PbCl2 
PbO.W03 
(MR,  Fe)O.TiO2 
9Pb0.3V205.PbCh 
PbO.MoOs 
Ti02 
PbO 
3Ag2S.As2S3 
3Ag2S.Sb2S3 
Fe203 

•  578 
.581  =*= 
•  592 
1.597 
.634 
•634 
.658 
.669 
.669* 
.682 
.700 
.723 
.768 
.818 
.818 
.820 
.875 
.050 
.070 
•135 
•'5° 
.269 
-310 
•354 
.402 
•554 
•  665 
•979 
3.084 
3.220 

•  551 

:£• 

.560 
.629 
•  631 
.486 
-658 
.638=*= 
•  503 
•  509 
.681 
.760 
.618 
•595 
715 
•635 
.042 
.050 
.118 
.040 
.182 
•950 
.299 
.  304  (Li  light) 
•  493 
.  535  (Li  light) 
.711     ' 
.881     "      " 
.940     ' 

Torbernite  
Meionite 

Melilite  

Apatite  ...    

Calcite 

Gehlenite  
Tourmaline 

Dolomite  
Magnesite 

Pyrochroite  

Corundum   .            ; 

Smithsonite  ;  

Rhodochrosite  

Jai'osite 

Siderite  
Pyromorphite 

Barysilite.  

Mimetite 

Matlockite  

Stolzite  
Geikielite 

Vanadinite.  .  . 

Wulfenite. 

Octahedrite  

Massicotite  
Proustite 

Pyrargyrite 

Hematite  

TABLE  342.  —  Miscellaneous  Uniaxial  Crystals. 


Crystal. 

Spectrum 
line. 

Index  of  refraction. 

Authority. 

Ordinary 
ray. 

Extraordinary 
ray. 

Ammonium  arseniate  NH^HisAsO^                       

D 
D 
D 
D 
Li 
D 
F 
D 
C 
D 
D 
D 
F 
D 
C 
D 

.5766 
.6588 
.769 
.308 
•  297 
-539 
.5762 
.5674 
•5632 
•457 
-586 
•447 
•5173 
•5109 
.5078 
.614 

•  5217 
.6784 
.760 
•  313 
•  304 
•541 
•  5252 
•  5179 
.5146 
.466 
.336 
•453 
•  4930 
.4873 
.4844 
•  599 

T.  and  C* 
Mean 
Osann 
Meyer 

Kohlrausch 
T.  and  C. 

Mean 
T.  and  C. 
Martin 

Benzil  (CeH&CO)2 

Corundum,  A12O3,  sapphire,  ruby  

Ice  at  —8°  C 

Ivory                                   .      

«                 «               « 

Sodium  arseniate  Na3AsO4  i2H2O                   

:t        nitrate  NaNOs 

"       phosphate  NasPO4  i2H2O 

Nickel  sulphate  NiSO4  6H2O                         

«             it                 « 

Topsoe  and  Christiansen. 


SMITHSONIAN  TABLES. 


286 


TABLE  SiS. 

INDEX   OF    REFRACTION. 
Selected  Biaxial  Minerals. 


The  values  are  arranged  in  the  order  of  increasing  /3  index  of  refraction  and  are  for  the  sodium  D  line,  except  where 
noted.  Selected  by  Dr.  Edga;  T.  Wherry  from  private  compilation  of  Dr.  Esper  S.  Larsen  of  the  U.  S.  Geological 
Survey. 


1  

Mineral. 

Formula. 

.  
Index  of  refraction. 

na 

5 

my 

(a)  BIAXIAL  POSITIVE  MINERALS. 

Stercorite                                             

Na2O.  (NH4)2O.P2O5.9H2O 
AhOs.SOa.gHjO 
SiO2 
Na2O.SO3 
KCl.MgCl2.6H2O 
Al203.3Sa.i6H20 
FeO.S03.7H20 
Na2O.Al203.3SiO2.2H2O 
K2O.S03 
(NH4)2O.2MgO.P205.i2H2O 
CaO.Al2O3.6SiO2.3H2O 
(Na»,  Ca)O.Al203.2Si02.3H20 
(K2,  Ba)O.A]2O3.5SiO2.5H2O 
Li^.AlzOs.SSiCfe 
2CaO.P205.H20 
2MgO.P205.7H2O 
CaO.S03.2H20 
fNHOiO.SO. 
"Ab"  =  Na2O.Al2O3.6SiO2 
4Mg0.3C02.4H20 

3Al2O3.2P2O6.I2(H2O,  2HF) 

MgO.S03.H20 
2Fe203.sS03.i8H2O 
CaO.C2a.H20 

Als04.Ps06.4lW) 

Ab2Ans 
A12C>3.3H2O 
3MgO.P205.MgF2 
CaO.S03 
2CaO.3B2O3.sH2O 
Na2O.Al203.P206.(H2O,  2HF) 
3FeO.P205.8H20 
Na2O.4CaO.6SiO2.H!!O 
2ZnO.Si02.H20 
4MgO.2Si02.Mg(F,  OH)2 
Cu0.3Al203.2P206.9H2O 
2A10F.Si02 
SrO.SOs 
2CaO.Al2O3.3Si02.H2O 
BaO.SO3 
MgO.Si02 
Al2O3.SiO2 
2MgO.SiO2 
MgO.Si02 
2BeO.AbQt.3SiOt.Hi0 
3MnO.P205.MnF2 
Li2O.Al2Os.4SiO2 
CaO.MgO.2SiO2 
2(Mg,  Fe)O.Si02 
Li2O.2(Fe,  Mn)O.P2O5 

•  439 
•  459 
.469 
•464 
.466 
•474 
.471 
.480 
•494 
•  495 
.498 
•497 
•  503 
•  504 
•515 
•  514 
.520 

•521 

•  525 
•  527 
•  525 
•  523 
•  530 
.491 
•  551 
•559 

£ 

:$ 

•594 
•  579 
•595 
.614 
.609 
.610 
.  619 
.622 
.616 
.636 
•  633 
.638 
.635 
•  650 
.652 
.050 
.660 
.664 
.662 
.688 

•441 

•464 
•470 
•474 
•475 
•476 
•478 
.482 
•495 
•496 
•499 
•503 
•  505 
.510 
.518 
•  519 
•523 
•  523 
•529 
•530 
•534 
•535 
•543 
•555 
•558 

•5^ 
•  566 

•  570 
•  576 
•592 
.603 
•  603 
.606 
.617 
.619 
.620 
.620 
.624 
.626 
.637 
.042 
.642 
.651 
•  653 
•655 
.660 
.666 
.671 
.680 
.688 

.469 

•  470 

•  473 
•485 
•494 
•  483 
.486 
•  493 
•497 
•504 
•505 
•525 
•  508 
•  5i6 
•  525 
•533 
•  530 
•  533 
•536 
•540 

•» 

•  595 
•  650 
•  582 
•  568 
.587 
.582 
.614 
.614 
.615 
•  633 
•  634 
•  636 
•  639 
.650 
.627 
.631 
•  649 
.648 
•  657 
•  653 
.670 
.658 
.671 
.672 
.676 
.694 
.699 
.692 

Tridymite                                      

Thenardite                                          

Camallite 

Alunogenite                                   

Natrolite                          

Arcanite 

Struvite  

Heulandite                                 

Thomsonite 

Petalite                                            

Gypsum 

Albite                                         

Wavellite  

Kieserite                                        

Whewellite  .                     

Variscite                                                 .    . 

Labradorite  

Gibbsite                                   

Wagnerite 

Anhydrite  

Colemanite 

Fremontite  

Vivianite                             

Pectolite 

Calamine        

Chondrodite 

Topaz                         

Cefestite 

Prehnite   

Barite                                                        .    . 

Anthophyllite  

Sillimanite     

Forsterite 

Enstatite  

Euclasite 

Triplite 

Spodumenite  

Diopside 

Olivine  

Triphylite  

SMITHSONIAN  TABLES. 


TABLE  343  (continued). 

INDEX   OF   REFRACTION. 

Selected  Biaxial  Minerals. 


287 


Mineral. 

Formula. 

Index  of  refraction. 

*a 

nft                    ny 

(a)  BIAXIAL  POSITIVE  MINERALS  (continued). 

Zoisite                             

4CaO.3Al2O3.6Si02.H2O 
Fe2O3.P2Oa.4H2O 
A1203.H20 
2FeO.5Al2O3.4SiO2.H2O 
BeO.AhQj 
3CuO.2C02.H20 
Fe2O3.As2Oo.4H2O 
4CuO.As206.H2O 
PbO.SOs 
CaO.TiOz.SiOz 
As2Os 

s 

PbClz 
MnO.WOs 
Mn2O3.H2O 
PbO.WOs 
2PbO.PbCl2 
(Fe,  Mn)O.Ta2Os 
(Fe,  Mn)O.W03 
PbO.CrOs 
2Fe2O3..3TiO2 
Sb2Os.Ta2Oo 
HgO 
Ti02 
PbO 

.700 
.710 
.702 
.736 
•747 
•  730 
.765 
•  772 
-877 

.000 

.871 
•  950 

.200 
.170 
.240 
.270 
.240 
.260 
.310 

.310 
.380 

•  374 
•  370 
•583 
•Sio 

.702 
.710 
.722 
.741 
•  748 
•  758 
•774 
.810 
.882 
.907 
.920 
•043 
.217 

.220 
.240 
.270 
.270 
•  320 
.360 
•370 
•390 
.404 
•  500 
.586 
.6lO 

1.706 

'1-745 

:3 
:g 

•797 
.863 
•894 
•  034 
.010 
.240 
.260 
-320 
•  530  (Li) 
•  300 
•  310 
.430  (Li) 
.460  (Li) 
.  660  (Li) 
.420  (Li) 

•'650  (Li) 
.741 
.710 

Diasporite      

Staurolite 

Chrysoberyl  

Azurite 

Scorodite 

Olivenite  

Anglesite  . 

Titanite  

Claudetite  

Sulfur 

Cotunnite  

Huebnerite.  .  . 

Manganite  

Raspite  

Mendipite 

Tantalite  

Wolframite 

Crocoite 

Pseudobrookite  

Stibiotantalite  ... 

Montroydite 

Brookite  

Lithargite.  .  . 

(b)  BIAXIAL  NEGATIVE  MINERALS. 

Mirabilite  
Thomsenolite 

Na2O.SO3.ioH20 
NaF.CaF2.AlF3.H2O 
Na2O.C02.ioH2O 
K2O.A12O3.4SO3.24H2O 
MgO.SO3.?H2O 
B2O3.H20 
Na2O.2B2O3.ioH2O 
ZnO.SOs.7H20 
MgO.Al2O3.4Sa.22H2O 
Na2O.MgO.2SOs.4H2O 
3Na2O.4C02.5H20 
Na2O.CO2.H20 
(Ca,  Na2)O.Al2O3.6SiO2.sH2O 
K2O.N205 
MgO.S03.KC1.3H20 
Na2O.CaO.2CO2.sH20 
CaO.Al2O3.3SiO2.3H;!O 
CaO.AhOs^SiCMHiiO 

K^.AhOt.esiCb 

Same  as  preceding 
(Na,  K)2O.Al203.6SiO2 
Na2O.Ca0.2S03 
4(Mg,  FeX>-4AijO*.ioSiO^H<0 
CuO.SOi.sHzO 
Ab4An 

•394 
.407 
•405 
•430 
•  433 
•  340 
•  447 
•  457 
.476 
.486 
.410 
.420 
•494 
•  334 
•494 
•  444 
•512 
•513 
.518 
•  522 
•  523 
•SIS 
•  534 
.516 
•539 

-396 
.414 
•425 

•  452 
•455 
•456 
•  470 
.480 
.480 
.488 
•  492 
•495 
•498 
•505 
•  505 
•  516 
•519 
•524 
.524 
.526 
•  529 
•  532 
•  538 
•539 
•  543 

•  398 
•  415 
.440 
•  458 
.461 
•459 
•472 
.484 
•483 
•489 
•542 
.518 
•500 
.506 
.516 
•  523 
•  519 
•525 
•  526 
•  530 
531 
-536 
•540 
.546 
•547 

Natron  

Kalinite                             

Sassolite  

Borax                                     .  '.  

Goslarite  

Pickeringite           

Bloedite 

Trona  

Thermonatrite                           

Stilbite 

Niter  

Gaylussite  

Scolecite 

Laumontite  

Orthoclase  

Anorthoclase  

Glauberite      .                

Chalcanthite  

Oligoclase                           

SMITHSONIAN  TABLES. 


288 


TABLE  343  (continued). 
INDEX  OF  REFRACTION. 
Selected  Biaxial  Minerals. 


Mineral. 

Formula. 

Index  of  refraction. 

"a                   «/J                  «y 

(b)  BIAXIAL  NEGATIVE  CRYSTALS  (continued). 

Bervllonite 

NaiO.2BeO.P205 

Al203.2SiO2.2H20 

K2O.4(Mg,  Fe)0.  2Al2a.6SiOj.HjO 
CaO.2UO3.P2Os.8H2O 
"An"  =  CaO.Al203.2SiOj 
La203.3C02.9H20 
AliOs^SiOj-HzO 
3MgO.4SiO2.H20 
3ZnO.P2Os.4H20 
K20.3Al203.6SiOj.2H2O 
Al203.P205.2LiF 
Al203.3SiOj.2(K,Li)F 
K20.6MgO.Al203.6SiO2.2HjO 
Ca0.3Mg0.4SiO2 
Ca0.3(Mg)Fe)O.4SiOj 
CaO.SiO2 
(Fe,  Mg)O.Al203.P205.H2O 
CaO.B2O3.2SiO2 
Na20.2FeO.Al2O3.6SiOj 
AhOs.SiOj 
Contains  Na2O,  MgO,  FeO,  Si02,  etc. 
2  CaO.  2  SiO2.B2O3.H2O 
3CoO.As205.8HjO 
CaO.MgO.SiOj 
SrO.COj 
BaO.COj 
CaO.C02 
6(Ca,  Mn)O.2Al203.B203.8SiO2.H2O 
8Al203.B203.6Si02.H20 
Al2Os.SiO2 
4Ca0.3(Al,  Fe)203.6SiOj.HjO 
3CuO.CuCl2.3H2O 
2FeO.SiO2 
2(Pb,  Cu)O.Sa.HjO 
2CuO.CO2.HjO 
2PbO.S03 
4PbO.S03.2COj.HjO 
PbO.COz 
PbCh.PbO.HjO 
PbO.PbClj 
ZrOj 
Fe203.H2O 
2Fe2O3.3H2O  in  part 
FejOs.HjO 
SbjOs 
2FejO3.HjO  in  part 
AsS 
Hg2OCl 
(Tl,  Ag)2S.PbS.2AsjS3 
SbjSs 

•552 
.561 
•  541 
•553 
•576 
•  520 
•  552 
•539 
•  572 
•  561 
•579 
.560 
.562 
.609 
.611 
.616 
.603 
.632 
.621 
.632 
.629 
.625 
.626 
.651 
.520 
•529 
-531 
.678 
.678 
.712 
.729 
.831 
.824 
.818 
-655 
-930 
.870 
.804 
.077 
.040 
.130 
•  930 
.170 

.210 
.ISO 
450 
460 

350 
3.078 
3-194 

.558 
.563 
•574 
•575 
•584 
.587 
-588 
.589 
•590 
•590 
•593 

!e 
is 

.029 
.632 
.634 
.638 
.638 
.642 

•&3 

.661 

.662 
.667 
.676 
.682 
.685 

.686 
.720 
-754 
.861 
.864 
.866 
•  875 
•990 
.000 
.076 
.116 
.150 
.190 
.210 
.290 
•  350 
•350 
•  550 
•  590 
.  040 
3-176 
4-303 

.561 
•565 
•  574 
•577 
-588 
.613 
.600 
•589 
•590 
•594 
-597 
-605 
.606 
•635 
.636 
.631 
•639 
.636 
.638 
•643 
.653 
.669 
.699 
.668 
.667 
-677 
.686 
.688 
.689 
.728 
.768 
.880 
.874 
-909 
.909 
.020 
.010 
.078 
.158 
.150 
.200 
•  510 
.310 
•  350  (Li) 
•  350 
-  550  (Li) 
.610  (Li) 
.  670  (Li) 
3-188 
4.460 

Kaolinite  

Biotite  ...    . 

Autunite 

Anorthite  

Lanthanite.  .  . 

Pyrophyllite  .  . 

Talc    

Hopeite 

Muscovite  

Amblygonite  . 

Lepidolite  .   . 

Phlogopite  

Tremolite.  . 

Actinolite 

Wollastonite  

Lazulite    . 

Danburite  

Glaucophanite  

Andalusite 

Hornblende  

Datolite  

Erythrite 

Monticellite  

Strontianite. 

\Yitherite 

Aragonite  

Axinite 

Dumortierite 

Cyanite  

Epidote 

Atacamite  

Fayalite  

Caledonite 

Malachite  

Lanarkite  . 

Leadhillite  

Cerussite  
Laurionite 

Matlockite  

Baddeleyite 

Lepidocrocite 

Limonite  

Goethite 

Valentinite 

Turgite  

Realgar 

Terlinguaite  

Hutchinsonite 

Stibnite 

SMITHSONIAN  TABLES. 


TABLES  344-345. 

INDEX  OF    REFRACTION. 

TABLE  344.  —  Miscellaneous  Biaxial  Crystals. 


289 


Crystal. 

Spectrum 
line. 

•  .. 

Index  of  refraction. 

Authority. 

"a 

»/3 

"y 

Ammonium  oxalate,  (NH4)2C2O4.H2O.  .  . 
Ammonium  acid  tartrate, 
(NH4)H(C4H4O6)  

D 

D 
D 
D 
D 
D 
D 
D 
Cd,  0.226/4 
H,    0.656/1 
D 
D 
red 
D 
F 
D 
C 
yellow 
D 
D 
red 
Tl 
D 
Li 
D 
F 
D 
C 

i.438i 
1.5188 

•  5697 
•  4932 
•  5390 
•495 
•432 
.4990 
•4307 
.7202 

•6873 
•3346 
.4976 
•4932 
.4911 

.6610 

.5422 
•5397 
•5379 
4953 
4620 
4568 
4544 

1-5475 

.5614 
.581 
•6935 
•4977 
•5435 
•  501 
•455 
•  5266 
•4532 
•738o 
•7254 
.722 
•5056 
•4992 
.4946 
.4928 
-526 
•555 
•6994 
•5332 
•  5685 
•5667 
•5639 
5353 
4860 
4801 
4776 

i  •  5950 
1.5910 

•  7324 
.5089 

.526 
.461 
•  5326 
•  4584 
•  8197 

•  7305 
.5064 
.5029 
.4980 

•4959 

•7510 

•  5734 
.57i6 
•5693 
.6046 
.4897 
.4836 
.4812 

Brio 

T.  and  C  * 

Cloisaux 
Liweh 
Schrauf 

Grailich 
Genth 
Means 
Borel 

Dufet 
T.  and  C. 

Mallard 
Schrauf 
T.  and  C. 

Groth 

Dufet 
Brio 
Calderon 

Means 
T.  and  C. 

Ammonium  tartrate,  (NH^C^Oe  
Antipyrin,  CnH^NOz 

Citric  acid,  CeHsO.I^O.  .  . 
Codein,  Ci8H21N03.H20  
Magnesium  carbonate,  MgCOs.3H2O.  .  .  . 
sulphate,  MgSO4.7H2O  

« 

Potassium  bichromate,  K2Cr2O? 

chromate,  K2CrO<  

nitrate,  KNO3  .............. 
sulphate,  K2SO4  

Racemic  acid,  C4H6O6.H2O  
Resorcin,  CeH6O2 

Sodium  bichromate,  Na2Cr2O7.2H2O  
acid  tartrate,  NaH(C4H4O6).2H2O 
Sugar  (cane),  Ci2H22Oii  

«         « 

Tartaric  acid,  C4H6O6  (right-)  
Zinc  sulphate  ZnSCu  7H2O 

«           it 

*  Topsoe  and  Christiansen. 

TABLE  345.  —  Miscellaneous  Liquids  (see  also  Table  346),  Liquefied  Gases,  Oils, 

Fats  and  Waxes. 


Substance. 

Temp. 
°C 

Index  for  D 
o.  589/4. 

Refer- 
ence. 

Substance. 

Temp 

Index  for  D 
o.  589/4- 

Refer- 
ence. 

Liquefied  gases: 
Br2 
Cls  
CO2 

15 

14 
15 
18 
6 
18.5 
-190 
16.5 
-90 
15 
-181 
IS- 
16.5 

10 

16.5 

iS-5 
IS 

20 
20 
15-5 

IS 

15.5 

27 

20 
IS-S 

•  659 
•  367 
•  i9S 
•  325 
.180 
•  384 
-205 
•325 
•  330 
•194 

.  221 

•350 
•  252 

:9 

.4728-1.4753 
.  4799-1  •  4803 
.  47-1  .  48 
.  5301-1  .  5360 
.4587 
.4790-1.4833 
•4737-1-4757 
.4757-1.4768 
.460-1.467 
.4702-1.4720 

a 
b 
b 
b 
b 
b 
c 
b 
c 
b 
c 
b 
b 
b 
b 

d 
e 
e 
e 
d 
e 
d 
e 
e 
d 

Oils: 

Lavendar  
Linseed  
Maize  
Mustard  seed.  .  . 
Neat's  foot  
Olive 

20 
IS 
15-5 
iS-5 
IS 

I5'5 
60 

15-5 
20 
15-5 

25 

15-5 

25 

15.5 
15.5 

15-5 
15-5 
19 
40 

40 
75 
84 
40 
40 
60 

.  464-1  •  466 
.4820-1.4852 
•4757-1-4768 
.4750-1.4762 
.  4695-1  •  47o8 
.4703-1-4718 
•  4510 
.4723-1.4731 
.464-1-468 
•  4770 
.4677 
.4748-1.4752 
•4741 
•4742 
.4760-1.4775 
.4665-1-4672 
•4739 
•503 
4649 

4552-1.4587 
4398-1.4451 
4520-1.4541 
4560-1.4518 
4584-1-4601 
4510 

e 

e 
d 
d 
e 

d 
d 
d 

e 
d 
e 
d 

e 
d 
e 

e 
d 

e 
e 

e 
e 
e 
e 
e 
e 

C2N2  
C2H4  
H2S 

N2  
NH3  
NO  
N2O  
02  
SO2 

Palm  
Peanut  
Peppermint  
Poppy  
Porpoise.  .  .  . 

Rape  (Colza)  .... 
Seal  

HC1  
HBr  
HI.. 

Soja  bean  
Sperm  
Sunflower 

Oils: 
Almond  
Castor  
Citronella.  .  .  . 
Clove  
Cocoanut.  .  .  . 
Cod  liver  
Cotton  seed  .  . 
Croton  
Eucalyptus  .  . 
Lard  

Tung  
Whale 

Fats  and  Waxes: 
Beef  tallow  
Beeswax  
Carnauba  wax.  .  .  . 
Cocoa  butter  
Lard  
Mutton  tallow  .  .  . 

References:    (a)  Martens;    (b)  Bleekrode,  Pr.  Roy.  Soc.  37,  339,  1884;    (c)  Liveing,    Dewar,  Phil.  Mag., 
1892-3;    (d)  Tolman,  Munson,   Bui.  77,  B.  of    C.,  Dept.   Agriculture,    1905;    (e)  Seeker,   Van   Nostrand's 
Chemical  Annual.    For  the  oils  of  reference  d,  the  average  temperature  coefficient  is  0.000365  per  °  C. 

SMITHSONIAN  TABLES. 


TABLE  346. 

INDEX  OF  REFRACTION. 
Indices  of  Refraction  of  Liquids  Relative  to  Air. 


Substance. 

Den- 
sity. 

Temp. 

Indices  of  refraction. 

Author- 
ity. 

0.397M 

0-4.UM 

0.486/4 

0.589JU 
D 

0.656^1 
C 

Acetaldehyde,  CHjCHO. 

0.780 
0.791 
i.  022 
0.794 
0.808 
0.800 

0.804 
0.880 

1.487 
1-293 
1.263 
1.591 
1.090 
1.512 
1.489 
0.728 
0-715 

1.109 
i.  219 
i.  260 
0.660 
0.679 
3-318 

0.962 

I.OI2 
0.707 
0.92 
0.99 
0.99 
I.  06 

1.05 
O.92 

0.77 
0.87 
0.625 
i.  060 

I.O2I 
O.9IO 
0.982 

20 

20 

20 
20 
0 

20 

20 
20 
20 
20 
2O 
0 
20 
20 
20 
20 
20 
14.9 
20 
20 
20 
20 
2O 
20 
23-3 
20 
20 
98.4 
22.4 
I5-I 
0 
I5-I 
21.4 
20 
10 
22.5 
23-5 
0 
O 

10.6 

20.7 

I5i 
40.6 

82.7 

16.6 

20 
20 
0 

40 
80 

1-3399 

1.7289 
I-7I75 
1.6994 

i.4<* 

1.8027 

I  .  6084 

I  .  7039 
1.6985 

i  •  4939 
I.49I3 

1-3435 
1-3444 
1.34" 
1-3332 

•  3394 
.3678 
.6204 
•3362 
•  3773 
.3700 
—  .  0004 
-3938 
•  5236 
—  .0007 
.7041 
.6920 
.6748 
.4729 
.6679 
.4679 
-458 
.4200 
.3607 
—  .0006 
-395 
.3804 
.4828 
-3836 
•4059 

•5439 

.4097 

1-5775 

1-3645 
1-5684 

1.5816 

1.5170 
i  -  3404 
I-34I3 
i.338o 
1.3302 

-3359 
-3639 
.6041 
•3331 
•  3739 
.3666 
—  .0004 
.3901 
.5132 
—  .0006 
.6819 
.6688 
-6523 
.4676 
.6470 
.4624 
-4530 
.4160 
.3576 
—  .  0006 
-392 
-3764 
.4784 
•3799 
.4007 
.7692 
—  .  0007 
.6031 

.4046 
.4847 
-5743 
•5647 
•  5623 
-6389 
.6314 
.6508 
-4825 
•4644 
.4817 
•4793 
.3610 
•5558 
.5356 
.5659 
-5386 
.5070 
•  3372 
.338o 
•3349 
.3270 

i^O^tf 
^ISO^ 
•5863 
-3290 
•3695 
•  3618 
—  .  0004 
.3854 
.5012 
—  .0006 
•  6582 
•  6433 
.6276 
.4607 
.6245 
•4557 
.4467 
.4108 
.3538 
—  .0006 
-3853 
-37I4 
-4730 
•  3754 
•3945 
•7417 
—  .  0007 
•5823 
•5239 
•  4007 
.4782 
•  5572 
•  5475 

.6104 
.6026 
.6188 
•  4763 
•  4573 
•4744 
•  4721 
.3581 
•5425 

.5485 

•4955, 
*^3S3Q 
.3338 
-3307 
•3230 

-3298 
-3573 
•5793 
.3277 
.3677 
•3605 
—  .  0004 
.3834 
•  4965 
—  .0006 
.6495 
-6336 
.6182 
•4579 
.6161 
•4530 
•4443 
.4088 
-3515 
—  .0006 
•  3830 
-3693 
.4706 
•3734 
-3920 
•  7320 
—  .0006 
•5746 
.5198 
•3987 
•4755 
.5508 
-5410 
•  5391 
.6007 
•5930 
.6077 
•  4738 
•4545 
•  4715 
.4692 
-3570 
•5369 
-5174 
•5419 
.5228 
.4911 
-3312 
-33I9 
.3290 
-3313 

la 
Means 

ib 
Means 

2 

i 
Means 

3 

4 

id 

1C 
1C 

Means 
te 
Means 

la 

5 

1C 
1C 

Means 
if 

1C 

ic 
6 

I 

5 
7 

I 

6 
6 

! 

le 

11 

li 
ih 

10 

Means 

Acetone,  CHsCOCHs.  .  . 
Aniline,  CaHs.NHj.  . 

Alcohol,  methyl,  CHs.OH.  .  . 
"       ethyl  CiH6.OH  

"  dn/dt  
n-propyl  CjH7.OH  
Benzene,  CBH6  

"          C«H«,  dn/dt  
Bromnaphthalene,  Ci0H7Br.  .  .  . 
Carbon  disulphide,  CSt  

"       tetrachloride,'  CCU  .  .  . 
Chinolin,  C9H7N  
Chloral,  CCb.CHO 

Chloroform,  CHCU  

Decane,  CioH« 

Ether,  ethyl,  C2H5.O.C2HB  
"       dn/dt  
Ethyl  nitrate,  C2Hs  O  NOj 

Formic  acid,  H.COiH  
Glycerine,  CsHsOs  
Hexane,  CHsCCH^CHs  .  '.  . 

Hexylcae,  CH3(CH2)3CH.CH2.  . 
Methyl  iodide,  CHsI 

"      dn/dt    

Naphthalene,  CioHs.  .  .    . 

Nicotine,  GoHuN? 

Octane,  CH3(CHz)8CHs  
Oil,  almond.   ..  . 

anise  seed    

bitter  almond 

cassia  

cinnamon  

olive 

rock  

turpentine  

Pentane,  CHafCH^aCHs.  '.  . 

Phenol,  CeHsOH 

Styrene,  CsHsCH.CHa. 

Thymol,  CioHi4O.  .  . 

Toluene,  CHs.CeHs  
Water,  H2O.  . 

" 

"     

References:   i,  Landolt  and  Bornstein  (a,  Landolt;    b,  Korten;  c,  Briihl;   d,  Haagen;  e,  Landolt,  Jahn; 
f,  Nasini,  Bernheimer;  g,  Eisenlohr;    h,  Eykman;    i,  Auwers,  Eisenlohr);    2,  Korten;  3,  Walter;  4,  Ketteler; 
5,  Landolt;  6,  Olds;  7,  Baden  Powell;  8,  Willigen;  9,  Fraunhofer;   10,  Briihl. 

SMITHSONIAN  TABLES. 


TABLE  347. 
INDEX  OF  REFRACTION. 

Indices  of  Refraction  relative  to  Air  lor  Solutions  of  Salts  and  Adds. 


291 


Substance. 

Indices  of  refraction  for  spectrum  lines. 

Density. 

Temp.  C 

G 

D 

F 

*v 

H 

Authority. 

(a)  SOLUTIONS  IN  WATER. 

Ammonium  chloride 

1.067 

27C-05 

I-3770: 

1  -37936  I-38473 

1  -39336 

Willigen. 

Calcium  chloride 

•39^ 

29-75 

-3485C 
.4400C 

•  3  S^  S^ 

44279 

•355'5 
44938 

.36243 
46001 

ti 

.215 

22.  Q 

•3941  1 

•39652 

40206 

41078 

" 

•143 

25-8 

•37152 

•37369 

•37876 

.38666 

" 

Hydrochloric  acid    . 
Nitric  acid  .... 

I.I66 

•359 

20.75 
18.75 

1.40817 
•39893 

141109 
.40181 

1.41774 

40857 

142816 
41961 

(4 

Potash  (caustic)   .     . 
Potassium  chloride  . 

416 
normal 

II.O 

solution 

40052 
.34087 

40281 
•34278 

.40868 
.34719 

1.35049 

41637 

Fraunhofer. 
Bender. 

" 

" 

double  normal 

.34982 

•35J79 

•35645 

•35 

994 

i 

" 

triple  normal 

•35831 

.36029 

•36512 

-36 

890 

it 

Soda  (caustic)      .     . 
Sodium  chloride  .     . 

1.376 
.189 

21.6 

18.07 

1.41071 

1.41334  1.41936 
•37789    -38322 

1.38746 

142872 

Willigen. 
Schutt. 

" 

.109 

18.07 

•35751 

•35959    -36442 

.36823 

M 

•°35 

18.07 

.34000 

.34I91 

.34628 

•34969 

1 

Sodium  nitrate     .     . 
Sulphuric  acid      .     . 

.811 

22.8 
I8.3 

1.38283 
43444 

1-385 
436 

£ 

I-39I34 
44168 

140121 

44881 

Willigen. 

M 

" 

.632 

18,3 

42227 

42466 

42967 

43 

694 

u 

" 

.221 

•36793 

.37009 

.37468 

.38 

• 

" 

" 

.028 

18.3 

•33663 

.33862 

•34285 

•34938 

< 

Zinc  chloride    .     .     . 

i-359 

26.6 

1-39977 

1.40222' 

140797 

141738 

( 

. 

.209 

264 

•37292 

•37515 

.38026 

.38845 

(b)  SOLUTIONS  IN  ETHYL 

ALCOHOL. 

Ethyl  alcohol  .     .     . 

0.789 

25-5 

I-3579I 

'•359 

7I 

1,36 

39S 

- 

1.37094 

Willigen. 

" 

•932 

27.6 

.35372 

•35556 

•3S 

986 

.36662 

' 

Fuchsin   (nearly  sat- 

urated)    . 

. 

- 

16.0 

.3918 

•398 

.361 

•3759 

Kundt. 

Cyanin  (saturated)    . 

— 

16.0 

•3831 

•3705 

•3821 

M 

NOTE.  — 

Cyanin  in  chloroform  also  acts  anomalouslv 

;  for  example,  Sieben  gives  for 

a  4.5 
For  j 

per  cent,  solution  AU=  i-4593>  P-B=  ^4695,  HF  (green)  =  14514,  PG  (blue)  =  14554. 
i  9.9  per  cent,  solution  he  gives  JJ.A=  14902,  /tf  (green)  =  14497,  /io(blue)  =  14597. 

(c)  SOLUTIONS  OF  POTASSIUM  PERMANGANATE  IN  WATER.* 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 

for 

Wave- 
ength 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

X  10°. 

Hue. 

i  %  sol. 

2  %  sol. 

3  %  sol. 

4  %  sol. 

n  cms. 
Xio". 

line. 

i  %  sol. 

2  %  SOI. 

3  %  sol. 

4  %  sol. 

68.7 

B 

1.3328 

1-3342 

_ 

L3382 

Si.6 

_ 

1.3368 

I-3385 

_ 

_ 

65.6 

C 

•3335 

-3348 

1.3365 

•339  r 

50-0 

- 

•3374 

.3383 

L3386 

1.3404 

6l.7 

— 

•3343 

•3365 

•3381 

.3410 

48.6 

F 

•3377 

- 

.3408 

594 

— 

•3354 

•3373 

•3393 

.3426 

48.0 

— 

•3395 

•3398 

•3413 

58-9 

D 

•3353 

•3372 

•3426 

46.4 

— 

•3397 

.3402 

.3414 

•3423 

56.8 

— 

•3362 

•3387 

•3412 

•3445, 

44-7 

— 

•3407 

•3421 

.3426 

•3439 

55-3 

— 

•3366 

•3395 

•3417 

•3438 

434 

— 

•3417 

— 

•3452 

52-7 

E 

•3363 

42.3 

— 

•3431 

•3442 

•3457 

.3468 

52.2 

•3362 

-3377 

.3388 

SMITHSONIAN  TABLES. 


*  According  to  Christiansen. 


292 


TABLE  348. 
INDEX  OF  REFRACTION. 

Indices  of  Refraction  of  Gases  and  Vapors. 


A  formula  was  given  by  Biot  and  Arago  expressing  the  dependence  of  the  index  of  refraction  of  a  gas  on  pressure  and 

«0_!   p 
temperature.     More  recent  experiments  confirm  their  conclusions.     The  formula  is  nt — i  =  —       /"A"'        ere 

nt  is  the  index  of  refraction  for  temperature  /,  «0  for  temperature  zero,  a  the  coefficient  of  expansion  of  the  gas 
with  temperature,  and/  the  pressure  of  the  gas  in  millimeters  of  mercury.  Fpr  air  see  Table  349. 


(a)     Indices  of  refraction. 

Spectrum 

10s  (n-i) 

Spectrum 

io»  (n-i) 

Wave- 

(n-i )  io». 

line. 

Air. 

line. 

Air. 

length. 

Air. 

0.                 N. 

H. 

A 

.2905 

M 

•2993 

.4861 

.2951 

.2734         .3012 

.1406 

B 

.2911 

N 

•3003 

.5461 

.2936 

•2/17          -299s 

.1397 

C 

.2914 

o 

•3OI5 

•5790 

.2930 

.2710            — 

•1393 

D 

.2922 

P 

3°23 

.6563 

.2919 

.2698          .2982 

.1387 

E 

•2933 

Q 

•3031 

.4360 

.2971 

.2743          co2 

.1418 

F 

•2943 

R 

•3043 

.5462 

•2937 

.2704        .4506 

.1397 

G 

.2962 

S 

•3°53 

.6709 

.2918 

.2683      .4471 

•T38S 

II 

.2978 

T 

.3064 

6.709 

.2881 

.2643      -4804 

.1361 

K 

.2980 

U 

•3075 

8.678 

.2888 

.2650      .4579 

.1361 

L 

.2987 

First  4, 

Cuthbertsons  ;  the  rest,  Koch,  1909. 

(V)  The 

following  are   compiled   mostly  from   a  table  published  by  Briihl  (Zeits.  fur  Phys.  Chem.  vol.  7, 

pp.  25-27). 

The  numbers  are  from  the  results  of  experiments  by 

Biot  and  Arago,  Dulong,  Jamin, 

Ketteler, 

Lorenz,  Mascart,  Chappius,  Rayleigh,  and  Riviere  and  Prytz.     When  the  number  given  rests  on  the  authority 

of  one  observer  the  name  of  that  observer  is  given.     The  values  are  for  o°  Centigrade  and  760  mm.  pressure. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Acetone 
Ammonia 

D 

white 

I.OOIO79-I.OOIIOO 

i  .00038  1  -  1  .  00038  5 

Hydrogen     .     . 

« 

white 
D 

.000138-1.000143 
.000132  Burton. 

« 
Argon  . 

D 
D 

1.000373-1.000379 
1.000281  Rayleigh. 

Hydrogen  sul-  ( 
phide     .     .     | 

D 
D 

.000644  Dulong. 
.000623  Mascart. 

Benzene 

D 

1.001700-1.001823 

Methane  .     .     . 

white 

.000443  Dulong. 

Bromine 

D 

1.001132  Mascart. 

u 

D 

.000444  Mascart. 

Carbon  dioxide 

white 
D 

i  .  000449-  l  •  0004  50 
1.000448-1.000454 

Methyl  alcohol  . 
Methyl  ether     . 

D 
D 

.000549-1.000623 
.000891  Mascart. 

Carbon  disul-    j 

white 

1.001500  Dulong. 

Nitric  oxide  .     . 

white 

.000303  Dulong. 

phide 

D 

1.001478-1.001485 

" 

u 

D 

.000297  Mascart. 

Carbon  mon-     ( 
oxide     .     .     j 

white 
white 

1.000340  Dulong. 
1.000335  Mascart. 

Nitrogen  .     .     . 

M 

white 
D 

.000295-1.000300 
.000296-1  .000298 

Chlorine 

white 

1.000772  Dulong. 

Nitrous 

oxide    . 

white 

.000503- 

i.ooocoy 

« 

D 

1.000773  Mascart. 

« 

u 

D 

.000516  Mascart. 

Chloroform  .     . 

D 

1.001436-1.001464 

Oxygen 

white 

.000272-1.000280 

Cyanogen 

. 

white 

1.000834  Dulong. 

« 

D 

.000271-1.000272 

" 

. 

D 

1.000784-1.000825 

Pentane 

. 

D 

.001711  Mascart. 

Ethyl  alcohol    . 
Ethyl  ether  .     . 

D 
D 

1.000871-1.000885 
1.001521-1.001544 

Sulphur  dioxide 
«             « 

white 
D 

.000665  Dulong. 
.000686  Ketteler. 

Helium 

•      • 

D 

1.000036  Ramsay. 

Water  . 

white 

.000261  Jamin. 

Hydrochloric    j 

white 

1.000449  Mascart. 

«     . 

. 

D 

1.000249-1.000259 

acid  . 

D 

i  .000447         " 

SMITHSONIAN  TABLES. 


293 

INDEX  OF  REFRACTION. 
TABLE  349.  —  Index  of  Refraction  of  Air  (15°C,  76  cm). 

Corrections  for  reducing  -wave-lengths  and  frequencies  in  air  (15°  C,  76  cm)  to  vacua. 

The  indices  were  computed  from  the  Cauchy  formula  (n  —  i)io7  =  2726.43  +  i2.288/(A*X  io~8)  +0.35557 
(A4  X  icr16).  For  o°  C  and  76  cm  the  constants  of  the  equation  become  2875.66,  13.412  and  0.3777  respectively,  and 
for  30°  C  and  76  cm,  2589.72,  12.259  and  0.2576.  Sellmeier's  formula  for  but  one  absorption  band  closely  fits  the 
observations:  n2  =  i  +  0.0005  73  78A2/(X2  —  595260).  If  n  —  i  were  strictly  proportional  to  the  density,  then  (n-i  V 
(»  —  i)t  would  equal  i  +  at  where  a  should  be  0.00367.  The  following  values  of  a  were  found  to  hold: 

A       o.Ss/i  o.75/i  0.65/1  0.55/1  0.45/4  0.35/1  0.25;* 

a       0.003672  0.003674  0.003678  0.003685  0.003700  0.003738  0.003872 

The  indices  are  for  dry  air  (0.05  ±  %  CO2).  Corrections  to  the  indices  for  water  vapor  may  be  made  for  any  wave- 
length by  Lorenz's  formula,  +  0.000041  (m/jfo),  where  m  is  the  vapor  pressure  in  mm.  The  corresponding  frequencies 
in  waves  per  cm  and  the  corrections  to  reduce  wave-lengths  and  frequencies  in  air  at  15°  C  and  76  cm  pressure  to  vacuo 
are  given.  E.g.,  a  light  wave  of  5000  Angstroms  in  dry  air  at  15°  C,  76  cm  becomes  5001.391  A  in  vacuo;  a  frequency 
of  20,000  waves  per  cm  correspondingly  becomes  19994.44.  Meggers  and  Peters,  Bui.  Bureau  of  Standards,  14,  p.  731, 
1918. 


Fre- 

Vacuo 

Fre- 

Vacuo 

Wave- 

Dry air 

Vacuo 

quency 

correction 

Wave- 

Dry  air 

Vacuo 

quency 

correction 

length, 

(n-i) 
X  io7 

correction 
or  X  in  air 

waves  per 
cm 

for  :-  in  air 

A 

.e-r, 

(n  -  i) 
X  io* 

correction 
for  A  in  air 

waves  per 
cm 

i  . 

for  -r  in  air 
A 

Ang- 
stroms. 

15°  C 

76  cm 

(n\  -  X). 
Add. 

i 
X 

/I           A 

\n\      \)  ' 

Ang- 
stroms. 

15°  C 
76  cm 

(n\  -  A) 
Add. 

i 
A 

GariD 

in  air. 

Subtract. 

in  air. 

Subtract. 

2000 

3256 

651 

50,000 

16.27 

55oo 

2771 

•  524 

18,181 

5-04 

2100 

3188 

670 

47,619 

15-18 

5600 

2769 

•  551 

17,857 

4-94 

2200 

3132 

689 

45,454 

14.23 

5700 

2768 

-578 

17,543 

4.85 

2300 
2400 

3086 
3047 

710 
73i 

43,478 
41,666 

13-41 
12.69 

5800 
59oo 

2766 
2765 

.604 
.631 

17,241 
16,949 

ta 

2500 

3014 

754 

40,000 

12.05 

6000 

2763 

.658 

16,666 

4.60 

2600 

2986 

776 

38,461 

11.48 

6100 

2762 

.685 

i6,393 

4-53 

2700 
2800 

2962 
2941 

800 
824 

37,037 
35,714 

10.97 
10.50 

6200 
6300 

2761 
2760 

.712 
•739 

16,129 
15,873 

1:3 

2900 

2923 

848 

34,482 

10.08 

6400 

2759 

.766 

15,625 

4-3i 

3000 

2907 

.872 

33,333 

9.69 

6500 

2758 

.792 

15,384 

4.24 

3100 
3200 

2893 
2880 

.897 
.922 

32,258 
31,250 

9-33 
9.00 

6600 
6700 

2757 
2756 

.819 
.846 

14,925 

4.18 
4.11 

3300 

2869 

•947 

30,303 

8.69 

6800 

2755 

-873 

14,705 

4-05 

3400 

2859 

.972 

29,411 

8.41 

6900 

2754 

.900 

14,492 

3-99 

3500 

2850 

.998 

28,571 

8.14 

7000 

2753 

-927 

14,285 

3-93 

3600 

2842 

.023 

27,777 

7100 

2752 

•954 

14,084 

3.88 

3700 

2835 

.049 

27,027 

7.66 

7200 

2751 

.981 

13,888 

3-82 

3800 

2829 

•  075 

26,315 

7-44 

73oo 

275i 

.008 

13,698 

3-77 

3900 

2823 

.101 

25,641 

7-24 

7400 

2750 

•035 

13,513 

3-72 

4000 

2817 

.127 

25,000 

7.04 

75oo 

2749 

.062 

13,333 

3-66 

4100 

2812 

•  153 

24,390 

6.86 

7600 

2749 

.089 

13,157 

3-62 

4200 

2808 

•  179 

23,809 

6.68 

7700 

2748 

.116 

12,987 

3-57 

4300 

4400 

2803 
2799 

.205 
.232 

23,255 
22,727 

6.52 
6.36 

7800 
7900 

2748 
2747 

•143 
.170 

12,820 
12,658 

3-52 
3.48 

4500 

2796 

.258 

22,222 

6.21 

8000 

2746 

.197 

12,500 

3-43 

s 

4600 

2792 

.284 

21,739 

6.07 

8100 

2746 

.224 

12,345 

3-39 

4700 
4800 
4900 

2789 
2786 
2784 

•  311 
•  338 
.364 

21,276 
20,833 
20,4O6 

5-93 
5-8o 
5.68 

8250 
8500 
8750 

2745 
2744 
2743 

.265 
•  332 
.400 

12,121 

11,764 
11,428 

3-33 
3-23 
3-13 

5000 
5100 
5200 

5300 

2781 
2779 
2777 
2775 

•  391 

.417 
•444 
.471 

20,OOO 
19,607 
19,230 
18,867 

5-56 
5-45 
5-34 
5-23 

9000 
9250 
9500 
9750 

2742 
2741 
2740 
2740 

.468 
•  536 
.604 
.671 

11,111 
10,810 
10,526 
10,256 

3-05 
2.96 
2.88 
2.81 

5400 

2773 

•497 

I8,5l8 

5-13 

IOOOO 

2739 

•739 

10,000 

2.74 

SMITHSONIAN  TABLES. 


294  TABLES  350-352. 

MEDIA  FOR  DETERMINATIONS  OF  REFRACTIVE   INDICES  WITH 
THE   MICROSCOPE. 

TABLE  350.  -Liquids,  nD  (0.689,*)  =  1.74  to  1.87. 

In  100  parts  of  methylene  iodide  at  20°  C.  the  number  of  parts  of  the  various  substances  in- 
dicated in  the  following  table  can  be  dissolved,  forming  saturated  solutions  having  the  permanent 
refractive  indices  specified.  When  ready  for  use  the  liquids  can  be  mixed  by  means  of  a  dropper 
to  five  intermediate  refractions.  Commercial  iodoform  (CHI3)  powder  is  not  suitable,  but  crys- 
tals from  a  solution  of  the  powder  in  ether  may  be  used,  or  the  crystalized  product  may  be 
bought.  A  fragment  of  tin  in  the  liquids  containing  the  SnI4  will  prevent  discoloration.  • 


CHIS. 

SnI4. 

AsI8. 

SbI3. 

s. 

«na  at  20°. 

12 

1.764 

25 

'•ZS 

25 

12 

1.  806 

3° 

6 

1.820 

40 

27 
27 

11 

7 

1.826 
1.842 

35 

3i 
3i 

14 

16 

8 
8 

10 
IO 

38 

TABLE  351.  —Resin-like  Substances,  nD  (0.589,*)  =1.68  to  2.10. 

Piperine,  one  of  the  least  expensive  of  the  alkaloids,  can  be  obtained  very  pure  in  straw-colored 
crystals.  When  melted  it  dissolves  the  tri-iodides  of  arsenic  and  antimony  very  freely.  The 
solutions  are  fluid  at  slightly  above  100°  and  when  cold,  resin-like.  A  solution  containing  3  parts 
antimony  iodide  to  one  part  of  arsenic  iodide  with  varying  proportions  of  piperine  is  easier  to 
manipulate  than  one  containing  either  iodide  alone.  The  following  table  gives  the  necessary  data 
concerning  the  composition  and  refractive  indices  for  sodium  light.  In  preparing,  the  constituents, 
in  powder  of  about  i  mm.  grain,  should  be  weighed  out  and  then  fused  over,  not  m,  a  low  flame. 
Three-inch  test  tubes  are  suitable. 


Per  cent  Iodides. 

oo. 

10. 

20. 

30. 

40. 

50. 

60. 

70. 

80. 

Index  of  refraction 

1.683 

1.700 

1.725 

i-756 

I-794 

1.840 

1.897 

1.968 

2.050 

TABLE  352.  —Permanent  Standard  Resinous  Media,  nD  (0.589^)  =  1.546  to  1.682. 

Any  proportions  of  piperine  and  rosin  form  a  homogeneous  fusion  which  cools  to  a  transparent 
resinous  mass.  The  following  table  shows  the  refractive  indices  of  various  mixtures.  On 
account  of  the  strong  dispersion  of  piperine  the  refractive  indices  of  minerals  apparently  matched 
with  those  of  mixtures  rich  in  this  constituent  are  0.005  to  o.oi  too  low.  To  correct  this  error  a 
screen  made  of  a  thin  film  of  7  per  cent  antimony  iodide  and  93  per  cent  piperine  should  be 
used  over  the  eye-piece.  Any  amber-colored  rosin  in  lumps  is  suitable. 


Per  cent  Rosin. 

oo. 

IO. 

20. 

3°- 

40. 

5°- 

60. 

7o. 

80. 

90. 

100. 

Index  of  refraction 

1.683 

1.670 

I-657 

1.643 

I.63I 

1.618 

1.604 

1.590 

i-575 

1.560 

r-544 

All  taken  from  Merwin,  Jour.  Wash.  Acad.  of  Sc.  3,  p.  35,  1913. 
SMITHSONIAN  TABLES. 


295 


TABLE     353. 
OPTICAL    CONSTANTS   OF   METALS. 

TABLE   353. 

Two  constants  are  required  to  characterize  a  metal  optically,  the  refractive  index,  n  and  the 
absorption  index,  k,  the  latter  of  which  has  the  following  significance :  the  amplitude  of  a  wave 
after  travelling  one  wave-length,  A1  measured  in  the  metal,  is  reduced  in  the  ratio1  i  :e  —  2**  or  for 

any  distance  d,  i  :  e  -  -jp.  for  the  same  wave-length  measured  in  air  this  ratio  becomes  i :  e  — ^~ -k 
nk  is  sometimes  called  the  extinction  coefficient.  Plane  polarized  light  reflected  from  a  polished 
metal  surface  is  in  general  elliptically  polarized  because  of  the  relative  change  in  phase  between 
the  two  rectangular  components  vibrating  in  and  perpendicular  to  the  plane  of  incidence.  For  a 
certain  angle,  <;>  (principal  incidence)  the  change  is  90°  and  if  the  plane  polarized  incident  beam 
has  a  certain  azimuth  ^  (Principal  azimuth)  circularly  polarized  light  results.  Approximately, 
(Drude,  Annalen  der  Physik,  36,  p.  546,  1889), 

k  =  tan  2$  ( i  —  cot  2<£)  and  n  = 

For  rougher  approximations  the  factor  in  parentheses  may  be  omitted.  R  =  computed  per- 
centage reflection. 


(The  points  have  been  so  selected  that  a  smooth  curve  drawn  through  them  very  closely  indicates  the  characteristics 
of  the  metal.) 


Metal. 

A 

* 

5 

Computed. 

Authority. 

n 

k 

nk 

R 

Cobalt 

0.231 

64°3'' 

29°39 

1.  10 

1.30 

'•43 

32. 

Minor. 

•275 

70    22 

29  59 

1.41 

1.52 

2.14 

46. 

11 

.500 

77     5 

3i  53 

1-93 

3-72 

66. 

" 

•650 

79    o 

3i   25 

2-35 

1.87 

4.40 

69. 

Ingersoll. 

I.OO 

81  45 

29    6 

3.63 

1.58 

5-73 

73- 

" 

1.50 

83    21 

26  18 

5.22 

1.29 

6-73 

75- 

" 

2.25 

83    48 

26    5 

5-65 

1.27 

7.18 

76. 

" 

Copper 

.231 

65  57 

26  14 

1.05 

1.45 

29. 

Minor. 

•347 

65     6 

28  16 

1.19 

1.23 

1.47 

32- 

" 

.500 

70  44 

33  46 

1.  10 

2.13 

2-34 

56. 

" 

.650 

74  16 

V  30 

0.44 

7-4 

3-26 

86. 

Ingersoll. 

.870 

78  40 
84     4 

42  30 
42  30 

0-35 
0.83 

II.  0 

11.4 

3.85 
9.46 

91. 
96. 

',! 

2.25 

85   13 

42  30 

1.03 

11.4 

II.7 

97- 

" 

4.00 

87    20 

42  30 

1.87 

11.4 

21.3 

Forst.-Fre'ed. 

5-50 

88  oo 

3-i6 

9.0 

28.4 

it           " 

Gold 

I.OO 

81  45 

44  oo 

0.24 

28.0 

6.7 

tt                  H 

2.00 

85  30 

43  56 

0.47 

26.7 

12.5 

"          " 

3.00 

87  05 

43  5° 

0.80 

24-5 

19.6 

"          " 

5-00 

88  15 

43  25 

1.81 

i  S.i 

33- 

«                il 

Iridium 

I.OO 

82  10 

29  X5 

3-85 

1.  60 

6.2 

4<                  K 

2.00 

83   10 

29  40 

4-30 

1.66 

7.1 

"                  «« 

3-00 

81  40 

30  40 

3-33 

1.79 

6.0 

K                    « 

Nickel 

5.00 
0.420 

79  oo 
72  20 

32  20 
3i  42 

227 
1.41 

2.03 
1.79 

4.6 
2-53 

54- 

Tool. 

0.589 

76     i 

31  41 

1.79 

1.86 

3-33 

62. 

Drude. 

0.750 

78  45 

32     6 

2.19 

1.99 

4-36 

70. 

Ingersoll. 

I.OO 

80  33 

32       2 

2.63 

2.00 

5.26 

74- 

" 

Platinum 

2.25 

I.OO 

84  21 
75  3° 

33  30 
37  °° 

3-95 
1.14 

2-33 

3.25 

9.20 
3-7 

85. 

Forst.-Fre'ed. 

2.OO 

74  30 

39  So 

0.70 

5.06 

3-5 

"           " 

3-00 

73  50 

41  oo 

0.52 

6.52 

3-4 

" 

S-oo 

72  oo 

42  10 

°-34 

9.01 

3-t 

<«           « 

Silver 

0.226 

62  41 

22    l6 

1.41 

0.75 

i.  ii 

18. 

Minor. 

•  293 

63   14 

18  56 

0.62 

0.97 

'7- 

" 

•316 

52  28 

15  38 

1-13 

0.38 

0-43 

4- 

" 

•332 

52     i 

37     2 

0.41 

1.61 

0.65 

32- 

N 

•395 

66  36 

43     6 

0.16 

12.32 

1.91 

87. 

" 

.500 

72  31 

43  29 

0.17 

17.1 

2-94 

93. 

" 

.589 

75  35 

43  47 

0.18 

20.6 

3.64 

95- 

" 

•750 

79  26 

44     6 

0.17 

30.7 

5-«6 

97- 

Ingersoll. 

I.OO 

82     o 

44     2 

0.24 

29.0 

6.96 

98. 

11 

1.50 

84  42 

43  48 

0-45 

23-7 

10.7 

98. 

1 

2.25 
3-oo 

86  18 
87  10 

43  34 
42  40 

0.77 
1.65 

19.9 

12.2 

'5-4 

20.1 

99. 

Fbrst.-Fre'ed. 

4.50 

88  20 

41    10 

4-49 

7-42 

33-3 

"           " 

Steel 

0.226 

66  51 

28  17 

1.30 

1.26 

1.64 

35- 

Minor. 

•257 

68  35 

28  45 

i.38 

1.35 

1.86 

40. 

" 

•325 

69  57 

3°     9 

*«37 

I.S3 

2.09 

45- 

" 

.500 

75  47 

29      2 

2.09 

1.50 

3-14 

57- 

" 

.650 
1.50 

7748 
81  48 

27     9 
28  51 

2.70 
3-71 

'•33 
i-55 

3-59 
5-75 

59- 
73- 

Ingersoll. 

2.25 

83    22 

30  36 

4.14 

1.79 

7-41 

80. 

Drude,  Annalen  der  Physik  und  Chemie,  39,  p.  481,  1890;  42,  p.  186,  1891;  64,  p.  159,  1898.  Minor,  Annalen 
der  Physik,  10,  p.  581,  1903.  Tool,  Physical  Review,  31,  p.  i,  1910.  Ingersoll,  Astrophysical  Journal,  32,  p.  265, 
1910;  Fbrsterling  and  Freedericksz,  Annalen  der  Physik,  40,  p.  201,  1913. 

SMITHSONIAN  TABLES. 


296 


TABLES  354-355. 


OPTICAL  CONSTANTS  OF    METALS. 

TABLE  354. 


Metal. 

A. 

n. 

k. 

R. 

Ref. 

Metal. 

A. 

n. 

k. 

R. 

Ref. 

Al* 

0.589 

1.44 

5-32 

83 

I 

Rh* 

0-579 

i-54 

4.67 

78 

3 

Sb.* 
Bi.tJ 

589 

white 

3-°4 
2.26 

4.94 

70 

I 

2 

Se.J 

.400 
.490 

2.94 
3.12 

2.31 
1.49 

44 
35 

5 
5 

Cd* 

•589 

1.13 

5.01 

85 

I 

.589 

2-93 

0-45 

25 

5 

Cr.* 

•579 

2.97 

4.85 

70 

3 

.760 

2.60 

0.06 

20 

Cb* 

•579 

1.  80 

2.II 

41 

3 

Si* 

•589 

4.18 

0.09 

38 

6 

Au.t 

•257 

0.92 

I.I4 

28 

4 

1.25 

3-67 

0.08 

33 

6 

.441 

1.18 

1.85 

42 

4 

2.25 

3-53 

0.08 

31 

6 

.589 

0.47 

2.83 

82 

4 

Na.  (liq.) 

.589 

.004 

2.61 

99 

i 

I.  crys. 
Ir.* 
Fe.§ 

•589 
•579 
-257 

3-34 
2.13 

I.OI 

30 

11 

4 
3 
4 

Ta.* 
Sn* 
W.* 

•579 
•589 
•579 

1.48 
2.76 

2.31 

5-25 
2.71 

44 
82 

49 

3 
i 

3 

•441 

1.28 

1.37 

28 

4 

V* 

•579 

3-03 

3-51 

58 

3 

•589 

i-S" 

1.63 

33 

4 

Zn* 

•257 

0-55 

0.61 

20 

4 

Pb* 

.589 

2.01 

3-48 

62 

i 

.441 

o-93 

3.19 

73 

4 

Mg* 

•589 

0-37 

4.42 

93 

i 

•589 

1-93 

4.66 

74 

4 

Mn* 

•579 

2.49 

3^9 

64 

3 

.668 

2.62 

5.08 

73 

4 

Hg.  (liq.) 

'.326 

0.68 

2.26 

66 

4 

•44  i 

I.OI 

1.62 

3-42 
4.41 

74 

4 
4 

A  =  wave-length,  n  =  refraction  index. 

°668 

1.72 

4.70 

77 

4 

k  =  absorption  index,  R  =  reflection. 

Fd* 
Pt.t 

•579 
•257 
•44  l 

1.62 
1.17 

1.94 

3-41 
1.65 
3.16 

I 

3 
4 
4 

(i)  Drude,  see  Table  205;  (2)  Kundt,  prism 
used,  Ann.  der  Physik  und  Chemie,  34,  p.  477, 
36,  p.  824,  1889;  (3)  v.   Wartenberg,  Verh. 

2.63 

2.QI 

59 
cq 

4 

4 

deutsch.   Physik.   Ges.  12,  p.  105,  1910;  (4) 
Meier,  Annales  der  Physik,  10,  p.  581,  1903; 

Ni* 

•275 
.441 
.589 

7 

1.09 

1.16 

1.30 

1.23 
1.97 

jy 
24 

25 
43 

t 
4 
4 
4 

(5)  Wood,  Phil.  Mag.  (6),  3,  607,  1902  ;  (6) 
Ingersoll,  see  Table  205. 
*  solid,   t  electrolytic,   J  prism,  §  deposited 

as  film  in  vacuo. 

TABLE  355. — Reflecting   Power  of  Metals.      (See  page  298.) 


Wave- 

A 

length 

4 

c/: 

•o 

u 

o 

U 

s* 

A 

•g 

A 

z 

A 

K 

A 

S 

c 
CO 

£ 

£ 

c 
N 

M 

Per  cents. 

•5 

72 

46 

_ 

76 

34 

38 

_ 

_ 

49 

57 

_ 

.6 

— 

53 

— 

— 

24 

— 

73 

48 

— 

77 

32 

45 

49 

— 

— 

.8 

— 

S4 

— 

— 

2S 

— 

74 

5- 

— 

81 

29 

64 

48 

— 

S6 

60 

— 

I.O 
2.0 

82 

II 

872 

67 
72 

27 

3S 

78 
87 

74 

77 

o2 

li 

84 

28 

28 

78 
90 

5° 
52 

54 
61 

62 
8S 

61 
69 

80 
92 

4.0 

92 

68 

96 

81 

48 

94 

84 

90 

88 

92 

28 

57 

72 

93 

79 

97 

7-o 

96 

71 

9S 

93 

54 

95 

91 

93 

94 

94 

28 

94 

68 

81 

88 

98 

10.0 

98 

72 

98 

97 

59 

96 

— 

94 

97 

9S 

28 

— 

84 

96 

— 

98 

12.0 

98 

99 

97 

96 

95 

97 

95 

: 

85 

96 

99 

Coblentz,  Bulletin  Bureau  of  Standards,  2,  p.  457,  1906,  7,  p.  197,  1911.  The  surfaces  of  some  of  the 
samples  were  not  perfect  so  that  the  corresponding  values  have  less  weight.  The  methods  for  polishing 
the  various  metals  are  described  in  the  original  articles.  The  following  more  recent  values  are  given 
by  Coblentz  and  Emerson,  But  Bur.  Stds.  14,0.  207,  1917;  Stellite,  an  exceedingly  hard  and  untarnish- 
able  alloy  of  Co,  Cr,  Mo,  Mn,  and  Fe  (C,  Si,  S,  P)  was  obtained  from  the  Haynes  Stellite  Co,  Kokomo, 
Indiana. 

Wave-length,  fi,     .15      .20      .30      .50      .75      i.oo      2.00      3.00      4.00      5.00      9.00 
Tungsten,  -        -        -      .50      .52        .576      .900      .943       -9^8      .953 

.32      .42      .50      .64      .67        .689      .747      .792      .825      .848       .880 
SMITHSONIAN  TABLES. 


TABLES356-358.-THE    REFLECTION    OF    LIGHT. 


297 


According  to  Fresnel  the  amount  of  light  reflected  by  the  surface  of  a  transparent  medium 

i  /  A    i    D\        l  i  sin2  (/' — r)    -    tan2  (/ — r)  ) 

=  i  (4  +  £}  =  -  \  sin-2  (/-  _|_  r)  +  tan2(/-fr)  5  '       1S        amount  polarized  in  the  plane  of  inci- 
dence ;  B  is  that  polarized  perpendicular  to  this  ;  i  and  r  are  the  angles  of  incidence  and  refraction. 
TABLE  356,  —  Light  reflected  when  i  =  0°  or  Incident  Light  is  Normal  to  Surface. 


«. 

l(A+B). 

n. 

i  (^  +  -ff). 

«. 

iU  +  ^). 

n. 

KA+B^\ 

1.  00 

0.00 

•4 

2.78 

2.O 

u.  ii 

5- 

44.44 

1.  02 

1.05 

0.01 

0.06 

.6 

4.00 
5-33 

2.25 
2-5 

14.06 
18.37 

5-83 

10. 

5O.OO 
66.67 

I.I 

1.2 

0.23 
0.83 

:I 

6.72 
8.16 

2.75 

3- 

22.89 
25.00 

100. 

oo 

96.08 
IOO.OO 

i-3 

1.70 

•9 

9-63 

4. 

36.00 

TABLE  357.  — Light  reflected  when  n  is  near  Unity  or  equals  1  +  dn. 


A 

T> 

A_B\ 

IP 

flu 

mft 

£  (A  +  B). 

A+B 

0° 

I.OOO 

I.OOO 

I.OOO 

O.O 

5 

1.015 

.985 

I.OOO 

1.5 

10 

1.063 

I.OOI 

6.2 

15 

1.149 

.862 

I.OO5 

14-3 

20 

1.282 

•752 

.017 

26.0 

25 

1.482 

.612 

.047 

41.5 

30 

1.778 

.444 

.III 

60.0 

35 

2.221 

.260 

.240 

79.1 

40 

2.904 

.088 

•496 

94-5 

45 

4-000 

.000 

2.OOO 

IOO.O 

50 

5.857 

.176 

3.016 

94-5 

9-239 

1.081 

5.160 

79.1 

60 

I6.OOO 

4.000 

10.000 

60.0 

65 
70 

3L346 

73-°79 

12.952 
42.884 

22.149 
57.98I 

41.5 
26.0 

75 

222.85 

167.16 

195.00 

14-3 

80 

1099.85 

971.21 

I035-53 

6.2 

85 

1  7330-64 

16808.08 

17069.36 

1.5 

90 

oo 

00 

00 

0.0 

TABLE  3§8.— Light  reflected  when  n  =  1.55. 


i. 

r. 

A. 

B. 

dA.\ 

dB.t 

I  (A+B). 

A-Bm 

A+B' 

o 

0   / 
O   O.O 

4-65 

4-65 

0.130 

0.130 

4-65 

0.0 

5 

3  J3-4 

4.70 

4.61 

.131 

.129 

4-65 

I.O 

10 

6  25.9 

4.84 

4-47 

•135 

.126 

4.66 

4.0 

IS 

9  36-7 

5-09 

4.24 

.141 

.121 

4.66 

9.1 

20 

12  44.8 

5-45 

3-92 

.150 

•"4 

4.68 

16.4 

25 

15  49-3 

5-95 

3-50 

.161 

.105 

4-73 

25.9 

18  49-1 

6.64 

3.00 

.175 

.094 

4.82 

37-8 

35 
40 

21  43-1 
24  30.0 

7-55 
8.77 

2.40 
i-75 

.191 

.210 

«8i 

.066 

4.98 
5.26 

S'-7 
66.7 

45 

27  8.5 

10.38 

1.08 

•233 

.049 

5-73 

81.2 

5° 

29  37-  * 

12.54 

0.46 

.263 

.027 

6.50 

92-9 

55 

3i  54-2 

15-43 

0.05 

•303 

.007 

7-74 

99-3 

60 

33  58-1 

19-35 

0.12 

.342 

-.013 

9-73 

98.8 

65 

35  47-° 

24.69 

'•'3 

•375 

—.032 

12.91 

91.2 

70 

37  J9-1 

31.99 

4.00 

.400 

—.050 

18.00 

77-7 

75 

38  32.9 

42.00 

10.38 

.410 

—.060 

26.19 

61.8 

80 

39  26.8 

55-74 

23-34 

.370 

-.069 

39  54 

41.0 

82  30 

39  45-9 

64.41 

34-04 

.320 

-.067 

49.22 

30.8 

85  o 

39  59-° 

49-03 

.250 

—.061 

61.77 

20.6 

86  o 

40  3.6 

79.02 

56.62 

.209 

-•055 

67.82 

16.5 

87  o 

40  6.7 

83.80 

65.32 

.163 

-.046 

74-  56 

12.4 

88  e 

40  8.9 

88.88 

75-3» 

.Il8 

—.036 

82.10 

8.3 

89  o 

40  10.2 

94.28 

86.79 

.063 

—  .022 

90.54 

4-' 

90  o 

40  10.7 

IOO.OO 

IOO.OO 

.000 

—  .000 

IOO.OO 

O.O 

Angle  of  total  polarization  =  57°  10^.3,  A  •=  16.99. 
*  This  column  gives  the  degree  of  polarization.  t  Columns  5  and  6  furnish  a  means  of 

determining  A   and  B  for  other  values  of  «.   They  represent  the  change  in  these  quantities  for  a  change  of  «  of  o.ox. 

Taken  from  E.  C.  Pickering's  "  Applications  of  Fresnel's  Formula  for  the  Reflection  of  Light." 
SMITHSONIAN  TABLES. 


TABLES  359-36O. 

REFLECTING  POWER  OF  METALS. 
TABLE  359,  —Perpendicular  Incidence  and  Reflection.    (See  also  Tables  352-355.) 

The  numbers  give  the  per  cents  of  the  incident  radiation  reflected. 


i 

j 

1 

a 

i  _ 

cTI" 

!'«• 

i 

^ 

| 

£ 

I 

1 

x-< 

1 

Wave-length,  , 

ilver-backed  G 

ercury-backed  1 

lach's  Magnali 
6gA  1+  ZiM£ 

les-Schiineman 
+  34^  +  *^. 

ss'  Speculum  1\ 
68.2CK  +  3I.8.S 

Nickel. 
trolytically  Det 

^ 
if 

11 
1 

Copper. 
'omtnercially  F 

& 

11 

^*^> 

Gold. 
trolytically  De 

Brass. 
(  Trowbridge 

| 

1 

N 

C/3 

a 

m 

sd 

o 

3 

^ 

^ 

S 

4j 

3 

MR 

N 

^ 

0) 

.«i 

_ 

_ 

67.0 

35-8 

29-9 

37-8 

_ 

32-9 

25-9 

33-8 

38-8 

_ 

34-i 

'   .288 

— 

— 

70.6 

37-1 

37-7 

42.7 

— 

35*0 

24.3 

38.8 

34.0 

— 

21.2 

•305 

-»  i  A 

- 

- 

72.2 

37-2 

41.7 

44-2 

— 

37-2 

25-3 

39-8 

31.8 

— 

9.1 

.316 
.326 

_ 

_ 

75-5 

39-3 

- 

45-2 

- 

40-3 

24.9 

41.4 

28.6 

- 

14.6 

•338 

- 

— 

- 

46.5 

— 

- 

— 

— 

— 

— 

55-5 

- 

_ 

81.2 

43-3 

51.0 

48.3 

— 

45-o 

27-3 

43-4 

27.9 

- 

74-5 

•385 

- 

- 

83.9 

44-3 

49.6 

- 

47-8 

28.6 

45-4 

27.1 

- 

81.4 

.420 

•45° 

85"? 

72^8 

83.3 
83-4 

47.2 
49.2 

56.4 

60.0 

56.6 
59-4 

4-8 

54-4 

32.7 

37-0 

51.8 

54-7 

29-3 

33-  1 

- 

86.6 
9°-5 

.500 

86.6 

70.9 

83-3 

49-3 

63-2 

60.8 

53-3 

54-8 

43-7 

584 

47.0 

- 

9i-3 

•55° 

88.2 

71.2 

82.7 

48.3 

64.0 

62.6 

59-5 

54-9 

477 

61.1 

74.0 

— 

92.7 

.600 

88.1 

69.9 

83.0 

47-5 

64-3 

64.9 

83-5 

55-4 

71.8 

64.2 

84.4 

- 

92.6 

.650 
.700 

89.1 
89.6 

71-5 
72.8 

82.7 
83-3 

5i-5 
54-9 

65-4 
66.8 

66.6 
68.8 

89.0 
90.7 

56.4 
57-6 

80.0 
83.1 

66.5 
69.0 

88.9 
92-3 

"• 

94-7 
95-4 

.800 

_ 

_ 

84-3 

63.1 

_ 

69.6 

_ 

58.0 

88.6 

70.3 

94-9 

_ 

96.8 

I.O 

— 

— 

84.1 

69.8 

70-5 

72.0 

— 

63.1 

90.1 

72.9 

— 

97-o 

'•5 

— 

— 

85.1 

79.1 

75-o 

78.6 

_ 

70.8 

93-8 

77-7 

97-3 

- 

98.2 

2.O 

— 

— 

86.7 

82.3 

80.4 

83-5 

76.7 

95-5 

80.6 

96.8 

9I.O 

97-8 

3-° 

- 

- 

87.4 

854 

86.2 

88.7 

- 

83.0 

97.1 

88.8 

- 

93-7 

98.1 

4.0 

- 

- 

88.7 

87.1 

88.5 

91.1 

- 

87.8 

97-3 

91-5 

96.9 

95-7 

98.5 

5>o 

— 

— 

89.0 

87-3 

89.1 

94.4 

— 

89.0 

93-5 

97-o 

95-9 

98.1 

7.0 

— 

— 

90.0 

88.6 

90.1 

94-3 

— 

92.9 

98.3 

95-5 

98.3 

97.0 

98.5 

9.0 

— 

— 

90.6 

90.3 

92.2 

95-6 

— 

92.9 

98.4 

95-4 

98.0 

97-8 

98.7 

I  I.O 

— 

— 

90.7 

90.2 

92.9 

95-9 

— 

94.0 

98.4 

95-6 

98.3 

96.6 

98.8 

14.0 

" 

92.2 

90.3 

93-6 

97.2 

" 

96.0 

97-9 

96.4 

97-9 

" 

98.3 

Based  upon  the  work  of  Hagen  and  Rubens,  Ann.  der  Phys.  (i)  352,  1000;  (8)  r,  1902;  (n)  873,  1903. 
Taken  partly  from  Landolt-Bbrnstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 

TABLE   360.  —  Percentage  Diffuse  Reflection  from  Miscellaneous  Substances. 


Lamp-blacks. 

i 

21 

jj 

Wave- 
length 
/* 

i 

& 

c. 

E- 

ll 

Acetylene 

0 

$i 

•°x 
^ 

Green  lea\ 

Lead  oxid 

1 

< 

Zinc  oxide 

£ 

£ 

15 

Lead 
carbonate 

•a 

< 

Black  veh 

Black  felt. 

Red  brick 

*.6o 

3-2 

25. 

52, 

84. 

82. 

89. 

is- 

1.8 

14. 

30. 

••95 

3-4 

i-3 

I.I 

0.6 

'•3 

I.I 

88. 

86. 

75- 

93. 

21. 

4-4 

3.3 

1.3 

•9 

.8 

1.2 

1.4 

SI- 

21. 

8. 

18. 

29. 

3-7 

8.8 

3-8 

1-3 

1.2 

1.6 

2.1 

26. 

2. 

3- 

,S- 

II. 

2-7 

12. 

24.0 

4-4 

3-o 

4.0 

2.1 

5-7 

4-2 

IO. 

6. 

5- 

7> 

*Not  monochromatic  (max.)  means  from  Coblentz,  ].  Franklin  Inst.  1912.  Bulletin  Bureau  of  Standards,  9,  p.  283, 
1912,  contains  many  other  materials. 


SMITHSONIAN  TABLES. 


TABLES  361-362. 

REFLECTING   POWER  OF   PIGMENTS- 
TABLE  361.  —  Percentage  Reflecting  Power  of  Dry  Powdered  Pigments. 


299 


Taken  from  "The  Physical  Basis  of  Color  Technology,"  Luckiesh,  J.  Franklin  Inst.,  1917.  The  total  reflecting 
power  depends  on  the  distribution  of  energy  in  the  illiuninant  and  is  given  in  the  last  three  columns  for  noon  sun,  blue 
sky,  and  for  a  7.9  lumens/ watt  tungsten  filament. 


Spectrum  color. 

Vio- 
let. 

Blue. 

Green. 

Yellow. 

Orange. 

Red. 

i 

i 

Ii 

Wave-length  in  /z 

0.44 

0.46 

0.48 

0.50 

0.52 

0-54 

0.56 

0.58 

0.60 

0.62 

0.64 

0.66 

0.68 

0.70 

£ 

fj 

American  vermilion  .... 

8 

6 

,•> 

5 

6 

6 

9 

ii 

24 

39 

S3 

61 

66 

65 

14 

12 

12 

Venetian  red  

5 

5 

S 

6 

7 

12 

19 

24 

28 

30 

32 

32 

10 

13 

Tuscan  red  
Indian  red  .  .    

I 

7 

7 

8 

8 

8 

8 

12 
II 

16 
15 

18 
18 

20 
20 

22 
22 

23 
23 

24 
24 

10 

IO 

9 

12 
II 

Burnt  sienna  
Raw  sienna  

12 

13 

13 

13 

18 

6 
26 

9 

3."> 

14 

43 

18 
46 

20 

46 

21 

45 

23 

44 

24 

45 

25 

43 

II 

33 

9 
30 

13 

37 

Golden  ochre  
Chrome  yellow  ochre.  .  . 

22 
8 

22 

9 

23 

7 

27 

7 

40 

10 

53 
19 

63 
30 

71 
46 

£ 

74 
62 

3 

11 

Ii 

72 
80 

33 

29 

63 

40 

Yellow  ochre  

20 

2O 

21 

24 

32 

42 

53 

OS 

64 

61 

00 

59 

59 

59 

49 

40 

S3 

Chrome  yellow  medium. 

5 

5 

6 

8 

18 

48 

66 

75 

78 

79 

81 

8! 

81 

81 

54 

So 

63 

Chrome  yellow  light.  .  .  . 

13 

13 

18 

30 

56 

82 

88 

89 

90 

89 

88 

8? 

85 

84 

76 

70 

82 

Chrome  green  light  .... 
Chrome  green  medium.  . 

10 

7 

10 

7 

14 

10 

23 

21 

26 

21 

23 

17 

20 
13 

17 
ii 

14 

9 

II 

7 

1 

8 
6 

7 
6 

6 

5 

19 
14 

19 
14 

18 

12 

Cobalt  blue  

59 
67 

58 

49 
38 

35 

23 

15 

ii 

IO 

IO 

10 

ii 

IS 

7 

20 

IO 

25 
17 

16 

7 

18 

IO 

1 

TABLE  362.  —  Infra-red  Diffuse  Percentage  Reflecting  Powers  of  Dry  Pigments. 


i 

Wave- 
length 
in  n 

8 

9 

rj 

1 

§ 

6 
£ 

i 

PL, 

1 

S 

1 

§ 

§ 

g 

N 

1 

I 

White  lead 
paint. 

IZn  oxide 
paint. 

0.60* 

3 

27 

52 

26 

74 

70 

84 

86 

82 

86 

85 

86 

88 

85 

76 

68 

0-95  * 

4 

24 

45 

41 

88 

— 

86 

— 

84 

93 

89 

79 

72 

4-4 

14 

is 

33 

5i 

30 

34 

41 

21 

47 

8 

16 

22 

23 

29 

ii 

— 

— 

8.8 

13 

5 

26 

4 

ii 

5 

20 

7 

3 

2 

4 

5 

10 

4 

— 

— 

24.0 

6 

4 

8 

IO 

9 

10 

7 

6 

10 

5 

9 

6 

5 

7 

9 

*  Non -monochromatic  means  from  Coblentz,  Bui.  Bureau  Standards  9,  p.  283,  1912. 

For  the  REFLECTING  (and  transmissive)  power  of  ROUGHENED  SURFACES  at  various  angles  of  incidence  see  Gorton, 
Physical  Review,  7,  p.  66,  1916.  A  surface  of  plate  glass,  ground  uniformly  with  the  finest  emery  and  then  silvered, 
used  at  an  angle  of  75°,  reflected  90  per  cent  at  4M,  approached  100  for  longer  waves,  only  10  at  m,  ess  than  5  in  the 
visible  red  and  approached  o  for  shorter  waves.  Similar  results  were  obtained  with  a  plate  of  rock  salt  for  transmitted 
energy  when  roughened  merely  by  breathing  on  it.  In  both  cases  the  finer  the  surface,  the  more  suddenly  it  cuts  off 
the  short  waves. 


SMITHSONIAN  TABLES. 


3oo 


TABLES  363-365. 

REFLECTING   POWER. 

TABLE  363.  —  Reflecting  Power  of  Powders  (White  Light). 

Various  pure  chemicals,  very  finely  powdered  and  surface  formed  by  pressing  down  with  glass  plate.    White  (noon 
light)  light.    Reflection  in  per  cent.    Nutting,  Jones,  Elliott,  Tr.  111.  Eng.  Soc.  9,  593,  1914. 


Aluminum  oxide 83 . 6 

Barium  sulphate 81 .  i 

Borax .  . 


Magnesium  carbonate 86 . 6 

(block)    88.0 


Sodium  chloride 78.1 

Sodium  sulphate 77. 

Starch. . 


Borax 81.6        Magnesium  oxide 85.7        Starch 80.3 

Boric  acid 83.2        Rochelle  salt 79-3         Sugar 87.8 

Calcium  carbonate 83 . 8        Salicylic  acid 81.1        Tartaric  acid 79 .  i 


Citric  acid 81.5        Sodium  carbonate 81 


TABLE  364.  —  Variation  of  Reflecting  Power  of  Surfaces  with  Angle. 

Illumination  at  normal  incidence,  i  J  watt  tungsten  lamp,  reflection  at  angles  indicated  with  normal.  111.  Eng.  Soc., 
Glare  Committee,  Tr.  111.  Eng.  Soc.  n,  p.  92,  1916. 


Angle  of  observation. 

0° 

i° 

3° 

5° 

10° 

15° 

30° 

45° 

60° 

Magnesium  carbonate  block  

0.88 
0.80 
0.78 
0.76 
0.69 
"-3 
0.29 
0-23 
0.83 
4-Q 

0.69 
II-  3 
0.29 

0.22 

0.69 
11.3 
0.29 

0.21 
0.78 

0.88 
0.80 
0.78 
0.76 
0.69 
0.31 
0.29 
o.  20 
0.72 
4-55 

0.88 
0.80 
0.78 
0.76 
0.69 

0.  22 
0.27 

o.  19 

0.62 

3-86 

0.87 
0.80 
0.78 
0.76 
0.69 

0.  21 
0.  20 

o.  16 
0.49 
3-03 

0.83 
0-77 
0.78 
o.73 
0.68 

0.  20 
O.I4 
O.II 

0.28 
0.78 

0.72 
o.7S 
o.  76 
0.70 
0.66 
o.  20 
0.13 

0.  II 
0.21 

0.42 

0.68 
0.66 

0.72 
0.67 
0.64 
0.18 

0.12 
O.I2 

o.  16 
0.35 

Magnesium  oxide 

Matt  photographic  paper 

White  blotter  
Pot  opal,  ground.  .  .  . 

Flashed  opal,  not  ground  

Glass,  fine  ground  

Glass,  course  ground 

Matt  varnish  on  foil  ...        .... 

Mirror  with  ground  face 

The  following  figures,  taken  from  Fowle,  Smithsonian  Misc.  Col.  58,  No.  8,  indicate  the  amount  of  energy 
scattered  on  each  side  of  the  directly  reflected  beam  from  a  silvered  mirror;   the  energy  at  the  center  of  the 
reflected  beam  was  taken  as  100,000,  and  the  angle  of  incidence  was  about  3°. 

Angle  of  reflection,  3°  ±  
Energy  

o' 

100,000 

8' 
600 

10' 

244 

15' 
146 

20' 
107 

30' 
66 

45' 

33 

60' 
22 

100' 
It 

Wave-length  of  max 

energy  of  Nernst  lamp  used  as  source  about  2/t. 

TABLE  365.  —  Infra-red  Reflectivity  of  Tungsten  (Temperature  Variation). 

Three  tungsten  mirrors  were  used,  —  a  polished  Coolidge  X-ray  target  and  two  polished  flattened  wires  mounted 
in  evacuated  soft-glass  bulbs  with  terminals  for  heating  electrically.    Weniger  and  Pfund,  J.  Franklin  Inst. 


Wave- 
length 

Absolute  reflec- 
tivity at  room 

Per  cent  increase  in  reflectivity  in 
going  from  room  temperature  to 

in  At- 

in  per  cent. 

1377°  K 

1628°  K 

1853°  K 

2056°  K 

0.67 

Si 

+6.0 

+7-4 

+8.7 

+9-8 

0.80 

55 

— 

— 

+8.2 

1.27 

70 

o.o 

o.o 

o.o 

0.0 

1.90 

83 

-6.6 

-8.2 

-9.6 

—  II.  0 

2.00 

85 

-7-5 

-9.3 

—  10.  9 

-12.3 

2.90 

92 

-7.7 

-9-4 

—  ii.  i 

-12.5 

4-00 

93 

—12.5 

See  also  Weniger  and  Pfund,  Phys.  Rev.  15,  p.  427,  igig. 


SMITHSONIAN  TABLES. 


TABLE  366. 
TRANSMISSIBILITY    OF    RADIATION    BY    DYES- 


301 


Percentage  transmissions  of  aqueous  solutions  taken  from  The  Physical  Basis  of  Color-Technology  Luckiesh   J 
Franklin  Inst.  184,  1917. 


Spectrum  color  —  » 

Violet. 

Blue. 

Green. 

Yellow. 

Orange. 

Red. 

Wave-length  in  p  —  » 

•44 

.46     .48 

•So     .52     .54 

•  56     .58 

.60     .62    .64 

.66     .68     .70 

Carmen  ruby  opt  
Amido  naphthol  red  

6 

i 
i 
4 

80 
69 

IS 
15 

17 

2 

4 
35 

3 
28 

2 

77 
58 

•s 

89 

:a 

83 

77 

84 

.  92 

21 

89 

50 

.  81 

84 

7 
39 
25 

3         7 

I            2 

3         i 

70       34 
51       40 

I       — 
—         I 

I       — 

—          I 

36       62 

4          7 
39       69 
49       64 

12          20 

29       57 
31       32 
6       14 
40       63 
84       89 

60       56 
23          9 
71        76 
75       5i 
18         6 
3i       13 
9i       84 
69       59 
79       66 
88       78 

8             2 

83       64 

28             2 

71       45 
76       68 
i       — 
23         i 

4       — 

13         14         12 

3         4         6 
—       —         i 

2 

6         i       — 

31     32     48 

—         7       52 
—       —         3 

2          20 
—         48          91 

7       43       84 

i        58       96 
4       53       77 
—       —         i 

i       43       84 
18       74      91 
—      —       10 
82       88       90 

21       30      36 
52       23         4 
70      60      37 
8         i       — 
57       39       19 
26       17         7 
24       34       40 
41       13         i 
92       92       89 

51       38       28 
i       —       — 
69       60       46 
26         7         i 

21         

31     — 
76     65     46 

48       35       24 
44       27        17 
52        27         9 

44       26       19 

13          2       — 
50       33        26 

—         4 
i       53 
13       25 

II          22 
2         38 

10       47 
12       34 

i       54 
14       82 
67       82 

75       86 

23       53 
43       60 
97       98 
96       96 
i       31 
97       97 
82       83 
43       88 

91       94 
96       97 
60       84 
92       93 

29       16 

13            2 

4         i 

2            I 

32       14 

80     67 

18         9 

32         20 

74      ~8 
IS         9 
14       19 
3         2 

I          22 

15       10 
—        6 

—       23 
27       34 

—          I 

-         4       18 
4       38       75 
56       96       98 
90       95       96 
44       54       63 
39       54       65 
78       88       90 
86       95       96 
55       72       84 
ii       35       55 
8?       93       92 
96       97       98 
87       90       90 

91       95       96 
2       23       50 
82       92       96 
67       75       81 
98      98       98 
96      96      96 
70       79       80 
97       97       97 
84      85       86 
95       96       97 
3       27       64 
95       95       95 

95       96       96 
721 

41       — 
52       36       19 

5         3         i 
—         i         4 
12         7         5 

I            2            6 
I            2         I4 

—      —         i 

557 
36       56       74 

2        4        8 

73       93       97 
13       42       75 
55       90       98 

83       96       96 
49       70       84 

27       79       97 
—       —         3 

37       49       60 
92       96       96 
98       98       08 
96       96       96 
73       78       82 
72       77       79 
91       92       92 
96       96       96 
88      90      92 
65       68      69 
92       92       92 
98      98      08 
90      90      90 

97       98       98 
7i       79       79 
96       96       96 
85       86      87 
98      98      98 
96       96      96 
81       81       81 
97       97       97 
86       87       87 
97       97       97 
85       93       93 

96       96       95 
2       23       64 

12         50 

=    j    5 

~6    ~    ^ 

21       49       73 
33       — 
18       37       60 
41       64       72 
4       16       40 
6       42       78 
14       29       53 
81       88       92 
16       25       45 

97       97       97 
92       93       94 
98       98       98 
93       ii       23 
96       95       94 
96       96       96 
i       13       23 
97       97       96 
26       63       89 

Erythrosine  

Hematoxyline 

Alizarinered  

Acid  rosolic  (pure)  
Rapid  filter  red  
Aniline  red  fast  extra  A 

Pinatype  red  fast  
Eosine 

Rose  bengal  

Cobalt  nitrate  
Tartrazine  

Chrysoidin  

Aurantia  

Aniline  yellow  phosphine  
Fluorescein  
Aniline  yellow  fast  S  
Methyl  orange  indicator  
Uranine 

Uranine  naphthaline  
Orange  B  naphthol  
Safranine  

Martius  gelb  
Naphthol  yellow 

Potassium  bichromate,  sat  .  .  . 
Cobalt  chromate  

Naphthol  green  

Brilliant  green 

Malachite  green  
Saurgriin 

Methylengriin  
Aniline  green  naphthol  B  
Neptune  green  
Cupric  chloride  

Turnbull's  blue  

Victoria  blau  .  .                .... 

Prussian  blue  (soluble)  

Wasser  blau  
Resorcine  blue 

Toluidin  blau  
Patent  blue  
Dianil  blue 

Filter  blue  

Aniline  blue,  methyl  

Magenta  
Gentiana  violet  .... 

Rosazeine  

Iodine  (dense)  
Rhodamine  B 

Acid  violet  
Cyonine  in  alcohol  "... 
Xylene  red 

Methyl  violet  B  

For  the  infra-red  transmission  (to  1 2/x)  and  reflection  powers  of  a  number  of  aniline  dyes,  see  Johnson  and  Spence, 
Phys.  Rev.  5,  p.  349,  1915. 


SMITHSONIAN  TABLES. 


3O2  TABLES  367-369. 

TRANSMISSIBILITY   OF  RADIATION   BY  JENA  GLASSES. 

TABLE  367. 

Coefficients,  a,  in  the  formula  It  =  ha*,  where  h  is  the  Intensity  before,  and  It  after, 
transmission  through  the  thickness  t.  Deduced  from  observations  by  Muller,  Vogel, 
and  Rubens  as  quoted  in  Hovestadt's  Jena  Glass  (English  translation). 


Coefficient  of  transmission,  a. 

Unit  t=i  dm. 

•375  M 

39°  M 

.400  M     .434  M      .436  , 

•455  M 

•477  M 

•503  M 

.580^1 

.677  fi 

O  340,  Ord.  light  flint 
O  102,  HVy  silicate  flint 

.388 

•456 
.02  S 

.614        .569       .680 
.463         .502       .566 

ft 

.880 
.700 

.880 
.782 

.878 
.828 

•939 
•794 

0   93.  Ord. 

— 

~          -7H 

.807 

.899 

.871 

•903 

•943 

O  203,      "            "    crown 

.583 

•S8} 

.695        .667        .806 

.822 

.860 

.872 

.872 

•903 

O  598,  (Crown) 

-       -797 

.770 

•77' 

.776 

.818 

.860 

Unit  t=i  cm. 

0.7  V- 

0,5, 

I.I  M 

1.4  f- 

1.7  n 

2.0  M 

2-3  M 

M, 

2.  7  /A 

2.9  >x 

3.., 

S  204,  Borate  crown 
S  179,  Med.  phosp.  cr. 

I.OO 

•99 

•94 
•95 

.90 
.90 

.85 

.84 

.81 
.67 

.69 

•49 

1 

.2Q 

.18 

- 

O  1  143,  Dense,  bor.  sil.  cr. 

.98 

- 

•97 

- 

•95 

•93 

.00 

.84 

•71 

•47 

•27 

O  1092,  Crown 

•99 

•96 

•95 

•99 

.99 

.91 

.82 

•71 

.60 

.48 

.29 

O  1151,       " 

.08 

•99 

•99 

.98 

•94 

.90 

•79 

•75 

•45 

•32 

O  451,  Light  flint 
O  469,  Heavy  " 

I.OO 

I.OO 

_ 

I 

.98 
•99 

? 

.92 
•98 

.84 
•97 

.78 
.90 

:%& 

•34 
•50 

0  500,       "       " 
S  163,       ««       " 

I.OO 
I.OO 

- 

I.OO 

•98 

- 

I.OO 

•99 

- 

I.OO 

•99 

•99 

.92 
•94 

•74 
•78 

£ 

TABLE    368. 

Note  :  With  the  following  data,  /  must  be  expressed  in  millimeters ;  i.  e.  the  figures  as  given 
give  the  transmissions  for  thickness  of  I  mm. 


No.  and  Type  of  Glass. 

Wave-length  in  /m. 

Visible  Spectrum. 

Ultra-violet  Spectrum. 

.644  /a 

•578  M 

.546  M 

•509  M 

.480  M 

•436, 

•405, 

384, 

.361, 

•340, 

•332M 

309  M 

.280^ 

F38i5  Dark  neutral 

•35 

•35 

•37 

•35 

•34 

•30 

•T5 

.06 

F45I2  Red  filter 

•94 

•05 

F2745  Copper  ruby 

.72 

•39 

•47 

•47 

•45 

•43 

•43 

F43I3  Dark  yellow 

.98 

•97 

•93 

•83 

.09 

F435I  Yellow 

.98 

•97 

.96 

•93 

•44 

•i.S 

F4937  Bright  yellow 
F  4930  Green  filter 

I.O 

•17 

I.O 

•50 

I.O 

•64 

•99 
.62 

•74 
•44 

.40 

•3i 

.28 

.22 

.18 

.14 

.06 

F3873  Blue  filter 

— 

— 

.18 

•5° 

•73 

.69 

•59 

.36 

.10 

F  3654     Cobalt    glass, 

transparent  for  outer 

red 

— 

— 

— 

•IS 

•44 

.8s 

I.O 

I.O 

I.O 

I.O 

I.O 

.58 

F  3653  Blue,  ultraviolet 
F  37  28  Didymium,  str'g 
bands 

•99 

.72 

•99 

.96 

.11 

•95 

.65 
.96 

I.O 

•99 

I.O 

•99 

I.O 

.89 

I.O 

.89 

I.O 

•77 

.81 

•  -54 

.18 

This  and  the  following  table  are  taken  from  Jenaer  Glas  fiir  die  Optik,  Liste  751,  1909 
TABLE  369.  -  Transmlsslblllty  by  Jena  Ultra-violet  Glasses. 


No.  and  Type  of  Glass. 

Thickness. 

0-397  M 

0.383  M. 

0.361  ft 

0.346  fj. 

0.325  M 

0.309  M 

0.280  M 

UV  3199  Ultra-violet 

i  mm. 
2  mm. 

I.OO 
0.99 

I.OO 

0.99 

I.OO 

0.99 

I.OO 

0.97 

I.OO 

0.90 

0-95 
0-57 

0.56 

«                «< 

i  dm. 

0-95 

o-95 

0.89 

0.70 

0.36 

UV  3248         " 

i  mm. 

I.OO 

I.OO 

I.OO 

I.OO 

0.98 

0.91 

o-35 

(i               » 

2  mm. 

0.98 

0.98 

0.98 

0.92 

0.78 

0.38 

((                                     U 

i  dm. 

0.96 

0.87 

0.79 

0.45 

0.08 

SMITHSONIAN  TABLES. 


TABLE  370. 
TRANSMISSIBILITY    OF    RADIATION    BY    GLASSES- 


303 


The  following  data  giving  the  percentage  transmission  of  radiation  of  various  substances, 
mostly  glasses,  are  selected  from  Spectroradiometric  Investigation  of  the  Transmission  of  Vari- 
ous substances,  Coblentz,  Emerson  and  Long,  Bui.  Bureau  Standards,  14,  p.  653,  1918. 


Glass  or  substance,  manufacturer. 

Thick- 
ness, 
mm 

Transmission  per  cents. 

Wave-lengths  in  p.. 

o-5 

I.O 

i.S 

2.0 

2.5 

3.0 

3-s 

4.0 

4-5 

S-o 

Purple  fluorite 

4.98 

.007 
.24 
IO 
IO 

1.95 

5-9° 
3-i8 
3-55 
i-55 
2.88 

2.2 

3-43 
5-n 

2.6 

i-5 
2-43 
2.58 
6.36 
3-70 
3-23 

2.  II 

4-43 
1.96 
1.98 
2.04 
2.04 
1.58 

22 
34 
O 

o 

90 
80 

12 
50 

52 

55 

90 
50 

72 

59 

76 

3 

8 

4i 
83 
73 
50 

5o 
60 
83 
50 
90 

75 

i 

4 

i 

2 
O 

74 

0 

o 
o 

23 

91 

0 

92 

o 
86 
76 
9i 

2 

3 
43 
63 
o 

0 

64 

70 

89 

62 
90 
60 

2 

53 
23 
4 

i 

43 

i 

15 
24 
60 
91 

0 

9i 
o 

91 

80 

91 

47 

i 

2 

44 
37 
o 
o 

72 
72 

89 
67 
91 
82 
6 
79 
53 

12 

63 
2 
50 
60 

74 
9i 

2 
90 

4 
91 
82 

91 

48 
i 
i 
46 
ii 

76 
65 
75 
68 

87 
75 
13 
83 
68 

19 

10 

79 
3i 
61 

75 
78 
88 

83 
ii 

89 
81 
90 

48 
i 
i 
46 
o 

40 

2 
IO 
15 

35 
23 
6 

25 
20 
ii 
3 
36 
ii 
ii 
45 
45 
42 
6 

1 

5i 
30 

70 

57 
o 

0 

47 
o 

33 

i 

IO 

3 
13 

4 
7 
9 
9 
4 
5 
27 
5 
i 

20 

13 
2O 

8 
23 

35 
20 
52 

60 
o 

0 

48 
o 

36 

o 
o 
I 
7 
4 
7 
o 
8 
6 
6 
28 
4 

2 
20 
12 

25 
12 
27 
II 
38 
25 
51 

62 
0 
O 

48 

o 

7 
o 
o 

0 
2 

0 

I 
o 

0 

o 
o 
o 
o 

0 

I 
I 
7 

2 

5 
3 
7 

2 
10 

62 
O 
O 

48 

o 

o 
o 
o 

0 

o 
o 
o 

0 
0 

o 
o 
o 

0 
0 

o 
o 
o 

0 

o 
o 
o 
o 

0 

Gold  film  on  Crooke's  glass.  .  . 
"      "      "    crown  glass  
Molybdenite  
Cr2(SO4)3.i8H2O  
Chrome  alum,  10  g  to  100  g  H20 
CoCl2,  10  g  to  100  g  H2O  
GLASSES: 
Copper  ruby,  flashed  

Pyrex   Corning                

Noviol,  B,  Corning,  yellow  .  .  . 
Novieweld3,  Corning,  dk-yellow 

Gi7ioN  green   Corning  

Gi74J,  Corning,  heat  abs'b'g.  . 

Gs&4   Corning    blue          .  .  .  .  . 

Gi72BWs.  Corning,  red-purple 
Crookes'  A  A.  O.  Co  

"        sage  green  30,  A.  O.  Co 
Lab.  58,  A.  O.  Co  

Fieurzal  B,  A.  O.  Co  

Akopos  green,  J.  K.  O.  Co  

Manufacturers:  Corning  Glass  Works,  Corning,  N.  Y.;  A.  O.  Co.,  American  Optical  Co., 
Southbridge,  Mass.;  J.  K.  O.  Co.,  Julius  King  Optical  Co.,  New  York  City.  For  other  glasses 
see  original  reference.  See  also  succeeding  table,  which  contains  data  for  many  of  the  same 
glasses. 


SMITHSONIAN  TABLES. 


304  TABLE  371. 

TABLE  371.  —  Transmission  of  the  Radiations  from  a  Gas-filled  Tungsten  Lamp,  the  Sun,  a 

Magnetite  Arc,  and  from  a  Quartz  Mercury  Vapor  Lamp  (no  Globe)  through  Various 

Substances,  especially  Colored  Glasses. 


Color. 

Trade  name. 

Source.* 

Thick- 
ness 
in  mm 

Transmission,  per  cent. 

Gas- 
filled 
tung- 
sten. 

Quartz 
mercury 
vapor.f 

Mag- 
netite 
arc.t 

Solar 
radia- 
tion. 

Greenish-yellow  

Smoky  green  
Yellow-green  

Fieuzal,  B 
Fieuzal,  63 
Fieuzal,  64 
Euphos 
Euphos,  B 
Akopos  green 
Hallauer,  65 
Hallauer,  64 
G  124,  IP 
Noviweld,  30% 
Noviweld,  shade  3 
Noviweld,  shade  4$ 
Noviweld,  shade  6 
Noviweld,  shade  7 

Saniweld,  dark 
G34 
Noviol,  shade  A 
Noviol,  shade  B 
Noviol,  shade  C 
Ferrous  No.  30 
No.  61 
Lab.  No.  59 
Gi24JA 
Smoke,  C 
Smoke,  D 
Crookes,  A 
Crookes,  B 
Pfund 
Pfund 
Lab.  No.  58 
Lab.  No.  57 
Shade  C 
Electric  smoke 
G  55  A  62 
Shade  D 
G53 
G  i7i-IZ 
0584 
G  172  BW  5 
Gs8s 
Selenium 

Flashed 
Window 
Crown 
Mica 
Mica 
Water 

A.  O.  C. 
F.  H.  E.  . 
F.  H.  E. 
B.  S. 
B.  &L. 
J.  K. 
B.  S. 
F.  H.  E. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
B.  S. 
J.  K. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
A.  O.  C. 
A.  0.  C. 
A.  O.  C. 
C.  G.  W. 
B.  &L. 
B.  &L. 
A.  O.  C. 
A.  O.  C. 
A.  0.  C. 
A.  O.  C. 
A.  O.  C. 
A.  0.  C. 
A.  O.  C. 
A.  O.  C. 
C.  G.  W. 
B.  &L. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
C.  G.  W. 
Schotts 
B.  S. 
B.  S. 
B.  S. 
B.  S. 
B.  S. 
B.  S. 

2.04 
i.  80 
1.65 
3-27 

3-12 

i.sS 

2.36 
1.35 

2.81 

2.14 

2.  20 
2.20 
2.17 
2.17 

3-12 

1-32 

3-57 

2.00 

2.88 

2.0O 

1-95 

2.10 

1-93 
*-S3 
2.26 

2-45 
1.97 

2.OO 

iTsS 

2.00 
2.  II 
1.89 
2.85 
2.09 
2-51 
3-21 

3-75 
4-93 
3-13 
2.90 

3-22 

1.85 
1.56 
1-30 
0.09 

10.  0 

71.6 
75-5 
50.7 
78.9 
78.8 
84.6 
70.3 
S8.7 
0.4 
S-i 
3-4 
1.6 
0.9 
0.8 
Si-  6 
78.1 
56.9 

74-1 

S-3 
82.7 
3-7 

£i 

Ill 

75-7 

2.6 

83.3 

82.8 
36.6 
17.4 
37-6 
2.9 
46.6 
24.9 
72.4 
35-8 
67.8 
69.4 

34-2 

26.9 
34-3 

22.0 
25-0 
24.7 
29-5 
17-7 
25-9 
0.  2 

7-8 

4-2 
I.  2 
0.4 
0.  2 
IS-2 

10.6 

17.0 

32.2 

I7-S 
28.6 
17.3 

21-  S 
3L2 

16.0 
46.1 
32.0 
7.2 
1-3 
40.0 
Si-9 
44-3 

2.2 
17.0 
20.7 

3-9 
41.7 
25.2 
26.5 
34-0 
7-9 

4~8 
59-5 
64.9 
35-4 
43-1 
}54-0 

46.0 
SS-o 

53-0 
59-0 

2.7 
0.8 

O.  2 

43-Q 
56.0 

ii.  5 
12.5 
52.0 
39-0 

64.0 

1.2 

66 
39 

48 

63 

72 

64 
74 

55 
9 

O.Q 

5° 

47 
81 
75 
72 
17 
72 

19 
60 

1 

69 

12 

88 

79 
ii 
16 

4i 
48 
46 

82 
92 

"         "     

Amber.  .  .  . 

Orange  
Yellow 

Sage  green  
Yellow-green  
Blue-green  

Black 

Neutral  tint 

Gold  plate 

"     (darker).. 
Colorless  

Amethyst. 

Purple 

Blue 

Blue,  dark  
Blue-green  
Blue-green,  pale  .... 
Red-purple  
Blue-purple 

Red  

Colorless  

Brown  
Colorless  

Clear  

*A.  O.  C.,  Amer.  Optical  Co.,  Southbridge,  Mass.;  C.  G.  W.,  Corning  Glass  Works,  Corning,  N.  Y.;  B.  &  L., 
Bausch  &  Lomb,  Rochester,  N.  Y.;  J.  K.,  Julius  King  Optical  Co.,  New  York  City;  F.  H.  E.,  F.  H.  Edmonds,  optician, 
Washington,  D.  C.;  B.  S.,  Bureau  of  Standards;  scrap  material,  source  unknown. 

t  Infra-red  radiation  absorbed  by  quartz  cell  containing  i  cm  layer  of  water.  Taken  from  Coblentz-Emerson  & 
Long,  Bui.  Bureau  Standards,  14,  653,  1918. 

J  Transmission  of  i  cm  cell  having  glass  windows. 

SMITHSONIAN  TABLES. 


TABLE  372. 
TRANSMISSIBILITY  OF   RADIATION. 

Transmissibility  of  the  Various  Substances  of  Tables  330  to  338. 


305 


Alum  :  Ordinary  alum  (crystal)  absorbs  the  infra-red. 

Metallic  reflection  at  9.05/1  and  30  to  40/4. 

Rock-salt :  Rubens  and  Trowbridge  (Wied.  Ann.  65,  1898)  give  the  following  transparencies  for 
a  i  cm.  thick  plate  in  %  : 


X 

% 

9 

10 

12 

13 

14 

IS 

16 

17 

18 

19 

20.7 

23-7/* 

99-5 

99-5 

99-3 

97.6 

93-i 

84.6 

66.1 

51.6 

27.5 

9.6 

0.6 

0. 

Pfliiger  (Phys.  Zt.  5.  1904)  gives  the  following  for  the  ultra-violet,  same  thickness :  280/1/1,  95.5% 

231,  86%;  210,  77%;  186,  70%. 
Metallic  reflection  at  0.110/1,  0.156,  51.2,  and  87/1. 
Sylvite :  Transparency  of  a  i  cm.  thick  plate  (Trowbridge,  Wied.  Ann.  60,  1897). 


X 

9 

IO 

II 

12 

U 

14 

'5 

16 

17 

18 

19 

20.7 

23-7M 

% 

100. 

98.8 

99.0 

99-5 

99-5 

97-5 

95-4 

93-6 

92. 

86. 

76. 

58. 

1S- 

Metallic  reflection  at  0.114,1*,  0.161,  61.1,  100. 
Fluorite :  Very  transparent  for  the  ultra-violet  nearly  to  o.i/i. 

Rubens  and  Trowbridge  give  the  following  for  a  i  cm.  plate  (Wied.  Ann.  60,  1897) : 


X 

8* 

9 

IO 

ii 

12/1 

% 

84.4 

54-3 

16.4 

I.O 

O 

Metallic  reflection  at  24/4,  31.6,  40/1. 

Iceland  Spar:    Merritt   (Wied.   Ann.  55,   1895)  giyes  the  following  values  of  k  in  the  formula 
i  =  i0e-kd  (d  in  cm.) : 
For  the  ordinary  ray  : 


X 

1.  02 

1-45 

1.72 

2.07 

2.  II 

2.30 

2-44 

2-53 

2.60 

2.65 

2.741* 

k 

o.o 

o.o 

0.03 

0.13 

0.74 

1.92 

3.00 

1.92 

1.  21 

1.74 

2.36 

X 

2.83 

2.90 

2-95 

3-04 

3-30 

3-47 

3.62 

3.80 

3.98 

4-35 

4-52 

4.83M 

k 

1.32 

0.70 

i.  80 

4-71 

22.7 

19.4 

9.6 

1  8.6 

00 

6.6 

14-3 

6.1 

For  the  extraordinary  ray  : 


X 

2-49 

2.87 

3.00 

3-28 

3.38 

3-59 

3.76 

3-90 

4.02 

4.41 

4-67M 

k 

0.14 

0.08 

0-43 

1.32 

0.89 

1.79 

2.04 

1.17 

0.89 

1.07 

2.40 

X 

k 

4.91 

5-°4 

5-34 

5-50/* 

1.25 

2.13 

4.41 

12.8 

Quartz  :  Very  transparent  to  the  ultra-violet ;  Pfliiger  gets  the  following  transmission  values  for 

a  plate  i  cm.  thick  :  at  0.222/1,  94.2%;  0.214,  92  ;  0.203,  83-6;  0.186,  67.2%. 

Merritt  (Wied.  Ann.  55,  1895)  gives  tne  following  values  for  k  (see  formula  under  Iceland  Spar) : 
For  the  ordinary  ray  : 


X 

2.72 

2.83 

2-95 

3-°7 

3-T7 

3-38 

3-67 

3.82 

3-96 

4.12 

4-5°M 

k 

0.20 

0.47 

o-57 

0.31 

O.2O 

O.I5 

1.26 

1.61 

2.04 

3-4i 

7-30 

For  the  extraordinary  ray 


X 

2.74 

2.89 

3.00 

3.08 

3-26 

3-43 

3-52 

3-59 

3.64 

3-74 

3-9i 

4.19 

4.36M 

k 

o.o 

o.n 

°-33 

0.26 

O.I  I 

0.51 

0.76 

1.88 

1.83 

1.62 

2.22 

3-35 

8.0 

For  X>7  /*,  becomes  opaque,  metallic  reflection  at  8.50/1,  9.02,  20.75-24.4/1,  then  trans- 
parent again. 

The  above  are  taken  from  Kayser's  "  Handbuch  der  Spectroscopie,"  vol.  iii. 

SMITHSONIAN  TABLES. 


306 


TABLES  373-374. 
TRANSMISSIBILITY    OF    RADIATION, 

TABLE  373.  -  Color  Screens. 


The  following  light-filters  are  quoted  from  Landolt's  "  Das  optische  Drehungsvermogen,  etc."  1898. 
Although  only  the  potassium  salt  does  not  keep  well  it  is  perhaps  safer  to  use  freshly  prepared 
solutions. 


Thick- 

Grammes  of 

Optical  cen- 

Color. 

ness. 

Water  solutions  of 

substance 

tre  of  band. 

Transmission. 

in  100  c.cm. 

M 

Red 

« 

20 
2O 

Crystal-violet,  560 
Potassium  monochromate 

0.005 
IO. 

0.6659 

j  begins  about  0.718)1*. 
{  ends  sharp  at  0.639/4. 

Yellow 

2O 

Nickel-sulphate,  NiSO^aq. 

3°- 

0.5919 

0.614-0.574^, 

M 

15 

Potassium  monochromate 

10. 

Green 

15 
2O 

Potassium  permanganate 
Copper  chloride,  CuCla.2aq. 

0.025 

60. 

0-533° 

0.540-0.505/1 

Bright  j 
blue  ) 

20 
20 
20 

Potassium  monochromate 
Double-green,  SF 
Copper-sulphate,  CuSO^aq. 

10. 
O.O2 
15- 

0.4885 

j  0.526-0.494  and 
|  0.494-0.458/4 

Dark     ( 

2O 

Crystal-violet,  5BO 

0.005 

0.4482 

0.478-0.410/4 

blue  \ 

2O 

Copper  sulphate,  CuSO^aq. 

IS- 

TABLE  374.  -  Color  Screens. 

The  following  list  is  condensed  from  Wood's  Physical  Optics  : 

Methyl  violet,  4R-  (Berlin  Anilin  Fabrik)  very  dilute,  and  nitroso-dimethyl-aniline  transmits  0.365/1. 

Methyl  violet  +  chinin-sulphate  (separate  solutions),  the  violet  solution  made  strong  enough  to 

blot  out  0.4359;*,  transmits  0.4047  and  ,0.4048,  also  faintly  0.3984. 
Cobalt  glass  +  aesculin  solution  transmits  0.4359/4. 
Guinea  green  B  extra  (Berlin)  -j-  chinin  sulphate  transmits  0.4916/1. 
Neptune  green  (Bayer,  Elberfeld)  +  chrysoidine.     Dilute  the  latter  enough  to  just  transmit  0.5790 

and  0.5461 ;  then  add  the  Neptune  green  until  the  yellow  lines  disappear. 
Chrysoidine  +  eosine  transmits  0.5790/4.     The  former  should  be  dilute  and  the  cosine  added  until 

the  green  line  disappears. 
Silver  chemically  deposited  on  a  quartz  plate  is  practically  opaque  except  to  the  ultra-violet  region 

0.3160-0.3260  where  90%  of  the  energy  passes  through.     The  film  should  be  of  such  thickness 

that  a  window  backed  by  a  brilliantly  lighted  sky  is  barely  visible. 
In  the  following  those  marked  with  a  *  are  transparent  to  a  more  or  less  degree  to  the  ultra-violet-. 

*  Cobalt  chloride:  solution  in  water,  —  absorbs  o.$o-.$3/j.;  addition  of  CaCl2  widens  the  band  to 
0.47-. 50.     It  is  exceedingly  transparent  to  the  ultra-violet  down  to  0.20.     If  dissolved  in  methyl 
alcohol  -(-  water,  absorbs  O-5O-.53  and  everything  below  0.35.     In  methyl  alcohol  alone  0.485- 
0.555  and  below  0.40/4. 

Copper  chloride:  in  ethyl  alcohol  absorbs  above  0.585  and  below  0.535  >  m  alcohol  -f-  50%  water, 

above  0.595  and  below  0.37/4. 
Neodymium  salts  are  useful  combined  with  other  media,  sharpening  the  edges  of  the  absorption 

bands.    In  solution  with  bichromate  of  potash,  transmits  O-535-.565  and  above  0.60/4,  the  bands 

very  sharp  (a  useful  screen  for  photographing  with  a  visually  corrected  objective). 
Praseodymium  salts  :  three  strong  bands  at  0.482,  .468,  .444.     In  strong  solutions  they  fuse  into  a 

sharp  band  at  0.435-. 4^5M-     Absorption  below  0.34. 
Picric  acid  absorbs  0.36-42/4,  depending  on  the  concentration. 
Potassium  chromate  absorbs  O.4O--35,  O-3O-.24,  transmits  0.23/4. 

*  Potassium  permanganate:  absorbs  0.5  5  5-.  50,  transmits  all  the  ultra-violet. 

Chromium  chloride :  absorbs  above  0.57,  between  0.50  and  .39,  and  below  0.33/4.     These  limits 

vary  with  the  concentration. 
Aesculin  :  absorbs  below  0.363/4,  very  useful  for  removing  the  ultra-violet. 

*  Nitroso-dimethyl-aniline :  very  dilute  aqueous  solution  absorbs  O.49-.37  and  transmits  all  the 
ultra-violet. 

Very  dense  cobalt  glass  -j-  dense  ruby  glass  or  a  strong  potassium  bichromate  solution  cuts  off 

everything  below  0.70  and  transmits  freely  the  red. 
Iodine':  saturated  solution  in  CS2  is  opaque  to  the  visible  and  transparent  to  the  infra-red. 

SMITHSONIAN   TABLES. 


TABLES    375,  376. 

TRANSMISSIBILITY  OF  RADIATION. 

TABLE  375. -Color  Screens.    Jena  Glasses. 


307 


Kind  of  Glass. 

Maker's 
No 

Color. 

Region  Transmitted. 

Thick- 
ness. 
mm. 

J 

Copper-ruby  .     . 

2728 

Deep  red      .... 

Only  red  to  O.6/*  .... 

I  1 

la 

Gold-ruby  . 

459111 

Red      .          ... 

j  Red,  yellow  ;  in  thin  layers  also 

••/ 

2 

2a 

3 

4 
4a 
4b 

Uranium     .     .     . 

« 

Nickel    .     .     .     . 

Chromium       .     . 
u 

Green  copper  .     . 

454111 
455UI 

440111 

4i4m 

433m 
43  1  »i 

Bright  yellow   .     .     . 

\  Bright  yellow,  fluo- 
/      resces. 

Bright  yellow-brown 

Yellow-green    .     .     . 
Greenish-yellow   .     . 
Green  

1      blue  and  violet, 
l  Red,  yellow,  green  to  Eb  ;   in  ) 
j      thin  layer  also  blue                 J 

(  Red,  yellow,  green  (weakened),  ) 
|      blue  (very  weakened)              J 
Yellowish-green    
Red,  green;  from  0.65-.  50/4   .     .     . 

id 

n. 

10. 

5- 

6 

Chromium  . 
Copper  chromium 

432™ 
436'" 

Yellow-green    .     .     . 
Grass-green      .     .     . 

Yellowish-green,  some  red    .     .     . 

2~3 

2-5 

8 

Green-filter      .     . 

437m 
4tfm 

Dark  green  .... 

Green  (in  thin  sheets  some  blue)    . 
Green       

5- 
5- 

10 

Copper  .     .     .     . 

2742 

Blue,  as  CuSO4    .     . 

Green,  blue,  violet    

c-i2 

ii 

Blue-violet      .     . 

447m 

Blue,  as  cobalt  glass 

12 

i<       <« 
Cobalt   .     . 

424111 

«      «      «          « 
Blue    

(  Blue,  violet,  blue-green  (weak-  ) 
I      ened),  no  red 
Blue  violet  extreme  red 

2-5 

13 

14 
i  ^ 

Nickel    .... 
Violet    .... 
Gray 

450111 
452m 
44dln 

Dark  violet  .... 

«         « 

Violet  (G-H),  extreme  red    ... 
Violet  (G-H),  some  weakened  .     . 

V 

7-J 

13 

M 

44  q"1 

f      nizable  color     J 

All  parts  of  the  spectrum  weakened 

0.1-3 

See  "  Uber  Farbglaser  fur  wissenschaftliche  und  technische  Zwecke,"  by  Zsigmondy,  Z.  fur  In- 
strumentenkunde,  21,  1901  (from  which  the  above  table  is  taken),  and  "  Cber  Jenenser  Licht- 
filter,"  by  Grebe,  same  volume. 
(The  following  notes  are  quoted  from  Everett's  translation  of  the  above  in  the  English  edition  of 

Hovestadt's  "  Jena  Glass.") 
Division  of  the  spectrum  into  complementary  colors : 

1st  by  2728  (deep  red)  and  2742  (blue,  like  copper  sulphate). 
2nd  by  454"'  (bright  yellow)  and  447'"  (blue,  like  cobalt  glass). 
3rd  by  433'"  (greenish-yellow)  and  424'"  (blue). 
Thicknesses  necessary  in  above:  2728,  1.6-1.7  mm.;  2742,  5;  454™,  16;  447IU,  1.5-2.0;  433"', 

2.5-3.5;  4241",  3  mm. 

Three-fold  division  into  red,  green  and  blue  (with  violet) : 
2728,  1.7  mm. ;  414'",  10  mm.;  447"',  1.5  mm.,  or  by 
2728,  1.7  mm.  ;  436'",  2.6mm. ;  447'",  1.8  mm. 

Grebe  found  the  three  following  glasses  specially  suited  for  the  additive  methods  of  three-color 
projection  : 

2745,  red  ;  438"',  green;  447"',  blue  violet ; 

corresponding  closely  to  Young's  three  elementary  color  sensations. 
Most  of  the  Jena  glasses  can  be  supplied  to  order,  but  the  absorption  bands  vary  somewhat  in 

different  meltings. 
See  also  "Atlas  of  Absorption  Spectra,"  Uhler  and  Wood,  Carnegie  Institution  Publications,  1907. 

TABLE   376.— Water. 
Values  of  a  in  I  =  I0  e  ftd,  d  in  c.  m.  I0;  I,  intensity  before  and  after  transmission. 


Wave-length  /*, 

.186 

•193 

.200 

.210 

.220 

.230 

.240 

.200 

.300 

.415 

a 

.0688 

.0165 

.009 

.OO6l 

.0057 

.0034 

.0032 

.0025 

.0015 

.00035 

Wave-length  /z, 

•43° 

•45° 

.487 

.500 

•550 

.600 

.650 

.865 

•945 

a 

.00023 

.0002 

.0001 

.O002 

.0003 

.OOl6 

.0025 

.272 

.206 

•538 

First  9;  Kreusler,  Drud.  Ann.  6,   190.1;  next  Ewan,  Proc.  R.  Soc.  57,  1894,  Aschkinass,  Wied  Ann. 

55,   1895;  last  3,  Nichols.  Phys.   Rev.   i,   i. 
See  Rubens,  Ladenburg,  Verb.  D.  Phys.  Ges.,p.  19,  1909,  for  extinction  coefs.,  reflective  power  and 

index  of  refraction,  i  /*  to   18  /*. 

SMITHSONIAN  TABLES. 


3o8 


TABLE  877. 

TRANSMISSION   PERCENTAGES  OF   RADIATION  THROUGH   MOIST  AIR. 

(For  bodies  at  laboratory  temperatures;  for  transmission  of  shorter -wave  energy,  see  Table  553.) 


The  values  of  this  table  will  be  of  use  for  finding  the  transmission  of  energy  through  air  containing  a  known  amount 
of  water  vapor.  An  approximate  value  for  the  transmission  may  be  had  if  the  amount  of  energy  from  the  source  be- 
tween the  wave-lengths  of  the  first  column  is  multiplied  by  the  corresponding  transmission  coefficients  of  the  subse- 
quent columns.  The  values  for  the  wave-lengths  greater  than  i8ju  are  tentative  and  doubtful.  Fowle,  Water-vapor 
Transparency,  Smithsonian  Misc.  Collections,  68,  No.  8,  1917;  Fowle,  The  Transparency  of  Aqueous  Vapor,  Astro- 
physical  J.  42,  p.  394,  1915. 


Range  of 
wave-lengths. 

Precipitable  water  in  centimeters. 

M                M 

.001 

.003 

.006 

.01 

•  03 

.06 

.  10 

•25 

•  50 

I.O 

2.0 

6.0 

IO.O 

o.rstoi.o 

_ 

_ 

_ 

IOO 

99 

99 

98 

97 

95 

93 

90 

83 

78 

i.o        1.25 

— 

— 

— 

99 

99 

98 

97 

95 

92 

89 

85 

74 

69 

i-2S       i.  5 

— 

— 

— 

96 

92 

84 

80 

66 

57 

5i 

44 

3i 

28 

1.5         2.0 

— 

— 

— 

98 

97 

94 

88 

79 

73 

70 

66 

60 

57 

*2             3 

06 

92 

8? 

84 

77 

70 

64 

— 

— 

— 

— 

3             4 

95 

88 

84 

?8 

72 

66 

63 

— 

— 

— 

— 

— 

— 

*4 

92 

83 

76 

?i 

65 

60 

53 

— 

— 

— 

— 

— 

— 

5             6 

95 

82 

75 

68 

56 

Si 

47 

35 

— 

— 

— 

— 

— 

6            7 

85 

54 

50 

3i 

24 

8 

4 

3 

2 

0 

0 

o 

0 

7            8 

94 

84 

76 

68 

57 

46 

35 

16 

IO 

2 

0 

0 

0 

8    -        9 

100 

IOO 

IOO 

99 

98 

96 

94 

65 





— 

— 

— 

t9          1° 

100 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

— 

— 

tio           n 

100 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

— 

— 

II               12 

IOO 

IOO 

IOO 

IOO 

IOO 

99 

98 

96 

95 

93 

— 

—  . 

— 

12              13 

100 

IOO 

IOO 

IOO 

99 

99 

97 

86 

82 

— 

— 

— 

*I3           14 

IOO 

IOO 

IOO 

99 

97 

94 

90 

80 

60 

— 

— 

— 

— 

*  14       is 

— 

— 

96 

93 

80 

75 

50 

15 

0 

o 

0 

o 

o 

*i5          16 

— 

— 

70 

55 

40 

o 

0 

0 

o 

o 

o 

16          17 

— 

— 

— 

— 

—  . 

50 

20 

o 

0 

0 

0 

0 

0 

17           18 

— 

— 

— 

— 

— 

25 

10 

0 

o 

o 

0 

0 

0 

18            oo 

98 

94 

89 

82 

45 

0 

0 

0 

0 

0 

0 

0 

0 

*  These  places   require  multiplication  by  the  following  factors  to  allow  for  losses  in  COa  gas.     Under 

average  sea-level  outdoor  conditions  the  COz  (partial  pressure 
per  cu.  m.    Paschen  gives  3  times  as  much  for  indoor  conditio 
2ju  to  3)U,  for  2  grams  in  m2  path  (95);  for  140  grams  in  m2 

=  0.0003  atmos.)  amounts  to  about  0.6  gram 
us. 
path  (93); 
'     (70);  more  CO2  no  further  effect: 

4  "  5        "   "      "       "   "      "     (93);     "     "      "       "    " 

13   "14,  slight  allowance  to  be  made; 
14  "  15,  80  grams  in  m2  path  reduces  energy  to  zero; 

15   "  16,   "       " 

t  These  places  require  multiplication  by  0.90  and  0.70  respectively  for  one  air  mass  and  0.85  and  0.65 
for  two  air  masses  to  allow  for  ozone  absorption  when  the  radiation  comes  from  a  celestial  body. 

In  the  above  table  italicized  figures  indicate  extrapolated  values. 

F.  Paschen  gives  (Annalen  d.  Physik  u.  Chemie,  51,  p.  14,  1894)  the  absorption  of  the  radiation  from  a  blackened 
strip  at  500°  C  by  a  layer  3.?  centimeters  thick  of  water  vapor  at  100°  C  and  atmospheric  pressure  as  follows: 


Wave-length  ................. 

Percentage  absorption  ......... 


2  .  20-3  . 

80 


5-33-7-67M 
94 


94-13 


The  following  table,  due  to  Rubens  and  Aschkinass  (Annalen  d.  Physik  u.  Chemie,  64,  p.  598,  1898),  gives  the 


Wave-length 

Percentage  absorption 


Wave-length I4-3M 

Percentage  absorption 43 

SMITHSONIAN  TABLES. 


35 


I5-7M 
6S 


16.0/4 
52 


80 


2O.O/J 
IOO 


3°9 


TABLES  378-379. 
REFLECTION    AND    ABSORPTION    OF    LONG-WAVE    RADIATIONS- 

TABLE  378.  —  Long- wave  Absorption  by  Gases. 

Unless  otherwise  noted,  gases  were  contained  in  a  20  cm  long  tube.    Rubens,  Wartenberg,  Verb.  d.  Phys.  Ges. 
13,  P-  7Q6,  IQU. 


g 

Percentage  absorption. 

g 

Percentage  absorption. 

Gas 

D 

B 

Long  X, 
Kg  lamp. 

Gas 

o 

1 

LongX. 
Hg  lamp. 

S 

23M 

52/i 

Fil- 

K 

23M 

52/i 

IlO/i 

Fil- 

CM 

tered, 

fe 

tered, 

3UM 

3I4M 

H2... 

?6 

IOO 
IOO 

IOO 

99  6 

IOO 

99-5 

IOO 

98.5 

IOO 

97-6 

NHa... 
CH4  .  .  . 

76 

76 

83.1 

o-S 

99-2 
99  2 

43-3 

IOO 

66.7 
IOO 

Br2.. 

20 

IOO 

IOO 

IOO 

IOO 

IOO 

C2H2.  .  . 

76 

99-5 

87  4 

97-3 

97-9 

IOO 

SO^. 

76 

22.6 

76.9 

12.7 

6 

4.8 

C2H«... 

76 

99 

96.4 

92.8 

IOO 

IOO 

CO2 

76 

IOO 

IOO 

IOO. 

IOO 

IOO 

CS2.  .  .  . 

26 

97-8 

IOO 

IOO 

99-5 

IOO 

CO... 
H2S.. 

76 
76 

IOO 

99  6 

IOO 

ii.  6 

94-1 

J-4 

92.1 

10.3 

91.6 

21.4 

C2H6O  . 
C<HioO. 

6 
Si 

85-4 
26.8 

5-4 
46 

58 

34 

52.4 

21.8 

49-9 
10.7 

N20.. 

76 

IOO 

96.8 

•4 

93  3 

90.8 

CsH12  .  . 

46 

66  f 

44-5 

88.8 

87 

84.2 

NO.. 

(CN). 

76 
76 

IOO 

94 
97-8 

99 

IOO 

87-3 
99-3 

85-5 

CH3CL. 
H^*.. 

98 
39-6 

IOO 

0-7 

IOO 

19.6 

95-4 
33-6 

94-7 
49-2 

*  Tube  40  cm  long. 


t  Pentane  vapor,  pressure  36  cm. 


TABLE  379.  —  Properties  with  Wave-lengths  108  ±  M. 

Rubens  and  Woods,  Verb.  d.  Phys.  Ges. '13,  p.  88,  1911. 
With  quartz,  1.7  cm  thick:   60  to  8o/x,  absorption  very  great;   63/1,99%;   82/1,97.5;  97M.  83. 


(a)   PERCENTAGE  REFLECTION. 


Wave-length. 


X   =   82/Z*.. 

X  =  io8/it- 


T«;land 
spar. 


Marble. 


43- 


25.8 
20.3 


Sylvile 


36.0 
19-3 


KBr 


82.6 
SX.l 


Kl 


29  6 

35-5 


5"°'       Glass.      Water.     Alcohol 


te 


19.7 

20.2 


19.2 


9.6 

II.  6 


*  Restrahlung  from  KBr. 


f  Isolated  with  quartz  lens. 


(b)  PERCENTAGE  TRANSPARENCY. 
Uncorrected  for  reflections. 


Solid. 


Thickness. 


Transparency. 


Liquid. 


Thickness. 


Thickness 
precipi- 


liquid. 


Trans- 
parency. 


Paraffin 

Mica 

Hard  rubber 

Quartz  1 1  axis 

Quartz,  amorph 

Rock  salt 

Fluorite 

Diamond 

Quartz  J_  axis 


3-03 

0.055 

0.40 

2.00 
3-85 
0.21 
0-59 
1.26 
2.00 


'4:8 


57-o 
16.6 
39-o 
62.6 

o 
21.  5 

5-3 
45-3 
81.3 
66.4 
49.8 
35-5 
29.0 


Benzene .  .  . 
Ethyl  alcohol. . . 
Ethyl  ether .... 

Water 

Water 

Vapors: 

Alcohol 

Ether 

Benzene ... 

Water 

CCh... 


I.  00 

0.158 
0.158 
0.029 
0.044 


2.00 
2.00 

2.00 
4.00 

2.00 


0.023 
0-350 
0.063 

O.2I 


56.8 
7-9 
37-1 
25.8 
13.6 


88 
33-S 

IOO 

19.6 

IOO 


(c)  TRANSPARENCY  OF  BLACK  ABSORBERS. 


Method  and  wave-length. 


Black  silk 

paper, 
.025  mm  thick 


Opaque  black 

paper, 
o.i  i  mm  thick 


0.4  mm  thick. 


Spectrometer 


Fluorite  "  restrahlung  " 
Rock  salt  "restrahlung" 
Quartz  lens  isolation 


2/4 

4 
6 

12 
26 

52 
108 


0 

0.9 
1.7 

8.2 
24.2 

46-0 
61  .  5 


0 

o 

0 

1.4 

3-2 


.6 


0.5 
8.6 
16.0 
37-6 
76.7 
91-3 
91.5 


SMITHSONIAN  TABLES. 


3IO    TABLES  3ffO,  381.— ROTATION  OF  PLPIME  OF  POLARIZED  LIGHT. 

TABLE  380. — Tartaric  Acid;  Camphor;  Santonin;  Santonio  Acid;  Cane  Sugar. 

A  few  examples  are  here  given  showing  the  effect  of  wave-length  on  the  rotation  of  the  plane  of  polarization.    The 
rotations  are  for  a  thickness  of  one  decimeter  of  the  solution.     The  examples  are  quoted  frc 


stein's 


'Phys.  Chem.  Tab."     The  following  symbols  are  used  : — 

/=  number  grams  of  the  active  substance  in  100  grams  of  the  solution. 
c=  solvent 

9=.  active          "  "  cubic  centimeter " 

Right-handed  rotation  is  marked  +,  left-handed  — . 


rom  Landolt  &  Born- 


Line  of 

Wave-length 
according  to 

Tartaric  acid,*  C4H6O«, 
dissolved  in  water. 

Camphor,*  Ci0H1(,O, 
dissolved  in  alcohol. 

Santonin.t  C15H1§O8, 
dissolved  in  chloroform. 

spectrum. 

Angstrom  in 

9  =  50  to  95, 

q  —  50  to  95, 

9=75  1096.5, 

cms.  X  io6. 

temp.  =  24°  C. 

temp.  =:  22.9^  C. 

temp.  =  2ou  C. 

B 
C 

68.67 
65.62 

+  2°748  -f  0.09446  q 

38°-  549  —  0.0852? 

—  140°.  i    +  0.2085  9 

—  149.3     +0.1555? 

D 

58.92 

+  1.950  +  0.13030? 

5  *  -945  —  0.0964? 

—  202.7     +0.3086? 

E 

52.69 

+  0.153-1-0.17514? 

74-33  i  —  0.1343? 

—  285.6    +0.5820? 

bi 
ba 
F 
e 

5I-83 
51.72 
48.61 
43-83 

—  0.832  +  0.19147? 
-^  3-598  +  0.23977  q 

—  9-657  +  Q-31  437? 

79-348  —  0.1451? 
99.601  —  0.1912  ? 
149.696  —  0.2346? 

—  302.38  +  0.6557  ? 

—  365-55  +  0.8284? 
—  534-98+I.5240? 

Santonin.t  C,5H18OS, 

Santonicacid,t 

Santonin.t  C15H18O3,  * 
dissolved  in  alcohol. 
c  —  1.782. 

dissolved  in 
alcohol. 

dissolved  in 
chloroform 

<2*H»0«, 

dissolved  in 
chloroform. 

C,2H«0,,, 
dissolved  in 

temp.  =  20°  C. 

^  =  4.046. 
temp.  — 

20°  C. 

c=  3.  1-30.5. 
temp.  = 

20°  C. 

f  =  27.I92.   ^ 

temp.  =  20°  C. 

/  :=  10  to  30. 

B 

68.67 

—  110.4° 

442° 

484° 

-49° 

47°.  56 

C 

65.62 

—  118.8 

5°4 

549 

—  57 

52.70 

D 

58.92 

—  161.0 

693 

754 

—  74 

60.41 

E 

52.69 

—  222.6 

991 

1088 

—  105 

84.56 

bi 

5I-83 

—  237.I 

I053 

1148 

—  112 

^ 

5x-72 

— 

_  • 

87.88 

F 

48.61 

—  261.7 

'323 

1444 

—  J37 

101.18 

e 

43-83 

—  380.0 

2OII 

22OI 

—  197 

- 

G 

43-07 

— 

— 

— 

131.96 

g 

42.26 

" 

238l 

26lO 

—  230 

*  Arndtsen,  "Ann.  Chim.  Phys."  (3)  54,  1858. 
t  Narini,  "  R.  Ace.  dei  Lincei,"  (3)  13,  zSSz. 

t  Stefan,  "  Sitzb.  d.  Wien.  Akad."  52,  1865. 

TABLE  381.  —  Sodium  Chlorate;  Quartz. 


Sodium  chlorate  (Guye,  C.  R.  108,  1889). 

Quartz  (Soret  &  Sarasin,  Arch,  de  Gen.  1882,  or  C.  R.  95,  1882).* 

Spec- 
trum 
line. 

Wave- 
length. 

Temp. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

a 

71.769 

I5°.0 

2°.o68 

A 

76.04 

i2°.66S 

Cd9 

36.090 

63°.628 

B 

67.889 

17.4 

2.318 

a 

71.836 

14.304 

N 

35-8I8 

64.459 

C 

65-073 

20.6 

2-599 

B 

68.671 

1  5-746 

Cdlo 

69-454 

D 

59.085 

18.3 

3.104 

O 

34.406 

70-587 

E 

53.233   ' 

16.0 

3.841 

C 

65621 

17.318 

F 

48.912 

11.9 

4-587 

D! 

58951 

21.684 

Cdn 

34-015 

72.448 

G 

45-532 

IO.I 

5-33' 

Da 

58.891 

21.727 

P 

33.600 

74-571 

G 

42-834 

14-5 

6.005 

Q 

32.858 

78.579 

H 

40.714 

6.754 

E 

52.691 

27.543 

Cdi2 

32.470 

80.459 

L 

38.412 

14.0 

F 

48.607 

32.773 

M 

37-352 

10.7 

8.100 

G 

43-072 

42.604 

R 

3I-798 

84.972 

N 

35-8l8 

12.9 

8.861 

CdM 

27.467 

121.052 

P 

33-93  i 

I  2.  1 

9.801 

h 

41.012 

47.481 

Cd18 

25-7I3 

143.266 

Q 

32-341 

II-9 

10.787 

H 

39.681 

Cd23 

23-125 

190.426 

R 

30-645 

I3-1 

11.921 

K 

39-333 

52.155 

T 

29.918 

12.8 

12.424 

Cd24 

22.645 

201.824 

Cd17 

28.270 

12.2 

13.426 

L 

38.196 

55.625 

Cd« 

21-935 

220.731 

CdJ8 

25-038 

II.6 

14.965 

M 

37.262 

58.894 

Cd26 

21.431 

235.972 

*  The  paper  is  quoted   from  a  paper  by  Ketteler  in  "  Wied.  Ann."  vol.  21,  p.  444.     The  wave-lengths  are  for 
the  Frauiiholer  lines,  Angstrom's  values  for  the  ultra  violet  sun,  and  Cornu's  values  for  the  cadmium  lines. 
SMITHSONIAN  TABLES. 


TABLE  382.  — ELECTRICAL    EQUIVALENTS.  311 

Abbreviations:  int'n'l,  international;  emu,  electromagnetic  units;  esu,  electrostatic  units; 
cgs,  centimeter-gram-second  units.  (Taken  from  Circular  60  of  U.  S.  Bureau  of  Standards, 
1916,  Electric  Units  and  Standards.) 


RESISTANCE  : 

i  international  ohm  = 
i .  00052  absolute  ohms 
i .  oooi  int'n'l  ohms  (France,  before  191 1) 
i. 00016  Board  of  Trade  units  (England, 

1903) 

1.01358  B.  A.  units 
1.00283  "legal  ohms"  of  1884 
i .  06300  Siemens  units 

i  absolute  ohm  = 

0.  99948  int'n'l  ohms 
i  "  practical "  emu 
io9  cgs  emu 

1 .  i T  24  x  io~12  cgs  esu 


CURRENT: 

i  international  ampere  - 

0.  99991  absolute  ampere 

1 .  00084  int'n'l  amperes  (U.  S.  before  1911) 
1.00130  int'n'l  amperes  (England,  before 

1906) 
i. 00106  int'n'l  amperes  (England,  1906- 

08) 
i.oooio  int'n'l  amperes  (England,  1909- 

10) 
1.00032  int'n'l  amperes  (Germany,  before 

1911) 
i .  0002 hit 'n'lamperes  (France, before  1911] 

i  absolute  ampere  - 

i  00009  int'n'l  amperes 
i  "practical"  emu 
o.  i  cgs  emu 
2.9982  X  io9  cgs  esu 


ELECTROMOTIVE  FORCE: 

i  international  volt  = 
.  00043  absolute  volts 
.00084  int'n'l  volts  (U.  S.  before  1911) 
.00130    int'n'l   volts    (England,    before 

1906) 

.00106  int'n'l  volts  (England,  1906-08) 
.00010  int'n'l  volts  (England,  1909-10) 
.00032  int'n'l  volts  (Germany,  before 

1911) 
i.  00032  int'n'l  volts  (France,  before  1911 

i  absolute  volt  = 
0.99957  int'n'l  volt 
i  "practical "  emu 
io8  cgs  emu 
o.  0033353  cgs  esu  


QUANTITY  OF  ELECTRICITY: 

(Same  as  current  equivalents.) 
i  international  coulomb  = 

1/3600  ampere-hour 

1/96500  farad  ay 


CAPACITY: 

i  international  farad  - 
0.99948  absolute  farad 

i  absolute  farad  = 
1.00052  int'n'l  farads 
i  "  practical  "  emu 
lo"9  cgs  emu 
8.9892  x  iou  cgs  esu 


INDUCTANCE: 

i  international  henry  = 
1.00052  absolute  henries 

i  absolute  henry  = 
o.  99948  int'n'l  henry 
i  "  practical  "  emu 
io9  emu 
1. 1124  x  io~12  cgs  esu 


ENERGY  AND  POWER: 

(standard  gravity  =  980. 665  cm/sec/sec.) 
i  international  joule  = 
i .  00034  absolute  joules 

i  absolute  joule  = 
o.  99966  int'n'l  joule 
io7  ergs 

o.  737560  standard  foot-pound 
o.  101972  standard  kilogram-meter 
0.277778x10"*  kilowatt-hour 


RESISTIVITY: 

i  ohm-cm  =  o.  393700  ohm-inch 

=  10,000  ohm  (meter,  mm2) 
=  12,732.4  ohm  (meter,  mm) 
=  393) 7°°  microhm-inch 
=  1,000,000  microhm-cm 
=  6,015,290  ohm  (mil,  foot) 


i   ohm   (meter,  gram) 
pound) 


5710.0  ohm  (mile 


MAGNETIC  QUANTITIES: 


i  int'n'l  gilbert     -  o.  99991  absolute  gilbert 
i  absolute  gilbert  =  i .  00009  int'n'l  gilberts 
i  int'n'l  maxwell  =  i .  00043  absolute  maxwells 
i  absolute  maxwell  =  o.  99957  int'n'l  maxwell 
i  gilbert  =  o. 7958  ampere-turn 

i  gilbert  per  cm  =o.  7958  ampere-turn  per 

cm 
-  2 . 021  ampere-turns  per 

inch 
i  maxwell  =  i  line 

=  io~*  volt-second 
i  maxwell  per  cm2  =  6. 45  2  max  wells  per  in2 


SMI-THSONIAN  TABLES. 


312  TABLE  3B3. 

COMPOSITION   AND   ELECTROMOTIVE   FORCE   OF  VOLTAIC  CELLS. 

The  electromotive  forces  given  in  this  table  approximately  represent  what  may  be  expected  from  a  cell  in  good  work- 
ing order,  but  with  the  exception  of  the  standard  cells  all  of  them  are  subject  to  considerable  variation. 


(a)  DOUBLE  FLUID  CELLS. 

Name  of 
cell. 

Negative  pole. 

Solution. 

Positive 
pole. 

Solution. 

E.M.F. 
in  volts. 

Bunsen  .     . 

Amalgamated  zinc 

{  I  part  H2SO4  to  ) 
)      12  parts  H2O  .  ) 

Carbon 

Fuming  HNO8 

1.94 

«      .     . 

«                « 

« 

«« 

HNO8,  density  1.38 

1.86 

Chromate  . 

«                « 

{12  parts  K2Cr2O7>| 
to  25  parts  of  1 
H2SO4  and  100  f 
parts  H2O  .     .  J 

« 

(  i    part   H2SO4  to  ) 
(      12  parts  H2O     .  [ 

2.00 

« 

«                « 

(  i  part  H2SO4  to  ( 
I      12  parts  H2O  .  ( 

« 

(  12  parts  K2Cr2O7  ( 
(    to  100  parts  H2O  J 

2.03 

Daniell*   . 

«                « 

(  i  part  H2SO4  to  ) 
]      4  parts  H2O    .  } 

Copper 

(  Saturated  solution  ) 
I   ofCuSO4+sH2O  J 

1.  06 

« 

«                « 

(  i  part  H2SO4  to  ( 
1      1  2  parts  H2O  .  j 

« 

M 

I.O9 

« 

«                «< 

(  5%    solution    of  / 
\    ZnS04  +  6H20( 

«( 

«< 

1.08 

«( 

<«                «« 

(  i   part  NaCl   to  J 
1      4  parts  H2O   .  f 

« 

M 

1.05 

Grove   .     . 

«                «« 

(  i  part  H2SO4  to  J 
(      1  2  parts  H2O  .  ) 

Platinum 

Fuming  HNO8  .     . 

i-93 

it 

«                <« 

Solution  of  ZnSO4 

«« 

HNO3,  density  1.33 

1.66 

« 

«<                « 

(  H2SO4  solution,  ) 
\      density  1.136  .) 

• 

Concentrated  HNO3 

i-93 

M 

«                « 

(  H2SO4  solution,  J 
I      density  1.136  .  ( 

« 

HNOa,  density  1.33 

1.79 

« 

M                             « 

(  H2SO4  solution,  ( 
|      density  1.06     .  ) 

« 

«« 

1.71 

« 

«                             (« 

(  H2SO4  solution,  ) 
I      density  1.14     .  J 

«< 

HNOa,  density  1.19 

1.66 

« 

««                             «« 

(  H2SO4  solution,  ) 
(      density  1.06     .  ) 

<« 

«(           «            « 

1.61 

"... 

<«                             « 

NaCl  solution  .     . 

<« 

"        density  1.33 

1.88 

Marie  Davy 

<«                             «< 

(  i  part  H2SO4  to  ) 
I      12  parts  H2O    ( 

Carbon 

(  Paste  of  protosul-  ) 
<    phate  of  mercury  ^ 
(    and  water  .     .     .  ) 

1.50 

Partz     .     . 

«(                             «< 

Solution  of  MgSO4 

" 

Solution  of  K2Cr2O7 

2.06 

*  The  Minotto  or  Sawdust,  the  Meidinger,  the  Callaud,  and  the  Lockwood  cells  are  modifications  of  the  Daniell, 
and  hence  have  about  the  same  electromotive  force. 

SMITHSONIAN  TABLES. 


TABLE  383  (continued}.  313 

COMPOSITION   AND   ELECTROMOTIVE   FORCE  OF  VOLTAIC  CELLS. 


Name  of  cell. 

Negative 
pole. 

Solution. 

Positive  pole. 

E.  M.  F. 

in  volts. 

(b)  SINGLE  FLUID  CELLS. 

Leclanche    .    .    . 

Chaperon    .     .     . 
Edison-Lelande    . 
Chloride  of  silver 
Law    

Amal.  zinc 

«        « 

«        « 

Zinc    .     . 

« 

«i 

Amal.  zinc 

«            u 
«            « 

Zinc   .     . 

(  Solution  of  sal-ammo-  \ 
I      niac                              C 

f  Carbon.  Depolari-  ] 
I  zer  :    manganese    1 
1  peroxide     with    j 
[  powdered  carbon  j 
(  Copper.  Depolar-  ( 
)  izer  :  CuO  .     .     .  ) 

(  Silver.    Depolari- 
(  zer:  silver  chl'ride 
Carbon  .... 

M 

<« 
M 

Cadmium    .     .    . 
Copper  .... 

1.46 

0.98 
0.70 
1.02 

i-37 
i-3 
i  .08 

2.OI 

0-34 
0.98 

(  Solution  of  caustic 
1      notash    . 

1  23  %  solution   of  sal-  ) 
(      ammoniac  .     .     .     .  J 

I  C  °J               "                " 

(  ipJznO,ipt.NH4Cn 
I    3  pts.  plaster  of  paris,  1 
j    2  pts.  ZnCl2,and  water  J 
[  to  make  a  paste     .     .  J 
(  Solution   of  chromate 
|      of  potash    .... 
(  12  parts  K2Cr2O7  + 
25  parts  H2SO4  -j- 
(      100  parts  H2O    .     . 
(  i  part  H2S04  -f 
I      12  parts  H2O  + 
(      ipartCaS04      .    .) 
H2O      

Dry  cell  (Gassner) 

Poggendorff     .    . 
« 

J.  Regnault  .    .    . 
Jolta  couple    .    . 

(c)  STANDARD  CELLS. 

Weston  normal    . 
Clark  standard     . 

jCadmi'm) 
j  am'lgamj 

Zinc     | 
am'lgam  \ 

(  Saturated  solution  of  ) 
1               CdS04              f 

(  Saturated  solution  of  ) 
j               ZnS04               ( 

Mercury. 
Depolarizer:  paste 
of    Hg2SO4     and 
CdS04    .    .     .     .( 
Mercury. 
Depolarizer:  paste 
of   Hg2SO4     and 
ZnSO4    .... 

1.0183* 

at  20°  C 

•434 

at  15°  C 

(d)  SECONDARY  CELLS. 

Lead  accumulator 
Regnier  (i)  .    .    . 

"          (2).      .      . 

Main  .          ... 

Lead  .     . 

Copper    . 

Amal.  zinc 
Amal.  zinc 

Iron    .     . 

(  H2SO4  solution  of         ) 
}      density  i.i       .     .     .  J 

CuSO4  +  H2SO4   .     . 

ZnSO4  solution  .     .     . 
H2SO4  density  ab't  1.  1 

KOH  20  %  solution    . 

PbO2           .     . 

2.2f 

(  1.68  to 
1  0.85,  av- 
(  erage  1.3. 
2.36 
2.50 
(  i.i,  mean 
of  full 
(  discharge. 

«« 

"    inH2SO4     . 

« 

A  nickel  oxide     . 

Edison     .... 

*The  temperature  formula  is  E,=  E20  —  0.0000406  (t— 20)— 0.00000095  (t  —  20 )»  4-0-0000000 1  (t  — ao)». 
t  The  value  given  for  the  Clark  cell  is  the  old  one  adopted  by  the  Chicago  International  Electrical  Congress  in  1893. 
The  temperature  formula  is  Et=  E15  — 0.00119  (t—  15)  — 0.000007  (t  —  15)*. 

t  F.  Streintr  gives  the  following  value  of  the  temperature  variation  —  at  different  stages  of  charge  : 

at 


E.  M.  F. 
dE/dtXio« 


1.9223 
140 


1.9828 

228 


2.0031 
335 


2.0084 
285 


2.010$ 
255 


2.2070 
73 


Dolezalek  gives  the  following  relation  between  E.  M.  F  and  acid  concentration  : 
Per  cent  H,SO4  64.5  52.2  35.3  21.4  5.2 
E.M.F.,  o°C  2.37  3.25  2.10  2.00  1.89 

SMITHSONIAN  TABLES. 


3'4 


TABLE  384. 


CONTACT    DIFFERENCE    OF 

Solids  with  Liquids  and 

Temperature  of  substances 


E 

s 

cL 

• 

c 

3 

u 

C 

1 

2 

1 

C 

H 

1 

(.01 

.269 

(   -285) 

(—  -I05 

Distilled  water                . 

1 

to 

.148 

171 

)     to   > 

177 

\        to 

I  -17 

.100 

.1/1 

I         1 

(  -345; 

•*// 

(+•156 

Alum  solution  :  saturated  / 
at  16°  q  C.  .                   .    ( 

- 

—.127 

-.653 

—•139 

.246 

-.225 

—536 

Copper  sulphate  solution  :  ) 
sp.  gr.  1.087  at  r6°.6  C.    ) 

- 

.103 

- 

- 

- 

- 

- 

Copper  sulphate  solution  :  ) 
saturated  at  15°  C.   .     .    ) 

- 

.070 

- 

- 

- 

- 

- 

Sea  salt  solution  :  sp.  gr.  ( 
1.18  at  20°.5  C.     .    .    .    J 

- 

—•475 

-.605 

- 

—.856 

—•334 

-.565 

Sal-ammoniac      solution  :  ) 
saturated  at  15°.  5  C.     .    [ 
Zinc  sulphate  solution  :  sp.  j 
gr.  1.125  at  i6°.9  C.  .     .    f 

; 

-396 

-.652 

-.189 

•059 

—•364 

-637 
-.238 

Zinc     sulphate    solution  :[ 

saturated  at  I5°.3  C.      .    \ 

—  -43° 

One  part  distilled  water  +  ) 

3    parts    saturated    zinc  > 

_ 

_ 

_ 

_ 

_ 

_ 

—  -444 

sulphate  solution  .     .     .    ) 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight      .     .     . 

- 

- 

- 

_ 

- 

- 

—•344 

i  to  10  by  volume     .     .     . 

(  about  > 

t  —  -°35  1 

i  to  5  by  weight  .... 

- 

- 

- 

- 

- 

- 

(.01   ) 

5  to  i  by  weight  .... 

to 

- 

- 

—  .I2O 

- 

—•25 

- 

(3-0) 

(  -55  ) 

(     .72 

j  ^   ^ 

Concentrated  sulphuric  acid 

{  to  > 

1.113 

_ 

!  to 

to     > 

_. 

_ 

(•85) 

(  1.252 

1.6    ) 

Concentrated  nitric  acid 

_ 

_ 

.672 

_ 

_ 

Mercurous  sulphate  paste  . 

- 

_ 

_ 

_ 

_ 

_ 

Distilled  water  containing  ) 
trace  of  sulphuric  acid       ( 

— 

- 

- 

- 

- 

- 

—.241 

*  Everett's  "  Units  and  Physical  Constants:  "  Table  of 


SMITHSONIAN  TABLES 


TABLE  384  (continued). 


POTENTIAL     IN     VOLTS. 

Liquids  with  Liquids  in  Air.* 
during  experiment  about  16°  C. 


i 

u 

o  o> 

|o 

g  J 

I 

1 

c  "• 

|| 

1^ 

:« 

5.  T 

-s 

11 

Is 

1 

3 
B 

1 

1 

•  -  « 

ll 

"C 

11 

P. 

!•« 

r  2 

t:  2 

1 

|| 

1 

i 

5 

E   3 

c.  s 

N  * 

N  * 

i+ 

V) 

.IOO 

.231 

—  .047 

.164 

Alum  solution:  saturated 

at  i6°.s  C  

~ 

—  .014 

~ 

~ 

" 

~ 

Copper  sulphate  solution  : 
sp.  gr.  1.087  at  i6°.6  C. 

- 

- 

- 

- 

- 

- 

.000 

- 

- 

- 

Copper  sulphate  solution  :  ) 
saturated  at  15°  C.   .     .    [ 

- 

- 

- 

—•043 

- 

- 

- 

.095 

.102 

- 

Sea  salt  solution  :  sp.  gr. 
1.18  at  20°.  5  C.     .     .     . 

- 

—•435 

- 

- 

- 

- 

- 

- 

- 

- 

Sal-ammoniac      solution  :  { 
saturated  at  15°.  5  C.      .    j 

- 

—•348 

- 

- 

- 

- 

- 

- 

- 

- 

Zinc    sulphate    solution  :  ) 

sp.  gr.  1.125  at  l6°9  C-    J 

Zinc    sulphate     solution  :  / 
saturated  at  15°.  3  C.      .    ( 

-.284 

- 

- 

—  .200 

- 

—.095 

- 

- 

- 

One  part  distilled  water  +  ) 

3    parts    saturated    zinc  > 

— 

— 

— 

— 

— 

—  .102 

— 

— 

— 

— 

sulphate  solution      .     .    ) 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight     .     .     . 

o 

i  to  10  by  volume     .     .     . 

—  -358 

i  to  5  by  weight  .... 

.429 

5  to  i  by  weight  .... 
Concentrated  sulphuric  acid 

.848 

—  .010 

- 

1.298 

1.456 

1.269 

- 

1.699 

- 

- 

Concentrated  nitric  acid 

Mercurous  sulphate  paste  . 

— 

— 

•4/5 

Distilled  water  containing  1 

078 

trace  of  sulphuric  acid  .    ) 

Ayrton  and  Perry's  results,  prepared  by  Ayrton. 
SMITHSONIAN  TABLES. 


TABLE  385. 


DIFFERENCE    OF    POTENTIAL    BETWEEN    METALS    IN    SOLUTIONS    OF 

SALTS. 

The  following  numbers  are  given  by  G.  Magnanini  *  for  the  difference  of  potential  in  hundredths  of  a  volt  between 
zinc  in  a  normal  solution  ot  sulphuric  acid  and  the  nieials  named  at  the  head  of  the  different  columns  when  placed 
in  the  solution  named  in  the  first  column.  The  solutions  were  contained  in  a  U-tube,  and  the  sign  of  the  differ- 
ence of  potential  is  such  that  the  current  will  flow  from  the  more  positive  to  the  less  positive  through  the  ex- 
ternal circuit. 


Strength  of  the  solution  in 
gram  molecules  per 
liter. 

Zinc.f 

Cadmium.  t 

Lead. 

Tin. 

Copper. 

I 

Silver. 

No.  of 
molecules. 

Salt. 

Difference  of  potential  in  centivolts. 

0-5 

H2SO4 

O.O 

36.6 

5J-3 

100-7 

121.3 

I.O 

NaOH 

—32.1 

19-5 

3'-8 

O.2 

80.2 

95-8 

I.O 

KOH 

—42.5 

'5-5 

32.0 

—  1.2 

77.0 

104.0 

0.5 

Na2SO4 

1.4 

35-6 

50.8 

51-4 

IOI-3 

120.9 

I.O 

Na2S208 

—5-9 

24.1 

45-3 

45-7 

38.8 

64.8 

I.O 

KNO3 

ii.Sj 

31.9 

42.6 

31-1 

8l.2 

!05-7 

I.O 

NaNO8 

"-5 

32-3 

51.0 

40-9 

95-7 

114.8 

0.5 

K2Cr04 

23-9t 

42.8 

41.2 

40.9 

94.6 

I2I.O 

0.5 

K2Cr2O7 

72.8 

DI.I 

78.4 

68.1 

123.6 

132.4 

K2S04 

1.8 

34-7 

51.0 

40.9 

95-7 

II4.8 

0.5 

(NH4)2S04 

—0-5 

37-r. 

53-2 

57-6* 

101.5 

125-7 

0.25 

K4FeC6N6 

—6.1 

33.6 

50-7 

41.2 

-t 

87.8 

0.167 

KeFe2(CN)i2 

4I.O§ 

80.8 

81.2 

130.9 

110.7 

124.9 

I.O 

KCNS 

—  1.2 

32.5 

52.8 

52-7 

52-5 

72.5 

I.O 

NaNOg 

4-5 

35-2 

50.2 

49-o 

103.6 

104.6? 

0.5 

Sr(N08)2 

14.8 

38-3 

50.6 

48.7 

103.0 

1  1  9-3 

0.125 

Ba(N08)2 

21.9 

39-3 

52.8 

109.6 

121.5 

I.O 

KN08 

—  t 

35-6 

47-5 

49-9 

104.8 

115.0 

0.2 

KClOa 

15—10$ 

39-9 

53-8 

57-7 

105-3 

120.9 

0.167 

KBrO8 

13-20* 

40.7 

5|-3 

5°-9 

111.3 

120.8 

I.O 

NH4C1 

2.9 

324 

5i.3 

5°-9 

81.2 

101.7 

I.O 

KF 

2.8 

22.5 

41.1 

50.8 

61.3 

61.5 

I.O 

NaCl 

— 

Si-2 

5°-3 

80.9 

101.3 

I.O 

KBr 

2-3 

3T-7 

47.2 

52-5 

736 

82.4 

I.O 

KC1 

32.1 

51.6 

52-6 

81.6 

107.6 

o-5 

NaaSOa 

—8.2 

28.7 

41.0 

31.0 

68.7 

103.7 

-II 

NaOBr 

18.4 

41.6 

73-1 

70.6  J 

89.9 

99-7 

I.O 

C4H606 

5-5 

39-7 

61.3 

54-4§ 

104.6 

123.4 

0.5 

C4H606 

4.1 

61.6 

57-6 

110.9 

125.7 

0.5 

C4H4KNaO« 

—7-9 

31-5 

51-5 

42-47 

100.8 

119.7 

*  "  Rend,  della  R.  Ace.  di  Roma,"  1890. 

t  Amalgamated. 

t  Not  constant. 

§  After  some  time. 

II  A  quantity  of  bromine  was  used  corresponding  to  NaOH  =  i. 


SMITHSONIAN  TABLES. 


TABLE  386. 
THERMOELECTRIC   POWER. 


317 


The  thermoelectric'power  of  a  circuit  of  two  metals  is  the  electromotive  force  produced  by  one  decree  C  difference 
of  temperature  between  the  junctions.  The  thermoelectric  power  varies  with  the  temperature,  thus:  thermoelectric 
power  =  Q  =  dE/dt  =  A  +  Bt,  where  A  is  the  thermoelectric  power  at  o°  C,  B  is  a  constant,  and  /  is  the  mean  tem- 
perature of  the  junctions.  The  neutral  point  is  the  temperature  at  which  dE/dt  =  o,  and  its  value  is  —  A/B.  When 
a  current  is  caused  to  flow  in  a  circuit  of  two  metals  originally  at  a  uniform  temperature,  heat  is  liberated  at  one  of 
the  junctions  and  absorbed  at  the  other.  The  rate  of  production  or  liberation  of  heat  at  each  junction,  or  Peltier  effect, 
is  given  in  calories  per  second,  by  multiplying  the  current  by  the  coefficient  of  the  Peltier  effect.  This  coefficient  in 
calories  per  coulomb  =  QT/y,  in  which  Q  is  in  volts  per  degree  C,  T  is  the  absolute  temperature  of  the  junction,  and 
3F  =  4.19.  Heat  is  also  liberated  or  absorbed  in  each  of  the  metals  as  the  current  flows  through  portions  of  varying 
temperature.  The  rate  of  production  or  liberation  of  heat  in  each  metal,  or  the  Thomson  effect,  is  given  in  calories 
per  second  by  multiplying  the  current  by  the  coefficient  of  the  Thomson  effect.  This  coefficient,  in  calories  per  coulomb 
=  BTd/3,  in  which  B  is  in  volts  per  degree  C,  T  is  the  mean  absolute  temperature  of  the  junctions,  and  6  is  the  differ- 
ence of  temperature  of  the  junctions.  (BT)  is  Sir  W.  Thomson's  "Specific  Heat  of  Electricity."  The  algebraic  signs 
are  so  chosen  in  the  following  table  that  when  A  is  positive,  the  current  flows  in  the  metal  considered  from  the  hot 
junction  to  the  cold.  When  B  is  positive,  Q  increases  (algebraically)  with  the  temperature.  The  values  of  A ,  B,  and 
thermoelectric  power  in  the  following  table  are  with  respect  to  lead  as  the  other  metal  of  the  thermoelectric  circuit. 
The  thermoelectric  power  of  a  couple  composed  of  two  metals,  i  and  2,  is  given  by  subtracting  the  value  for  2  from 
that  for  i;  when  this  difference  is  positive,  the  current  flows  from  the  hot  junction  to  the  cold  in  i.  In  the  following 
table,  A  is  given  in  microvolts  per  degree,  B  in  microvolts  per  degree  per  degree,  and  the  neutral  point  in  degrees. 

The  table  has  been  compiled  from  the  results  of  Becquerel,  Matthiessen  and  Tait;    in  reducing  the  results,  the 
electromotive  force  of  the  Grove  and  Daniell  cells  has  been  taken  as  1.95  and  1.07  volts.    The  value  for  constantan 
reduced  from  results  given  in  Landolt-Bornstein's  tables.    The  thermoelectric  p 


are  given  by  Becquerel  in  the  reference  given  below. 


:tric  powers  of  antimony  and  bismuth  alloys 


Substance. 

A 
Microvolts. 

B 

Microvolts. 

Thermoelectric  power 
at  mean  temp,  of 
junctions  (microvolts). 

Neutral 
point 

~  B 

Author- 
ity. 

20°  C 

50°  C 

Aluminum 

—0.76 
-11.94 

+2.63 

+I.34 

+2.80 
+17-15 

+  2.22 

-21.8 
-83.57 
-3-04 

+0.0039 
—0.0506 

+0.0424 
+0.0094 

+O.OIOI 

—0.0482 

0.0000 

-0.0094 

—0.0506 
+0.2384 
—0.0506 

-0.68 
+6.0 

+  22.6 

+26.4 
-12.95 

—  13.56 
—97.0 
—89.0 
—65.0 
—45-0 
+3.48 

—  22 

+  1.52 
+O.IO 

+3-8 

—0.2 

+3-0 
+16.2 
+17-5 

—  o.oo 
+  2.03 

+5.9 

-0.413 

-2278 

—0.56 

—14.47 
-12.7 

+4-75 
+2-45 
+8.9 

—  19-3 
+1.81 

+7-30 
+14-74 

+  12.  IO 
+9.10 
0.00 

+I.7S 

—3-30 
-15-50 
-24-33 

+195 
-"^36 

-62 
-143 

C-T77D 
+356 

+T36 

[-"431] 

T 
M 

T 
B 
M 

T 
B 
S' 
M 

T 
M 

S 
T 

M 

B 

T 
S 
MB 
B 
T 

Antimony,  comm'l  pressed  wire..  . 
axial  

"          equatorial  

Argentan  

•  Arsenic  

Bismuth,  comm'l  pressed  wire.  .  .  . 
pure                       "  
crystal,  axial  
equatorial  
Cadmium.  .  . 

fused    

Cobalt               

CoDoer 

commercial  

Gold                                   

'     pianoforte  wire  

Lead                     

Molybdenum      

Nickel            

"       (-18°  to  175°)  

SMITHSONIAN  TABLES. 


318 


TABLES  386  (continued). -387.-THERMOELECTRIC  POWER. 

TABLE  386. — Thermoelectric  Power  (continued). 


Substance. 

A 

Microvolts. 

D 
Microvolts. 

Thermoelectric  power 
at  mean  temp,  of 
junctions  (microvolts). 

Neutral 
point 

f\ 

Au- 
thority. 

20'  C. 

So-C. 

B' 

Palladium        .... 
Phosphorus  (red)  . 

—6.18 

+2-57 
—  0.60 

+7.90 
+5-90 
+6.15 

+  2.12 
+  11.27 

—0.43 
+2-32 

—0.0355 

—  0.0074 
—  0.0109 

+O.OO62 
—0.0133 
+0.0055 

+0.0147 
—0.0325 

+0.0055 
+0.0238 

-6.9 
+29.9 
+  0.9 
+  2.42 
—  .8l8 

+8.03 
+5-63 
+6.26 
+807. 
+2.41 
+3.00 

+  10.62 

—2.6 

+500. 

+  160. 
+0.8 

+0.1 

—0.33 

—2.0 

+2.79 
+3-7 

-7.96 

+  2.20 
—  I-  15 

+0.94 
—2.14 

+8.21 

+5-23 
+6.42 

+2.86 

+2.18 
+9.65 

+0.33 
—  0.16 

+3.51 

—174 

347 

—55 

[—1274] 
444 
[-1118] 

—  144 
347 

78 
-^98 

T 
M 

T 
« 

B 
T 

M 
T 
M 
B 
T 

H 

H 

H 

M 
T 

T 
M 

'         (hardened)     . 
(malleable)    . 
'        wire 
'        another  specimen 
Platinum-iridium  alloys: 
85%Pt+i5%Ir       .       . 
90%Pt  +  io%Ir       .       . 
,95%  Pt+    5%  IT       .       . 
Selenium  
Silver 

(pure  hard)  . 
"      wire        .... 
Steel  

Tantalum        .... 
Tellurium  /3     . 
a    .... 
Thallium  
Tin  (commercial)  . 

« 

Tungsten  

'    pure  pressed  . 

B     Ed.    Becquerel,  "Ann.   de   Chim.   et   de   Phys."    [4]    vol.  8.     S.   Bureau    of 
Standards. 
M     Matthiesen,  "Pogg.  Ann."  vol.  103,  reduced  by  Fleming  Jenkin. 
T     Tait,  "Trans.  R.  S.  E."  vol.  27,  reduced  by  Mascart. 
H     Haken,  Ann.  der  Phys.  32,  p.  291,  1910.    (Electrical  conductivity  of  Te/3  =  o.o4, 
Tea  1.7  e.  m.  units.)     Swisher,  igi/. 

TABLE   387. — Thermoelectric  Power   of  Alloys, 


The  thermoelectric  powers  of  a  number  of  alloys  are  given  in  this  table,  the  authority  being  Ed.  Becquerel.    The/  are 
relative  to  lead,  and  for  a  mean  temperature  of  50°  C.     In  reducing  the  results  from  cc 


the  thermoelectric  power  of  lead  to  copper  was  taken  as —  1.9. 


:opper  as,  a  reference  metal, 


Substance. 

Relative 
quantity. 

Thermoelec  1 
tricpower  in  1 
microvolts.  1 

Substance. 

Relative  j 
quantity.  [ 

Thermoelec-  1 
trie  power  in  1 
microvolts.  1 

Substance. 

Relative  ' 
quantity.  ! 

Therraoelec-  1 
trie  power  in  1 
microvolts.  1 

Antimony 
Cadmium 

806) 

227 

Antimony 
Zinc 

2  ) 
I   > 

43 

Bismuth 
Antimony 

J! 

-5M 

Antimony 
Cadmium 
Zinc 

4) 

2  > 
I  ) 

146 

Tin 

Antimony 
Cadmium 

Sj 

35 

Bismuth 
Antimony 

!l 

—  63.2 

Antimony 
Cadmium 
Bismuth 
Antimony 
Zinc 
Antimony 
Zinc 
Bismuth 

806) 

121  ) 
806? 

806) 
406  > 
121  ) 

137 

95 
8.1 

Zinc 

Antimony 
Tellurium 

Antimony 
Bismuth 

Antimony 
Iron 

3) 

4» 
i  \ 

10.2 

8.3 

Bismuth 
Antimony 

Bismuth 
Antimony 

Bismuth 
Tin 

Bismuth 
Selenium 

"1 

12   | 
I   ) 

10  I 

—68.2 
—66.9 
60 
—24.5 

Antimony 

4l 

Antimony 

8  / 

1.4 

Cadmium 

2! 

•?/: 

Magnesium 

i  ) 

Bismuth 

12  ) 

Lead 

7\  nr* 

i  r 

,  i 

7° 

Antimony 

8  1 

—0.4 

Zinc 

1  ' 

—  31-1 

Zsinc 

1  J 

Lead 

i  ) 

Bismuth 

12   I 

Antimony 
Cadmium 

H 

Bismuth 

- 

-43-8 

Arsenic 

I   j 

—  46.0 

Zinc 

i  r 

40 

Bismuth 

2  ) 

Bismuth 

1   ( 

f<3 

Tin 

ij 

i  Antimony 

i  C 

—33-4 

Bismuth  sulphide 

I   J 

Go.  I 

Tatti 


TABLE  388. 


TABLES   388,  389. 

Theimoelectrlc  Power  against  Platinum. 


One  junction  is  supposed  to  be  at  o°C;  +  indicates  that  the  current  flows  from  the  o°  junction 
into  the  platinum.     The  rhodium  and  indium  were  rolled,  the  other  metals  drawn.* 


Tempera- 
ture, °  C. 

Au. 

Ag. 

9o%Pt-f 

IO%Pd. 

IO%Pt+ 

90%Fd. 

Pd. 

90%Pt+ 
io%Rh. 

9°%Pt+ 
io%Ru. 

Ir. 

Rh. 

-185 

—0.15 

—  0.16 

—  O.I  I 

+0.24 

+0.77 

_ 

—0.53 

—0.28 

—  0.24 

—80 
+  100 

-0-31 
+0.74 

-0-30 
+0.72 

—  0.09 
+0.26 

4-0.15 
—  0.19 

4-0-39 
—0.56 

— 

-0-39 

+0.73 

—0.32 
+0.65 

—0.31 
+0.65 

+  2OO 

+  1.8 

+  1-7 

+0.62 

—0.31 

—  1.  20 

— 

+  '•5 

+  I.C 

+  300 

+3.0 

+  1.0 

—0-37 

—  2.O 

4-2-3 

+  2.6 

+2.5 

+  2.6 

+  400 

+4-5 

+4-5 

+  1-5 

—0-35 

—2.8 

+3-2 

+3-6 

+3-6 

+3-7 

+  500 

+6.1 

+6.2 

+  1.9 

—o.i  8 

-3.8 

+4-6 

+4-8 

45.i 

+  600 
+  700 

+7-9 
4-9-9 

+8.2 

+  10.6 

+2.4 

+2.9 

+0.12 

+0.61 

-4.9 

—  6-3 

S:! 

4-5-7 
+6.9 

+6.1 
+7.6 

+6.5 
+8.1 

+800 
+900 

+  I2.O 

4-13-2 
+16.0 

# 

+  1.2 
+2.1 

-7-9 
—9.6 

+7.2 
+8.3 

+8.0 
+9-2 

+9.1 
+  10.8 

+9-9 
+  11.7 

+  IOCO 
+  1100 

+  i6Jf 

— 

is 

+3-i 
+4.2 

-"•5 

~13-S 

+  10.6 

+  10.4 
+  11.6 

+  12.6 

+  13-7 
+  15.8 

+(1300) 

— 

— 

4~T3  l 

+  '4-2 

+  18  6 

+20.4 

+(1500) 

" 

" 

" 

" 

™* 

+  15-6 

+  16.9 

+23-' 

+25.6 

*  Holborn  and  Day. 


TABLE  389.  —Thermal  B.  M.  F.  of  Platinum-Rhodium  Alloys  Against  Pure  Platinum,  In  Millivolts.* 


10  p.  ct. 

t 

i  p.  ct. 

5  P-  ct. 

Low. 

High. 

Stan- 
dard. 

15  p.  ct. 

20  p.  Ct. 

30  p.  ct.t 

40  p.  ct.t 

loop.  Ct.t 

100° 

O  T 

O  c  c 

0.6^ 

0.64 

0.64 

o  6<; 

06? 

2OO 

O  J."7 

i  18 

I  4.1 

I  4^ 

I  4^ 

i  <;o 

J    C  I 

300 

0.63 

1.85 

2.28 

2.32 

2.32 

2.41 

.... 

2-34 

2.45 

•O* 

2-57 

400 

0.84 

2.53 

3.2I 

3.26 

3.25 

3-45 

3-50 

3-50 

3.64 

3-76 

500 

1.05 

3.22 

4.17 

4-23 

4.23 

4-55 

4.60 

4-74 

493 

5-08 

60O 
700 

»'2S 

i-45 

3.92 

4.62 

ci6 

6.19 

5-24 
6.28 

is 

5-71 
6.94 

h 

6.06 
7-49 

6.31 
7.80 

6.55 
8.14 

800 

i.6S 

5-33 

7-25 

7-35 

7-33 

8.23 

8.60 

9.01 

9-37 

9.87 

900 

i.8S 

6.05 

8-35 

8.46 

8.43 

9-57 

10.09 

10.67 

11.09 

11-74 

IOOO 

2.05 

6.79 

9-47 

9.60 

9-57 

10.96 

11.65 

12.42 

12.94 

1374 

I  100 

2.25 

7-53 

10.64 

10.77 

10.74 

12.40 

13.29 

14-33 

14.99 

M.87 

I2OO 

2-45 

8.29 

11.82 

11.97 

"•93 

13-87 

14.96 

16.39 

17-13 

I8.IO 

I3OO 
I4OO 

2.65 
2.86 

9.06 
9.82 

13.02 
14.22 

13.18 
14-39 

i3-J3 
14-34 

I5-38 
16.98 

16.65 
18.39 

18.51 
20.67 

I9-51 
21-73 

20.46 

•3  06 

i  S  61 

T  C    C  C 

18  41 

-»o  i  c 

3-00 

1663 

i68-> 

15-ii 

T  A  7  C 

IQ  Q4. 

T  QO 
flMf 

2 

11.31 

1781 

18  03 

17    QC 

21  47 

2~i  nc 

3-4° 

I/.°j 

~  c< 

_ 

T«     Aa 

18  70 

18  61 

T>    11 

^4   s  ^ 

I75S 

3-5° 

1.2.44 

10-49 

~-.Jl 

-4OJ 

*  Carnegie  Institution,  Pub.  157,  1911. 
t  Holborn  and  Day,  mean  value,  1899. 


t  Holborn  and  Wien,  1892. 


SMITHSONIAN  TABLES. 


3'20 


TABLES  390-391. 


THERMOELECTRIC  PROPERTIES:   PRESSURE  EFFECTS- 
TABLE  390.  —  Thermoelectric  Power;  Pressure  Effects. 

The  following  values  of  the  thermoelectric  powers  under  various  pressures  are  taken  from  Bridgman,  Pr.  Am.  Acad. 
Arts  and  Sc.  53,  p.  269,  1018.  A  positive  emf  means  that  the  current  at  the  hot  junction  flows  from  the  uncompressed 
to  the  compressed  metal.  The  cold  junction  is  always  at  o°  C.  The  last  two  columns  give  the  constants  in  the 
equation  E  =  thermoelectric  force  against  lead  (o°  to  100°  C)  =  (At  +  BP)  X  io~«  volts,  at  atmospheric  pressure,  a 
positive  emf  meaning  that  the  current  flows  from  lead  to  the  metal  under  consideration  at  the  hot  junction. 


Metal. 

Thermo-electric  force,  volts  X  io» 

Formula 
coefficients. 

Pressure,  kg/cm2 

2000                    4000          !           8000 

12,000 

Temperature,  °  C 

50° 

100° 

50° 

100° 

50° 

100° 

20° 

50° 

100° 

A 

B 

Bit.. 
Znf.   . 

53,000 

6,200 

4.930 

2,040 
2,850 
2,190 
1,810 
1,190 

C 

Jg 

456 

+292 
—  70 

a 

—123 
-84 
-156 

85,000 

14,100 
10,870 
7,120 
5,950 

4,380 

3,600 
2,530 
i,  680 
1,870 
1,670 
1,050 
1,052 
584 

IOI 

140 

+87 

—232 

-167 
-348 

110,000 
13,000 

9,380 
4,620 
5,800 
4,400 

3,600 
2,360 
1,500 
1,720 

590 

920 

905 

+580 

—91 

+187 
+58 

—242 
-181 
>  —316 

185,000 
28,500 
20,290 
14,380 
11,810 
8,800 
7,3io 
4,990 
3,400 
3,720 
3,250 
2,120 
2,051 
i,  216 
294 
278 
+165 
—452 
-362 
-692 

255,000 
26,100 
17,170 
10,960 
ii,53o 
8,630 
7,370 
4,690 
3,230 
3,350 
5,300 
i,  860 
i,79i 
1,124 
32 
375 
+70 
-489 
-395 
—630 

425,000 
58,100 
37,630 
28,740 
23,790 
17,690 
14,350 
10,120 
7,190 
7,190 
5,820 
4,210 
3,974 
2,420 
929 
555 
+292 
-894 
-791 
—  1,360 

185,000 
14,400 
8,780 
6,680 
6,750 

5,ooo 
3,88o 
2,700 
i,  880 
+1,900 
—990 
+880 
+990 

+^ 

+146 
-182 
-308 
-259 
-352 

452,000 
38,500 
23,750 
19,180 
17,200 
12,970 
11,030 
7,050 
5,140 
4,950 

220 
28l 
2,627 

1,616 
312 

562 

+  10 

—  719 
-648 
—937 

710,000 
87,400 
52,460 
45,56o 
35,470 
26,520 
21,570 
15,140 
11,440 
10,560 
7,680 
6,330 
5,76o 
3,546 
1,962 
833 
+390 
—  1,314 
—  1,296 
—  2,061 

—  74.42 
+3  •  047 
+  1.659 

+  12.002 
-34.76 
,-5-496 

—   3  092 
+1-594 
—  17.61 
+  2.556 
+16.18 

+2.899 
+2-777 
—0.416 
+5-892 
+0.230 
+1.366 
-0.095 
-17.32 

+  .0160 
-.00495 
-.  00134  l 
+  .1619 
-  •  0397 
—  .01760 
-.01334 
+  .01705 
—  .0178 
+  .00432 
-.00892 

+  .  00467  s 
+  .00483 
+  .  00008  4 
+  .02167  6 
—  .00067 
+  .000414* 
+  .  00004 
—  .  0390      j 

TU  ::::: 

Cd  t  
Constantant  .  .  . 
Pd*  
Pt*.. 

wt  

Ni*.. 

Ag* 

IFef. 

Pbl. 

Au* 

Cu  t.  .  . 

§  Alt 

§  Mo  t  
§Snt... 

Manganin  t.  .  .. 
Mgf..  ........ 
Cot  

*  Identical  wire  of  Table  398.     t  Another  wire  of  same  sample,     t      Different  sample. 
§  Results  too  irregular  for  interpolation  for  values  at  other  temperature  and  pressures;  see  original  article, 
(i)  —  .0556/8;   (2)   —  .0486/3,  annealed  ingot  iron;   (3)  —  .O5I66/3;  (4)   —  .out*;  (5)   —  .  0425/8;   (6)  —  .041  12/3. 

TABLE  391.  —  Peltier  and  Thomson  Heats;  Pressure  Effects. 


They  refer 
itive  if  heat  is  absorbed  by  the  positive 


The  following  data  indicate  the  magnitude  of  the  effect  of  pressure  on  the  Peltier  and  Thomson  heats. 
to  the  same  samples  as  for  the  last  table.    The  Peltier  heat  is  considered  positive  if  heat  is  absorbed  by 
current  from  the  surroundings  on  flowing  from  uncompressed  to  compressed  metal.    A  positive  <PE/dP  means  a  larger 
Thomson  heat  in  the  compressed  metal,  and  the  Thomson  heat  is  itself  considered  positive  if  heat  is  absorbed  by  the 
positive  current  in  flowing  from  cold  to  hot  metal.    Same  reference  and  notes  as  for  preceding  table. 


Metal. 

Peltier  heat, 
io«  X  Joules/coulomb. 

Thomson  heat, 
io8  X  Joules/coulomb/0  C 

Pressure  kg/cm2 

Pressure  kg/cm2 

6000              ||              12,000 

6000                    ||                      12  ,000 

Temperature  °  C 

Temperature  °  C 

0° 

50° 

100° 

0° 

50° 

1  00° 

0° 

50° 

100° 

0° 

50° 

100° 

§Bit.. 

+1070 
+98 
+66 
+19 
+46 
+35 
+23 
+17 

T" 

+13 
—ii 

+  7 
+6 
+4 

—  2 
+  1 
—  I 

—  2 

-16 
—  23 

+  1210 
+  140 

+95 
+7i 
+57 
+43 
+37 

+  25 

+17 
+17 
+18 

+  10 

+10 
+6 

+  2 
+  2 
+  1 
—  2 

-18 
—33 

+790 
+  124 
+  118 
+70 

+  52 

+35 
+32 
+  23 

+  23 

+  15 
+16 
+14 
+8 
+8 
+o 
+i 

—  2 
—  21 

-44 

+2580 
+190 

+  112 

+81 
+90 
+68 

ts 

i 

-38 

+14 
+-S 

3 

-5 
—4 
—35 
-46 

+2810 
+278 
+171 
+148 
+114 
+86 
+76 
+49 
+37 
+34 
+38 

+  20 

+  18 
+  n 
+  7 
+4 

+  2 

—4 
—42 
-67 

+412 
+  229 

+  22! 
+  140 
+  103 
+  65 
+  65 

+50 
+44 
+36 
+30 

+  25 

+  16 

++J 

+  2 

—4 
-48 
-90 

+1150 
+41 
+38 
+109 
+5 

1 

fc 
$ 

+4 
+4 
+6 
+i 
+6 
+i 

0 

-14 

+650 

ts 
+x 
5 

+7 

1 

+6 
+4 
+i 
+9 
—  5 

+0 

+i 
o 
—ii 

+56 
+26 
+63 

+6 
+4 
—  18 
+6 
+8 
+6 

—  121 
+  10 

+  5 
+4 
+n 
—  i 
—  i 
+o 

0 
—  10 

-520 

+63 

+  79 
+  105 
+  13 
+9 
+96 
+9 
+  16 
+  7 
—347 
+6 
+6 
+6 

+  21 
+  2 

++1 

0 
—  2O 

-405 
+  133 
+63 

+92 
+  14 

,+9 
+17 

+  14 
+  15 
+8 

+  120 

+8 
+6 
+3 
+  16 
—  ii 

i; 

0 

—24 

+  220 

+50 
+93 

+  17 
+8 
+59 

+  20 
+  10 
+  10 

-194 

+  20 

+7 
+8 

+  20 
—  2 

+J 

0 
-28 

§Znt 

§T1  1 

|  Cd  t  

Constantan  J.  .  . 
§  Pd  *  

§Pt*.. 

I  W  1 

§  Ni  *  

Ag*.  .. 

§Fct 

Pb  t..... 

Au* 

Cu  t  .  . 

§  Alt 

I  Mo  i 

§Snt  
§  Manganin  t 

Mg  t-  . 

§Cot  

*  t  t  §  Same  significance  as  in  preceding  table. 


SMITHSONIAN  TABLES. 


-_ 


TABLES  392-394. 

TABLE  392.  -Peltier  Ettect. 

The  -coefficient  of  Peltier  effect  may  be  calculated  from  the  constants  A  and  B  of  Table   386    as 
there  shown.     With   Q    (see  Table  386)    in  microvolts  per  '  C.  and   T=   absolute  temerature     JC 


the    coefficient    of   Peltier  effect 


^  cal.    per   coulomb=o.ooo86  QT   cal.    per  ampere-hour  =Qr/iooo 

millivolts  (=millijoules  per  coulomb).  Experimental  results,  expressed  in  slightly  different  units, 
are  here  given.  The  figures  are  for  the  heat  production  at  a  junction  of  copper  and  the  metal 
named,  in  calories  per  ampere-hour.  The  current  flowing  from  copper  to  the  metal  named,  a  posi- 
tive- sign  indicates  a  warming  of  the  junction.  The  temperature  not  being  stated  by  either  author, 
and  Le  Roux  not  giving  the  algebraic  signs,  these  results  arc  not  of  great  value, 


Calories  per  ampere-hour. 

J 

fl 

§ 

- 

3 

1.1 

JjOT 

£ 

.J 

& 

* 

C 

N 

Jahn*     .     . 

- 

- 

- 

- 

—.62 

- 

-3-61 

4.36 

0.32 

—.41 

-.58 

Le  Rouxt  . 

13.02 

4.8 

19.1 

25.8 

0.46 

2.47 

*, 

- 

- 

- 

•39 

*  "  Wied.  Ann."  vol.  34,  p.  767. 
t  "Ann.  de  Chim.  et  de  Phys.''  (4)  vol.  10,  p.  201. 
f  Becquerel's  antimony  is  806  parts  Sb  -f  406  parts  Zn  +  121  parts  Bi. 
§  Becquerel's  bismuth  is  10  parts  Bi  -f- 1  part  Sb. 


TABLE  393.  — Peltier  Effect,  Fe  Constantan,  Ni  Cu,  0-560°  0. 


[— 

Temperature. 

0° 

20° 

130° 

240° 

320° 

560° 

Fe-Constantan  .     .     . 

3-1 

3-6 

4-5 

6.2 

8.2 

I2.S 

{in  Gram.  Cal  'X-io» 

Ni-Cu       .     .     . 

I  Q2 

2  I  C 

2  A.Z 

206 

I  QI 

2  l8 

per  coulomb 

TABLE  394.  -  Peltier  Electromotive  Force  In  Millivolts. 


Metal 
against 
Copper. 

d 

£ 

s 

^ 

$ 

C 

< 

A 

z 

< 

£ 

t 

j| 
55 

5 

Le  Roux 

-5.64 

—2.93 

—•53 

—•45 

- 

- 

- 

- 

- 

- 

- 

- 

+«-3 

Jahn  .     .     . 

- 

-3-68 

—.72 

—.68 

-.48 

- 

- 

- 

- 

+•37 

- 

+5-°7 

- 

Edlund   .     . 

- 

-2.96 

—.16 

—  .01 

+.03 

+•33 

+.50 

+.56 

+.7o 

+  1.02 

+*..7 

- 

+  17-7 

Caswell  .     . 

- 

- 

- 

- 

+•03 

- 

- 

- 

+.70 

+.85 

- 

+6.0 

+  16.1 

Le  Roux,  1867;  Jahn,  1888;  Edlund,  1870-71  ;  Caswell,  Phys.  Rev.  33,  p.  381,  1911. 
SMITHSONIAN  TABLES. 


I  ABLES    3VO-39O. 


TABLE  395. 
THE  TRIBO-ELECTRIC  SERIES. 

In  the  following  table  it  is  so  arranged  that  any  material  in  the  list  becomes  positively  electrified  when, 
rubbed  by  one  lower  in  the  list.  The  phenomenon  depends  upon  surface  conditions,  and  circum- 
stances may  alter  the  relative  positions  in  the  list. 


i   Asbestos   (sheet). 

13  Silk. 

24  Amber. 

2  Rabbit's  fur,  hair,  (ITg). 

14  Al,  Mn,  Zn,  Cd,  Cr,  felt, 

25   Slate,  chrome-alum. 

3  Glass  (combn.  tubing). 

hand,   wash-leather. 

26  Shellac,  resin,  sealing-wax. 

4  Vitreous   silica,  opossum's 

15  Filter  paper. 

27  Ebonite. 

fur. 

16  Vulcanized  fiber. 

28  Co,    Ni,    Sn,    Cu,    As,    T.i, 

5  Glass  (fusn.). 

17  Cotton. 

Sb,  Ag,  Pd,  C,  Te,  Eu- 

6  Mica. 

1  8  Magnalium. 

reka,  straw,  copper  sul- 

7 Wool. 

19  K-alum,      rock-salt,      satin 

phate,  brass. 

8  Glass  (pol.),  quartz  (pol.), 

spar. 

29  Para  rubber,  iron  alum. 

glazed  porcelain. 

20  Woods,  Fe. 

30  Guttapercha. 

9  Glass  (broken  edge), 

21  Unglazed     porcelain,     sal- 

31    Sulphur. 

ivory. 

ammoniac. 

32  Pt,   Ag,   Au. 

10  Calcite. 

22  K-bichromate,    paraffin, 

33   Celluloid. 

1  1   Cat's  fur. 

tinned-Fe. 

34  Indiarubber. 

12  Ca,    Mg,    Pb,    fluor    spar. 

23   Cork,  ebony. 

borax. 

Shaw,  Pr.  Roy.  Soc.  94,  p.   16,  1917;  the  original  article  shows  the  alterations  in  the  series  sequence 
due  to  varied  conditions. 


TABLE  396, 
AUXILIARY  TABLE   FOR  COMPUTING  WIRE  RESISTANCES. 

For  computing  resistance  in  ohms  per  meter  from  resistivity,  p,  in  michroms  per  cm.  cube  (see 
Table  397,  etc.).  e. g.  to  compute  for  No.  23  copper  wire  when  p=  1.724  :  I  meter  =  0.0387  + 
.0271  -f  .0008  +  .0002  =  0.0668  ohms  ;  for  No.  1 1  lead  wire  when  p  =  20.4  ;  I  meter  =  0.0479  + 
.0010  =  0.0489  ohms.  The  following  relation  allows  computation  for  wires  of  other  gage  num- 
bers :  resistance  in  ohms  per  meter  of  No.  N  =  2\n  —  3)  within  I  %  :  e.  g.  resistance  of  meter  of 
No.  i8  =  2XNo.  15. 


Gage. 

No. 

Diam. 
in 
mm. 

Section 

nun  '-. 

p  in  micro-ohms  per  cm.  cube. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8- 

9. 

10. 

Resistance  of  wire  i  meter  long  in  ohms. 

oooo 

11.7 

107.2 

•o4933 

.03187 

.03280 

•o3373 

.03466 

.os56o 

•03653 

•03746 

.03840 

•o3933 

00 

9.27 

67-43 

.03.48 

.03297 

•o3445 

•°3593  !     -03742 

.03890 

.0,104 

.o2i  19 

•o2i33 

.o2i48 

I 

7-35 

42.41 

•03236 

.03472 

.03707 

.03943       .o2n8 

•0214I 

,o2i65 

.o2i89 

.022I2 

•02236 

3 

5-83 

26.67 

•o3375 

.03750 

.02112 

.0,150 

.o2i87 

.O2262 

.02300 

.02337 

«o2375 

5 

4.62 

16.77 

.03596 

•o2ii9 

.02179 

.0,239 

.02298 

•02358 

.02417 

>°2477 

•°2537 

.02596 

7 

3-66 

10.55 

.03948 

.0,190 

.02284 

•o2379 

.02569 

.0,664 

•°2758 

.02853 

.02948 

9 

2.91 

6.634 

.0,151 

.0,301 

.0,452 

.02603 

•02754 

.03904 

.0106 

.0121 

.0136 

.0151 

II 

2.30 

4.172 

•°27I9 

.0,959 

.0120 

.0144 

.0168 

.0192 

.0216 

.0240 

13 

1-83 

2.624 

.0,381 

.0,762 

.0114 

.0152 

.0191 

.0229 

.0267 

.0305 

.0343 

.0381 

15 

1.45 

1.650 

.o26o6 

.0121 

.0182 

.0242 

•0303 

.0364 

.0424 

.0485 

•0545 

.0606 

1.038 

.0,963 

.0193 

.0289 

.0385 

.0482 

.0578 

.0674 

.0771 

.0867 

.0963 

|M 

.912 

.6527 

•0153 

.0306 

.0460 

.0613 

.0766 

.0919 

.1072 

.1226 

.1379 

.1532 

21 

•723 

.4105 

.0244 

.0487 

-0731 

.0974 

.1218 

.1462 

.1705 

.1949 

.2192 

.2436 

23 

•573 

.2582 

.0387 

•°775 

.1162        .1549 

.1936 

.2324 

.2711 

.3098 

•3486 

.3873 

25 

27 

.455 
.361 

.1624 
.1021 

.0616 
.0979 

.1232 
.1959 

.1847 
.2938 

£3 

•3079 

.4897 

•3695 
•5877 

.4310 
.6856 

.4926 
.7835 

•5542 
.8815 

.6158 
•9794 

29 

.286 

.0642 

.'557 

•3"4 

.4671 

.6228 

.7786 

•9343 

1.090 

1.246 

1.401 

1-557 

31 

.227 

.0404 

.2476 

.4952 

.7428 

.9904 

1.238 

1.486 

1-733 

I.gSl 

2.228 

2.476 

33 

.180 

•0254 

•3937 

.7874 

I.  ill 

1-575 

1.968 

2.362 

2.756 

3-I50 

3-543 

3-937 

35 

.'43 

.0160      .6262 

1.252 

1.879 

2-505 

3-131 

3-757 

4-383 

5.009 

5-636 

6.262 

37 

.113 

.0100      .9950 

1.990 

2-985 

3.980 

4-975 

5-97° 

6.965 

7.960 

8-955 

9-95° 

39 
40 

.090 
joSo 

.0063 

.0050 

'•583 
1.996 

3.166 
3.992 

4.748 
5.988 

7.984 

9.980 

9-497 
11.98 

1  1.  08 
13-97 

12.66 

15-97 

14-25 
17.96 

19.96 

SMITHSONIAN  TABLES. 


TABLE  397. 
RESISTIVITY  OF    METALS  AND  SOME  ALLOYS- 


323 


The  resistivities  are  the  values  of  pin  the  equation  R  =  pl/s,  where  R  is  the  resistance  in  microhms  of  a  length 
/  cm  of  uniform  cross  section  s  cm1.  The  temperature  coefficient  is  a»  in  the  formula  Rt  =  R»\i  +  0««  —  M|-  The 
information  of  column  2  does  not  necessarily  apply  to  the  temperature  coefficient.  See  also  next  table  for  tempera- 
ture coefficients  o°  to  100°  C. 


Substance. 

Remarks. 

Tempera- 
ture, 
°C 

Microhm- 
cm 

Refer- 
ence. 

Temperature  coefficient. 

t, 

* 

Refer- 
ence. 

Advance  
Aluminum 

see  constantan 
see  p.  334 
c.p. 

liquid 

drawn 
liquid 

solid    \ 
liquid  / 
99.57  pure 
see  constantan 

99  .  8  pure 
60%  Cu,  40%  Ni 

annealed 
hard  -drawn 
electrolytic 

pure 
very  pure,  ann'ld 
see  constantan 

18%  Ni 
99.  9  pure 

pure,  drawn 
99.9  pure 
see  constantan 

20. 
-189. 
—  100. 
o. 

+  100. 

400. 

20. 
-190. 

+860. 
0. 

18. 

100. 
20. 

-160. 
18. 

100. 

318. 
-187. 

0. 

27. 

30. 

20. 

0. 
20. 
2O. 
20. 

20. 
20. 
-206. 
+  205. 
400. 
20. 

20. 
0. 
20. 
-I83. 
0. 
20. 

194-5 

o. 
-186. 
o. 

+  100. 

2.828 
0.64 

1% 

3-86 
8.0 

4i-7 
10.  S 

120. 

35- 
119.0 
160.2 
7- 
2.72 
7-54 
9.82 
34-1 
S-2S 
19. 

22.  2 
36.6 

4.6 

2.6 

87. 
9-7 
49- 

1.724 
1.77 
0.144 
2.92 
4.10 
1.692 

92. 
Sa- 
te' 

0.68 

2.  22 
2.44 
3-77 

8.37 
1.92 
o.io 
8.3 

i 
3 
3 
3 
3 
3 
5 
6 

1 

9 
9 

S 

10 

9 
9 
II 

12 
II 
13 
13 
14 

IS 

16 
5 

i 

i? 
i? 
3 
18 

5 

12 

5 
17 
ii 
9 
17 

19 

20 
20 
20 

18° 
25 

IOO 

500 

20 

2O 

20 
2O 

2O 

12 
25 
IOO 

200 
500 

20  see  col.  2 

IOO 

400 

IOOO 

20 

2O 
20 

loo  ann'ld 
500 

IOOO 

+  •0039 
+  .0034 
+  .0040 
+  .0050 

+  .0036 
+  .004 

+  .002 
+  .0038 

+  .0036 

+  .0007 

+  .000008 
+  .OO0002 
—  .000033 
—  .000020 
+  .OO0027 
+  •  00393 
+  .00382 
+  .0038 
+  .0042 
+  .0062 

+  .000l6 
+  .0004 

+  .0034 
+  .0025 

+  •0035 
+  .0049 

2 

4 
4 
4 

S 

S 

5 
5 

14 

S 

4 
4 
4 
4 
4 
5 
5 
4 
4 
4 

5 

5 

5 
4 
4 

4 

H 



« 

Antimony 

« 

.      Arsenic 

Bismuth  

Brass  
Cadmium  

;;    

Caesium  

« 

« 

Calcium 

Calido  
Chromium  
Climax  
Cobalt  
Constantan 

Copper 

Eureka  
Excello  

German  silver  
Gold  

((     •  

la  la... 

Ideal  

Iridium  



SMITHSONIAN  TABLES. 


324 


TABLE  397  (continued). 
RESISTIVITY    OF    METALS    AND    SOME    ALLOYS- 


Substance. 

Remarks. 

Tempera- 
ture, 
°G 

Microhm- 
cm 

Refer- 
ence, 

Temperature  coefficient. 

t, 

a» 

Refer- 
ence. 

Iron.  .  . 

99  -98%  pure 
pure,  soft 

E.  B.  B. 
B.B. 
Siemens-Martin 
manganese 
35%  Ni,  "invar." 
piano  wire 
temp,  glass,  hard 
'     ,  yellow 
"     ,blue 
"     ,  soft 

cold  pressed 

solid 

liquid 
free  from  Zn 

pure 
84Cu,i2Mn,4Ni 

solid 
liquid 

drawn 
pure 

20. 

'-•ft? 

o. 
+98.5 
196.1 
400. 

20. 
2O. 
20. 
2O. 
20. 
0. 
O. 
0. 
0. 

o. 

20. 

-183. 
-78. 

o. 

+90.4 
196.1 

318. 
-187. 

0. 

99.3 

230. 

20. 
-I83. 
-78. 
O. 

+98.5 
400. 

20. 

20. 
-183.5 
—  102-9 
-50-3 

—39-2 
-36.1 
o.o 

50. 

IOO. 
2OO. 
350. 
20. 

2O. 
2O. 
20. 
-182.5 
-78.2 
0. 

94  9 
400. 

10. 
0.652 
5-32 
8.85 
17.8 
21.5 
43-3 
10.4 
It.  g 
18. 
70. 
81. 
n.  8 
45-7 
27. 
20.5 
iS-9 

22. 

6.  02 
14.1 
20.4 
28.0 
36.9 
94- 
1-34 
8-55 
12.7 
45-2 
4.6 

I.OO 

2.97 

4-35 
5-99 
II.  9 
5.o± 
44. 

95  •  783 
6.97 
15-04 
21.3 
25-5 
80.6 
94.07 
98.50 
103.25 
114.27 
135-5 
5-7 

42. 

IOO. 

7-8 
1.44 
4-31 
6-93 
11.  i 
60.2 

5 
17 
17 
17 
17 
17 
3 
5 
5 
5 
5 

22 

23 
23 
23 
23 
23 
5 
17 
17 
i? 
17 
17 
24 

12 
12 
12 
25 
5 
17 
17 
17 
17 

3 
IS 
S 

5 
17 
17 
17 
17 
17 
17 
27 
24 
24 
24 
5 

5 

5 

28 
28 
28 
28 
3 

20 
0 
25 
IOO 

500 

IOOO 

20  see  col.  2 

+  .0050 
+  .0062 
+  .0052 
+  .0068 
+  .0147 
+  .0050 

+  .005 
+  .004 
+  .003 

+  .001 

+  .0032 
+  .0016 

+.0033 

+  .0039 
+  .0043 

+  .004 
+  .0038 
+  .0050 
+  .0045 
+  .0036 

+  .0100 

+  .000006 

.000000 

—  .000042 

—  .  00005  2 

—  .000000 
—  .0001  1 
+  .00089 
+.00088 

+  .0033 
+  .0034 
+  .0048 

+  .O020 

^.0004 
.006 
+  .0062 
+  .0043 
+  .0043 
+  .0030 
+  .0037 

5 

21 

4 
4 
4 
4 

5 
5 
5 
5 

23 

23 

23      • 
5 

2 

5 
24 
4 

4 
4 

4 
4 

26 

4 
4 
4 
5 
5 
5 
24 
4 
4 
4 
4 

i 

i 

« 

i 

steel  

„    

o  see  col.  2 

o  see  col.  2 

20 
18 

20 

o 

25 
IOO 

500 
600 

12 
25 
IOO 

250 
475 
500 

20 
0 

Rt  =  Rod  + 
.  00089*  + 

.OOOOOI/2) 

25 
IOO 
IOOO 
20 

20 
20 
o 

25 

IOO 

500 

IOOO 

« 

M 

M 

11 

« 

M 

Lead  

M 

« 

« 

" 

M 

Lithium  

j     Magnesium  

« 

«< 

Manganese  

Manganin  



« 

Mercury  

i< 

« 

„       

M 

« 

<« 

Molybdenum  

N 

Monel  metal  
Nichrome  
Nickel  

SMITHSONIAN  TABLES. 


TABLE  397  (continued). 
RESISTIVITY    OF    METALS    AND    SOME    ALLOYS. 


325 


Substance 

Remarks. 

Tempera- 
ature, 
°C 

Michrom- 
cm 

Refer- 
ence. 

Temperature  coefficient. 

t. 

«• 

Refer, 
ence. 

Osmium  

very  pure 
wire 

solid 

liquid 

99.  98  pure 
electrolytic 

solid 
liquid 
pure 

1000°  K 
1500°  K 

2000°  K 

3000°  K 
35oo°  K 
trace  Fe 

liquid 

20. 

20. 
-I83. 
-78. 

o. 

08.5 

20. 
—  203  .  1 
-97-5 

0. 
IOO. 

400. 
-75- 
o. 
55- 
-186. 
—78.3 
o. 

IOO. 

-190. 

o. 
35- 
40. 
20. 
18. 
-183. 
-78. 
o. 
98.15 
192.1 
400. 
-180. 
-75- 
o. 

A 

20. 

20. 
19.6 
-183. 
-78. 
0. 
98.5 

20. 
20. 

-184. 
-78. 

o. 
91  -45 

20. 
727. 
1227. 
1727. 
2727. 
3227. 
-183. 
-78. 

0. 

92.45 
191-5 

440. 

60.2 
ii. 

2.78 
7.17 

10.21 
13-79 
IO. 
2.44 
6.87 
10.96 
14.85 
26. 

*:? 

8.4 
0.70 
3.09 

l£9 
6.60 

2-5 
ii.  6 
13-4 
19.6 
58.* 
.629 
•  390 

.021 
.468 
.062 
.608 

3-77 

I.O 

2.8 

4.3 

5-4 

10.2 
24.8 
IS-S 
200,000 
4-08 

ii.  8 
17.60 
24.7 
47- 
ii.  5 

If 

o.o 

13-0 
18.2 

3-2 

5.51 
25.3 
41.4 
59.4 
98.9 

118. 
1.62 
3-34 

5-75 
8.00 
10.37 
37-2 

3 

5 
17 
17 
17 
17 
5 
17 
17 
17 
17 
3 
13 
13 
13 

20 

20 
20 
20 
13 
13 
13 
13 

2 
17 
17 
17 
17 
17 

3 
13 
13 
13 
13 
13 
8 

17 
17 
17 
17 
S 
5 
17 
17 
17 
IT- 
IS 
29 
29 
29 
29 
29 
29 
17 
17 
17 
17 
17 
7 

20 
o 

20 
0 

2O 
25 
IOO 

500 

20 

2O 
20 

IS 

Soo 

1000 
20 

+  •0033 

+  •0035 

+  .003 
+  .0037 

+  .0038 
+  .0030 
+  .0036 
+  .0044 

+  .0031 

-j-.OOOOI 

+.0042 
+.0045 

+  .0057 
+  .0089 

+  •0037 

S 

21 

5 

21 

5 

4 
4 
4 

5 

5 
5 

2 

4 
4 

5 

Palladium. 

ii 

•I 

«i 

Platinum  

ii 

ii 

M 

Potassium  

Rhodium  

"        

Rubidium  

n 

•• 

Silicium.  . 

Silver 

ii 

<i 

ii 

n 

•• 

Sodium 

ii 

ii 

M 

Strontium 

Tantalum  

Tellurium 

Thallium 

<< 

Therlo.  .  . 

Tin.   . 

ii 

it 

'  Titanium.  .  . 

Tungsten 

S 

ii 

«i 

ii 

M 

Zinc 

ii 

11 

ii 

ii 

References  to  Table  397:    (i)  See  page  334;    (2)  Jager,  Diesselhorst,  Wiss.  Abh.  D.  Phys.  Tech.  Reich.  3,  p.  269. 
1900;    (3)  Nicolai,  1907;    (4)  Somerville,  Phys.  Rev.  31,  p.  261,  1910;   33,  p.  77,  1911;    (5)  Circular  74  of  Bureau  of 
Standards,  1918;    (6)  Eucken,  Gelhoff;    (7)  de  la  Rive;    (8)  Matthiessen;    (9)  lager,  Diesselhorst;    do)  Lees,  1008; 

(17)  Dewar,  Fleming,  Dickson,  1898;  (18)  Wolff,  Bellinger,  1910;  (19)  Erhardt,  1881;  (20)  Broniewski,  Hackspill, 
IQII;  (21)  Dewar,  Fleming,  1893,  1896;  (22)  Circular  58,  Bureau  of  Standards,  1916;  (23)  Strouhal,  Barns,  1883; 
(24)  Vincentini,  Omodei,  1800;  (25)  Bernini,  1905;  (26)  Glazebrook,  Phil.  Mag.  20,  p.  343,  1885;  (27)  Grimaldi. 
1888;  (28)  Fleming,  1900;  (29)  Langmuir,  Gen.  Elec.  Rev.  19,  1916. 

SMITHSONIAN  TABLES. 


326 


TABLES  398-399. 
TABLE  398.  —  Resistance  of  Metals  under  Pressure. 


The  average  temperature  coefficients  are  per  °  C  between  o°  and  100°  C.  The  instantaneous  pressure  coefficients 
are  the  values  of  the  derivative  (i/r)\dr/dp\t,  where  r  is  the  observed  resistance  at  the  pressure  />  and  temperature  /. 
The  average  coefficient  is  the  total  change  of  resistance  between  o  and  12,000  kg/cm1  divided  by  12,000  and  the  resist- 
ance at  atmospheric  pressure  and  -the  temperature  in  question.  Table  taken  from  Proc.  Nat.  Acad.  3,  p.  n,  1917.  For 
coefficients  at  intermediate  te.nperatures  and  pressures,  see  more  detailed  account  in  Proc.  Amer.  Acad.  52,  p.  573, 
1917.  Sn,  Cd,  Zn,  Kahlbaum's  "K  "  grade;  Tl,  Bi,  electrolytic,  high  purity;  Pb,  Ag,  Au,  Cu,  Fe,  Pt,  of  exceptional 
purity.  Al  better  than  ordinary,  others  only  of  high  grade  commercial  purity. 


Average  temperature 
coefficient 
o°  to  100°  C 

Pressure  coefficients. 

Instantaneous  coefficient. 

Average  coefficient 
o  to  12,000  kg/cm2 

Ato°C 

At  100°  C 

At 

okg 

At 
12,000  kg 

okg 

12,000  kg 

o  kg 

12,000  kg 

Ato° 

At  100° 

In. 

+  .00406 
.00447 
.00517 
.00424 
.00421 
.00416 
•00434 
.004074 
.003968 
.  004293 
.004873 
.003657 
.006206 
.003178 
.003868 
.  004336 
.002973 
.003219 
.  00390  * 
.00473 
+  .  00438 
-.oo63t 

+  .00383 
.00441 
.00499 
.00418 
.00412 
.00420 
•00435 
.004069 
.  003964 
.004303 
.004855 
.003676 
.006184 
.003185 
.003873 
.  004340 
.002967 
.003216 

.00403 

+  .00395 

—  .041226 
.041044 
.041319 
.041063 
.041442 
.040540 
.040416 
.040358 
.040312 

.O4020I 
.040158 

.040094 
.040241 
.  040198 
.040198 
.040133 
.040149 

.  0401  28 

.04055 

+  .041220 
+  .04154 
—  .03129 

—  .041016 
.  040936 
.041180 
.040837 

.041220 
.040425 
.040365 
.040321 
.040286 
.O40I79 
.04OI42 
.040081 
.040218 
.O4OI9O 
.040l8l 
.040126 

.040139 

.040121 

+  .041064 
+  .040213 

—  .041510$ 
.041062 
.041456 
.041106 

.041483 
.040524 

.040397 
•040355 
.040304 
.040184 
.040163 
.040076 
.040247 
.040189 
.040190 
.040130 
.040153 
.040130 

+.040768 
+.04152  § 

—  .041072  + 
.040973 

.041200 
.040887 

•041237 
.040407 
•040373 
.040331 
.040292 
•040175 
.040156 
.040070 
.040230 
.040187 
.040182 
.040125 
.040147 
.040123 

+  .040723 
+  .04i895§ 

—  .O4IO2I 
.04O920 
.041151 
.040894 
.041212 
.040470 
.O40382 

•040333 
.040287 
.040183 
.040147 
.040087 
.040226 
.040190 
.040187 
.040129 
040143 
.040123 
.04055 

+  .041220 
+  .042228 

-.041131  I 
.040951 
.041226 
.040927 
.041253 
.  040454 
.040377 
.040336 
.040292 
.040177 
.040158 
.040073 
.040235 
.040186 
.040184 
.040126 
.040149 
.  040126 

+  .040768 
+  .041980  § 

Sn 

Tl  . 

Cd 

Pb  

Zn 

Al  
Ag 

Au  

Cu    ... 

Ni... 

Co  
Fe 

Pd  
Pt 

Mo... 

Ta 

W 

Mg  
Sb 

Bi... 

Te           .... 

*  0°  tO   20°. 


t  o°  to  24°. 


J  Extrapolated  from  50°. 


§  Extrapolated  from  75°. 


Additional  data  from  P.  Nat.  Acad.  Sc.,  6,  505,  1920.     Data  are  10,000  x  mean  pressure  coefficient,  o  —  12,000  kg, 
and  10,000  x  instantaneous  pressure  coefficient  at  o  kg.     1  =  liquid  ;  s  =  solid. 
Li,    s,  o°            +.0772       +   .068  Ca.   o° 

Li,    1,  240°        +.093         +    .093  Sr,    0° 

Na,  s,o°  —.345         —.663  1I-,  s,o° 

Na,  1,200°          —.436         —    .922  Hg,  1    25° 

K,   s,  25°  -  .604        — 1.86  Ga,  s,  o° 

K,  1,  165°          —  .8o9a       —1.68  Ga,   1,  30° 


+  ..06 
+  .680 

—  .236b 

—  .219 

—  .0247 

—  •0531 


+  .502 
—  •334 
-.064 


Ti,  o° 
Zr,  o° 
Bi,  1,  275° 
W,  o° 
La,  o° 
P,  black,  o 


±.00!? 

— .0040 

—  .ioic 

—  •0135 

—  -0331 

—  .81 


-  .004 

—  -123 

—  .014 

—  -039 

—  2.OO 


a,  o  -  9,000  kg;  b,  7,640  -  12,000  kg;  c,  o  -  7,000  kg.     The  Ga,  Na,  K,  Mg,  Hg,  Bi,  W,  P,  of  exceptional  purity. 


TABLE  399.  —  Resistance  of  Mercury  and  Manganin  under  Pressure. 

Mercury,  pure  and  free  from  air  and  with  proper  precautions,  makes  a  reliable  secondary  electric-resistance  pres- 
sure gage.  For  construction  and  manipulation  see  "The  Measurement  of  High  Hydrostatic  Pressure;  a  Secondary 
Mercury  Resistance  Gauge,"  Pr.  Am.  Acad.  44,  p.  221,  1919. 


Pressure,  kg/cm2 

— 

500 

IOOO 

1500 

2000 

2500 

3OOO 

4000 

5000 

6000 

6500 

R(p  —75°) 

0.9186 

I.  0000 
I.OOOO 

1.0970 

0.9055 
0.9836 
0.9854 

1.0770 

0.8930 
0.9682 
0.9716 
1.0580 

0.8818 
0-9535 
0.9588 
i  .  0400 

0.8714 
0.9394 
0.9462 
1.0230 

0.8582 
0.9258 
0.9342 
I.OO70 

0.8478 
O.9I28 

o.  9228 

0.9908 

0.8268 
0.8882 
0.9010 
0.9614 

0.8076 
0.8652 
0.8806 
0.9342 

0.7896 

0.8438 
0.8616 
0.9086 

0.7807 
0-8335 
0.8527 
0.8966 

R(i>  2$e) 

R(p  125°) 

*  This  line  gives  the  Specific  Mass  Resistance  at  25°,  the  other  lines  the  specific  volume  resistance. 

The  use  of  mercury  as  above  has  the  advantage  of  being  perfectly  reproducible  so  that  at  any  time  a  pressure  can 
be  measured  without  recourse  to  a  fundamental  standard.  However,  at  o°  C  mercury  freezes  at  7500  kg/cm2.  Man- 
ganin is  suitable  over  a  much  wider  range.  Over  a  temperature  range  o  to  50°  C  the  pressure  resistance  relation  is 
linear  within  i/io  per  cent  of  the  change  of  resistance  up  to  13,000  kg/cm2.  The  coefficient  varies  slightly  with  the 
sample.  Bridgman  s  samples  (German)  had  values  of  (AR/pR0)  X  io»  from  2295  to  2325.  These  are  +  instead  of 
— ,  as  with  most  of  the  above  metals.  See  "The  Measurement  of  Hydrostatic  Pressure  up  to  20,000  Kilograms  per 
Square  Centimeter."  Bridgman,  Pr.  Am.  Acad.  47,  p.  321,  1911. 


SMITHSONIAN  TABLES. 


TABLE  4OO. 


327 


CONDUCTIVITY  AND   RESISTIVITY  OF    MISCELLANEOUS  ALLOYS. 

TEMPERATURE  COEFFICIENTS. 


Conductivity  in  mhos  or 


=7(=7o(l_fl/  +  &/2)  and  resi,tivity  in  microhma_cm 


Metals  and  alloys. 

Composition  by  weight. 

7o 

aXio« 

"  ! 

<3 

Gold-copper-silver  . 

58.3  Au  +  26.5  Cu+  15.2  Ag 
66.5  Au+  i5.4Cu  +  18.1  Ag 

7-58 
6.83 

574* 

13.2      I 
14.6      I 

• 

7.4Au  +  78.3Cu+  14.3  Ag 

28.  c6 

1830$ 

3.6      i 

Nickel-copper-zinc  . 

\  6.57Zn  by  volume  .     .     .J 

4.92 

444  § 

20.3      i 

Brass   

Various 

12.  2-15.  £ 
12.  16 

1-2X10 

6.4-8.4     2 

8.2      3 

1     hard  drawn     . 

70.2  Cu  +  29.8Zn  .... 

1     annealed    . 

"                 " 

14-35 

- 

^•m         ^ 

7.0     3! 

German  silver     . 

Various  

7_e 

f6o.i6Cu  +  25.37Zn+          "} 

O   0 

33-     2( 

* 

j  14-03  Ni  +  .30  Fe  with  trace  [ 
l^of  cobalt  and  manganese    .  J 

3-33 

360 

30.        4 

Aluminum  bronze   . 

_ 

7-5-8.5 

5-7Xio2 

12-13        2 

Phosphor  bronze     . 

_ 

10-20 

- 

5-10       2 

Silicium  bronze  .     . 

-             -             - 

41 

- 

2.4     5 

Manganese-copper  . 

30  Mn  +  70  Cu  .... 

1  .00 

40 

IOO 

Nickel-manganese- 

. 

copper  .... 

3  Ni  +  24  Mn  +  73  Cu       .     . 

2.10 

—30 

48.        4 

"i8.46Ni+6i.63Cu  + 

Nickelin    . 

i9.67Zn  +  o.24Fe  + 

3s°l 

300 

33.        4 

,  0.19  Co  +  o.iSMn  .      .      .J 

'25.1  Ni  +  74.4iCu  + 

Patent  nickel      .      . 

o.42Fe  +  o.23Zn  + 

2.92 

190 

34-        4 

.0.13  Mn  +  trace  of  cobalt  J 

r53-28Cu  +  25.3iNi+           ] 

Rheotan    .... 

16.89  Zn  +  4.46  Fc  +                       1.90 

410 

53-        4 

o  37  Mn           .     .                .  J 

Copper-manganese- 

iron  . 

91  Cu  +7.1  Mn  +  1.9  Fe 

4.08 

1  20 

20.           5 

Copper-manganese- 

70  .  6  Cu  +  23  .  2  Mn  +  6.2  Fe  . 

*T  *  y1-^ 

' 

22 

T"~             O 

Copper-mangancse- 

/  /  * 

iron 

69.7  Cu  +  29.9  Ni  +  0.3  Fe 

2.60 

i  ^n               7$R            ~ 

Manganin 

84  Cu  +  12  Mn  +  4  Ni  . 

2-3 

6                 44-          2 

Constantan 

6oCu  +  4oNi    .           ...          2.04            8 

*iQ  • 

1  Matthiessen.     3W.  Siemens.                        5VanderVcn.       7  Feussner. 

2  Various.             4  Feussner  and  Lindeck.     6  Blood.                     8  Jaeger-Diesselhorst. 

*f  t»  k  §»  b  X  io'=924,  93,  7280,  51,  respectively. 

SMITHSONIAN  TABLC*. 


328 


TABLE  401. 
CONDUCTING   POWER   OF  ALLOYS. 


This  table  shows  the  conducting  power  of  alloys  and  the  variation  of  the  conducting  power  with  temperature.*  The 
values  of  C0  were  obtained  from  the  original  results  by  assuming  silver  =:  — j-  mhos.  The  conductivity  is  taken 
as  Ct=  C0  (i — at-^-At2),  and  the  range  of  temperature  was  from  o°  to  100°  C. 

The  table  is  arranged   in  three  groups  to  show  (i)  that  certain  metals  when  melted  together  produce  a  solution 
which  has  a  conductivity  equal  to  the  mean  of  the  conductivities  of  the  components,  (2)  the   behavior  of  those 
metals  alloyed  with  others,  and  (3)  the  behavior  of  the  other  metals  alloyed  together. 
It  is  pointed  out  that,  with  a  few  exceptions,  the  percentage  variation  between  o"-  and  100°  can  be  calculated  from  tha 

formula  P  =  Pe  -^  where/  is  the  observed  and  /'  the  calculated  conducting  power  of  the  mixture  at  100°  C., 
and  Pe  is  the  calculated  mean  variation  of  the  metals  mixed. 


Weight  % 

Volume  % 

c 

Variation  per  100°  C. 

10* 

b  X  10 

j 

of  first  named. 

Observed. 

Calculated. 

GROUP  i. 

Sn6Pb    

77.O4 

83.96 

7.C7 

890 

8670 

30.18 

2Q.67 

Sn4Cd   

82.41 

Q.l8 

4080 

11870 

28.89 

3O.O7 

SnZn      

78.06 

77.71 

7880 

8720 

30.12 

70.16 

PbSn     

64  11 

6  do 

•5780 

84^0 

2Q.  IO 

24  76 

2C  06 

16  16 

7780 

8OOO 

2986 

y  , 

2Q  67 

SnCd4 

23-05 

23.50 

13-67 

j/oij 
3850 

9410 

29.08 

30.25 

CdPb6   

7-37 

10-57 

5.78 

3500 

7270 

27-74 

27.60 

GROUP  2. 

Lead-silver  (Pb2oAg)   . 
Lead-silver  (PbAg)      . 

95-05 
48.97 

94.64 
46.90 

5.60 
8.03 

3630 
1960 

7960 
3100 

28.24 

19.96 

7-73 

Lead-silver  (PbAg2)    . 

3244 

30.64 

13.80 

1990 

2600 

I7-36 

10.42 

Tin-gold  (Snt2Au)  .     . 

77-94 

90.32 

5-20' 

3080 

6640 

24.20 

14.83 

"      "     (SngAu)    .     . 

59-54 

79-54 

,  3-03 

2920 

6300 

22.0X) 

5-95 

Tin-copper     .... 

92.24 

80.58 

93-57 
83.60 

7-59 
8.05 

3680 
333° 

8130 
6840 

28.71 
26.24 

19.76 

H-57 

"        "       t  .     .     .     . 
"       t.     .     .     . 
"       t  .     .     .     . 

12.49 
10.30 
9.67 

14.91 
12.35 

II.OI 

5-57 
6.41 
7.64 

m 

691 

1185 
3°4 

5.18 
6.60 

3-99 
4.46 

5-22 

"        "       t  . 

4.96 

6.02 

12.44 

995 

705 

9-25 

7-83 

"       t  .    .     .     . 

1.15 

1.41 

39-41 

2670 

5070 

21.74 

20-53 

Tin-silver 

91.30 

96.52 

7.81 

3820 

8190 

3O.OO 

23-3I 

53-85 

75-51 

8.65 

3770 

8550 

29.18 

11.89 

Zinc-copper  t      .     .     . 

36.70 

42.06 

13-75 

1370 

1340 

12.40 

11.29 

t      .     .     . 

25.00 

29-45 

13-70 

1270 

1240 

11-49 

10.08 

t      .     .     . 

16.33 

23.61 

13-44 

1880 

1800 

1  2.80 

I2.3O 

t      .     .     . 

8.89 

10.88 

29.61 

2040 

3030 

17.41 

1742 

"        t      .     .     . 

4.06 

5-03 

38.09 

2470 

4IOO 

20.61 

20.62 

NOTE.  —  Barus,  in  the  "  Am.  Jour,  of  Sci."  vol.  36,  has  pointed  out  that  the  temperature  variation  of  platinum 
alloys   containing  less  than  10%  of  the  other  metal  can  be  nearly  expressed  by  an  equation  y  =:  ——  nt,  where  y  is  the 

temperature  coefficient  and  x  the  specific  resistance,  m  and  n  being  constants.     If  a  be  the  temperature  coefficient  at 
o°  C.  and  j  the  corresponding  specific  resistance,  J  (a  +  m)=n. 

For  platinum  alloys  Barus's  experiments  gave  m  —  —  .000194  and  n  =  .0378. 

For  steel  m  =  — .000303  and  n  =  .0620. 
Matthiessen's  experiments  reduced  by  Barus  gave  for 

Gold  alloys  nt  =r  —  .000045,  n  —  .0072 1. 

Silver  m  —  —  .000112,  n=z  .00538. 

Copper  "     m  =  —  .000386,  n  —  .00055. 

*  From  the  experiments  of  Matthiessen  and  Vogt,  "  Phil.  Trans.  R.  S."  v.  154. 
t  Hard-drawn. 

SMITHSONIAN  TABLES. 


TABLES  401  (continued)  -402. 
TABLE  401.  —Conducting  Power  ol  Alloys. 


329 


GROUP  3. 

Alloys. 

Weight  % 

Volume  % 

C0 

10* 

a  X  io6 

£X  io» 

Variation  per  100°  C. 

of  first  named. 

Observed. 

Calculated. 

Gold-copper  t     .     .     . 

"        "       t     .    .     . 

99-23 
90-55 

98-36 
81.66 

35-42 

10.16 

2650 

749 

4650 

21.87 
7.41 

23.22 

7-53 

Gold-silver  t  .     .     .    . 
"        ''      *  .... 

«    t  '.  !  '.  '. 
«<     u    % 

87-95 
87.95 
64.80 
64.80 

79-86 
79.86 
52.08 
52.08 

13.46 
13.61 
9.48 
9-51 

1090 
1140 

673 
721 

793 
1160 
246 
495 

10.09 
10.21 

6-49 
.      6.71 

9.65 

959 
6.58 
6.42 

"    t  .  .  .  . 

31-33 

19.86 

13.69 

885 

8.23    . 

8.6? 

"     u    *  .... 

3*«33 

19.86 

13-73 

908 

641 

8-44 

8.31 

Gold-copper  t     .    .    . 

34-83 

19.17 

12.94 

864 

570 

8.07 

8.18 

"      t     .    .    . 

1.52 

0.71 

53-°2 

3320 

7300 

25.90 

25.86 

Platinum-silver  t     .     . 

33-33 

19.65 

4.22 

330 

208 

3.10 

3.21 

"      t     .     . 

9.81 

5-05 

11.38 

774 

656 

7.08 

7-2^ 

"      t     .     . 

5.00 

2-51 

19.96 

1240 

1150 

11.29 

u.88 

Palladium-silver  t   •     • 

25.00 

23-28 

5-38 

324 

154 

3-40 

4.21 

Copper-silver  t    .     .     . 

98.08 

98.35 

56-49 

3450 

7990 

26.50 

27.30 

"      t    .     .     . 

94.40 

95-17 

51.93 

3250 

6940 

25-57 

25-41 

"      t    '.     .     . 

76.74 

77.64 

44.06 

303° 

6070 

24.29 

21.92 

"      t    .     .     . 

42-75 

46.67 

47.29 

2870 

5280 

22.75 

24.00 

"      t    .     .    . 

7.14 

8.25 

50.65 

2750 

436o 

23-17 

25-57 

"      t    .     .     . 

1-31 

50-3° 

4120 

8740 

26.51 

29-77 

Iron-gold  t      .     .     .     . 

13-59 

27-93 

i-73 

3490 

7010 

27-92 

14.70 

"       "     t      .     .     .     . 

9.80 

21.  18 

1.26 

2970 

1220 

17-55 

11.20 

"       "    t-    ...... 

4.76 

10.96 

1.46 

487 

103 

3-84 

13.40 

Iron-copper  t      .     .     . 

0.40 

0.46 

24-51 

1550 

200X) 

13-44 

I4-03 

Phosphorus-copper  t  • 

2.50 

_ 

4.62 

476 

I45 

- 

- 

"      t  • 

0-95 

— 

14.91 

1320 

1640 

- 

- 

Arsenic-copper  t     •     • 

5-40 

- 

3-97 

516 

989 

- 

- 

"       t     .     . 

2.80 

_ 

8.12 

736 

446 

— 

— 

"       t 

trace 

38-52 

2640 

4830 

; 

*  Annealed. 


t  Hard-drawn. 


TABLE  402.  — Allowable  Carrying  Capacity  of  Rubber-covered  Copper  Wires. 
(For  inside  wiring  —  Nat.  Board  Fire  Underwriters'  Rules.) 


B-f  S  Gage 

18 

16 

14 

12 

10 

8 

6 

5 

4 

3 

1 

• 

o 

00 

0000 

Amperes 

3 

6 

12 

17 

24 

33 

46 

54 

65 

76 

90 

107 

I27 

150 

2IO 

500,000  circ.  mills,  390  amp.;  1,000,000  c.  m.,  650  amp.;  2,000,000  c.  m.,  1,050  amp.     For 

insulated  al.  wire,  capacity  =84%  of  cu.     Preece  gives  as  formula  for  fusion  of  bare  wires 

I  =  ad*,  whered=diam.  in  inches,  a  for  cu.  is  10,244;  al.,  7585;  pt.,5172;  German  silver, 

5230;  platinoid,  4750;  Fe,  3148;  Pb.,  1379;  alloy  2  pts.  Pb.,  i  of  Sn.,  1318. 

SMITHSONIAN  TABLES. 


33°  TABLE  403. 

RESISTIVITIES   AT  HIGH   AND   LOW  TEMPERATURES. 

The  electrical  resistivity  (p,  ohms  per  cm.  cube)  of  good  conductors  depends  greatly  on  chemical  purity.  Slight  con- 
tamination even  with  metals  of  lower  p  may  greatly  increase  p.  Solid  solutions  of  good  conductors  generally  have  higher 
p  than  components.  Reverse  is  true  of  bad  conductors.  In  solid  state  allotropic  and  crystalline  forms  greatly  mod- 
ify p.  For  liquid  metals  this  last  cause  of  variability  disappears.  The  +  temperature  coefficients  of  pure  metals  is  of 
the  same  order  as  the  coefficients  of  expansion  of  gases.  For  temperature  resistance  (t,  p)  plot  at  low  temperatures  the 
graph  is  convex  towards  the  axis  of  t  and  probably  approaches  tangency  to  it.  However  for  extremely  low  temper. 
atures  (Junes  finds  very  sudden  and  great  drops  in  p.  e.g.  for  Mercury,  p,  5^  <C4XIO~10  P0  and  for  Sn.,  p,  K  <io-'p 
The  t,  p  graph  for  an  alloy  may  be  nearly  parallel  to  the  t  axis,  cf.  constantan  ;  for  poor  conductors  p  may  decrease  with 
increasing  t.  At  the  melting-points  there  are  three  types  of  behavior  of  good  conductors:  those  about  doubling  p  and 
then  possessing  nearly  linear  t,  p  graphs  (Al.,  Cu.,  Sn.,  Au.,  Ag.,  Pb.) ;  those  where  p  suddenly  increases  and  then  the 
-f-  temp,  coefficient  is  only  approximately  constant ;  (Hg.,  Na.,  K.);  those  about  doubling  p  then  having  a -,  slowly 
changing  to  a  -f-  temp.  coef.  (Zn.,  Cd.) ;  those  where  p  suddenly  decreases  and  thereafter  steadily  increases  (Sb.,  Bi.). 
The  values  from  different  authorities  do  not  necessarily  fit  because  of  different  samples  of  metals.  The  Shimank  values 
(t  given  to  tenths  of  °)  are  for  material  of  theoretical  purity  and  are  determined  by  the  a  rule  (see  his  paper,  also  Nernst, 
Ann.  d  Phys.  36,  p.  403,  191 1  for  temperature  resistance  thermometry).  The  Shimank  and  Pirrani  values  aie  origi  ally 
given  as  ratios  to  p0.  (Ann.  d.  Phys.  45,  p.  706,  1914,  46,  p.  176,  1915.)  Resistivities  are  in  ohms  per  cm.  cube  unless  stated. 
Italicized  figures  indicate  liquid  state. 


Gold. 

Copper. 

Silver. 

Zinc. 

Pt 

Pt 

Pt 

Pt 

c» 

Pt 



C. 

Pt 

O  (^ 

Pt 

O  {^ 

Pt 

PO 

PO 

PO 

"PO 

-252.8 

0.018 

.0081 

-258.6 

0.014 

.0091 

-258.6 

0.009 

.0057 

-252-9 

.0511 

.0089 

-200. 

.601 

.267 

-252.8 

.016 

.0103 

-252.8 

.014 

.0090 

-200. 

1-39 

.242 

-192.5 

.520 

-231 

-251.1 

.028 

.0178 

-189.5 

•334 

.222 

-I9I.I 

1-23 

.214 

!  -'50- 

•997 

•444 

-206.6 

.163 

•  1035 

-200. 

•357 

•237 

-ISO. 

2.00 

-348 

-IOO. 

1.400 

•  623 

-192.9 

.249 

•  1580 

-I50. 

-638 

.424 

-100. 

2.0X> 

•5°4 

-77-6 

1.564 

.696 

-150. 

.567 

•359 

-IOO. 

.916 

.608 

-  77-8 

3-97 

.691 

-50. 

1.813 

.806 

-IOO. 

.904 

•573 

-76.8 

1.040 

.600 

4.04 

-703 

0. 

2.247 

I.OO 

-5°- 

1.240 

.786 

-50. 

1.  212 

-805 

o. 

5-75 

1.00' 

IOO. 

2-97 

1-32 

0. 

1-578 

1.00 

o. 

1.506 

I.OO 

IOO. 

7-95 

•  -38 

200. 

3-83 

1.70 

IOO. 

2.28 

1-44 

IOO. 

2.15 

1-43 

300. 

13-25 

2.30 

500. 

6.62 

2.94 

200. 

2.96 

1.88 

200. 

2.80 

1.86 

415. 

17.00 

2.96 

750. 

9-35 

4.16 

500. 

5.08 

3-22 

400. 

3.46 

2.30 

427. 

37-30 

IOOO. 

12-54 

5.58 

750. 

7.03 

4-46 

750. 

6.65 

4-42 

450. 

37.08 

6.46 

1063. 

13-50 

6.01 

1000. 

9.42 

5-97 

960. 

8.4 

500. 

36.60 

6.36 

1063. 

30.82 

'3-7 

1083. 

IO.2O 

6-47 

960. 

76.6 

II.O 

000. 

35-90 

6.23 

1200. 

32.8 

14.6 

1083. 

2I.3O 

13-5 

IOOO. 

77.07 

a  3 

700. 

33.60 

6./Q 

1400. 

35-0 

15.8 

1200. 

22.30 

14.1 

1200. 

19.36 

12.9 

800. 

35  oo 

6  ig 

1500. 

37-0 

16.3 

1400. 

23.86 

15.1 

1400. 

21.72 

14.4 

850. 

35-74 

6.21 

1500. 

24.62 

15-0 

1500. 

23.0 

15-3 

Mercury. 

Potassium. 

Sodium. 

Iron. 

°C. 

Pt 

P_t 

°C 

Pt 

ft 

°C 

Pt 

Pt 

°C 

Pt 

Pt 

PO 

PO 

PO 

PO 

-200. 

5-38 

.057 

-200. 

1.720 

.246 

-200. 

0.605 

•'-37 

-252.7 

0.01  I 

.0010 

-I50. 

10.30 

.109 

-I50. 

2.654 

•379 

-150. 

1-455 

•330 

-200. 

2.27 

.212 

-IOO. 

15.42 

.164 

-100. 

3-724 

-532 

-IOO. 

2.380 

•541 

-192.5 

.844 

.079 

-50. 

21.4 

.227 

-50- 

5.124 

•732 

-50. 

3-365 

-764 

-loo. 

5.92 

•554 

1  -30. 

07.7 

•975 

o. 

7.OOO 

I.OO 

0. 

4.40 

I.OOO 

-  75-i 

6-43 

.602 

o. 

94-1 

I.OOO 

20. 

7.II6 

1.016 

20. 

4.873 

1.107 

-  50- 

8.15 

•763 

50. 

08.3 

1-045 

60. 

8.790 

1.256 

93-5 

6.290 

1.429 

-     o. 

10.68 

I.OO 

IOO. 

103.1 

7.096 

65. 

13-40 

1.914 

IOO. 

9.220 

2.095 

IOO. 

16.61 

1  -554 

200. 

114.0 

1.212 

IOO. 

15-31 

2.187 

120. 

9.724 

2.209 

200. 

24-50 

2.293 

300. 

127.0 

1-350 

1  20. 

76.7O 

2.386 

140. 

10.34 

2-349 

400. 

43-29 

4.052 

Manganin. 

German  Silver. 

Constantan. 

90%Pt.      10%  Rh. 

Pt 

Pt 

Pt 

Pt 

°c. 

Pt 

PO 

°C. 

Pt 

PO 

Pt 

PO 

°c. 

Pt 

PO 

-200. 

37-8 

•  974 

-200. 

27.9 

.930 

-200. 

42.4 

.961 

-200. 

14.49 

.685 

-I50. 

38.2 

•985 

-150. 

28.7 

•957 

-I50. 

•975 

-I50. 

16.29 

.770 

-IOO. 

38.5 

.992 

-IOO. 

29-3 

•977 

-IOO. 

43-5 

.986 

-IOO. 

.8.05 

•854 

-50- 

38.7 

•997 

-50. 

29-7 

.000 

-5°- 

43-9 

•995 

-  5°- 

19.66 

•93° 

0. 

38.8 

i.ooo 

o. 

30.0 

I.OOO 

o. 

44.1 

l.COO 

o. 

21.14 

I.OOO 

IOO. 

^8  9 

1.003 

IOO. 

33-i 

1.103 

IOO. 

44-6 

1.  012 

IOO. 

24.20 

1.145 

400. 

38.3 

.987 

400. 

44.8 

I.OI6 

. 

Au.  below  o°,  Niccolai,  Lincei  RenH.  (5),  i6,p.  757,906,  1907;  above,  Northrnp,  Jour.  Franklin  Inst.  177,  p-  85,  1914. 
Cu.  below,  Niccolai,  1.  c.  above,  Northrup,  ditto,  177.  p.  i,  1914.  Ag.  below,  Niccolai,  I.e.  above  Northrup,  ditto,  178, 
p.  85,  1914.  Zn.  below,  Dewar,  Fleming,  Phil.  Mag.  36,  p.  271,  1803  ;  above,  Northrup,  175,  p.  153,  1913.  Hg.  below 
Dewar,  Fleming,  Proc.  Roy.  Soc.  66,  p.  76,  IQOO;  above,  Northrupi  see  Cd.  K.  below  Guntz,  Broniewski,  C.  R.  147, 
p.  1474,  1008,  148,  p.  204,  looo-  Above,  Northrnp,  Tr.  Am.  Electroch.  Soc.  p.  185,  1911.  Na,  below,  means,  above, 
see  K.  Fe.,  Manganin,  Constantan.  Niccolai,  I.e.  German  Silver,  90%  Pt.  90%  Rh.,  Dewar  and  Fleming— Phil. 
Mag.  36,  p.  271,  1893. 

SMITHSONIAN   TABLES. 


TABLE  4O3  (continue^. 
RESISTIVITIES  AT   HIGH  AND   LOW   TEMPERATURES. 

(Ohms  per  cm.  cube  unless  stated  otherwise.) 


Platinum. 

Lead. 

Bismuth. 

Cadmium. 

Pt 

Pt 

Pt 

Pt 

Po 

°C. 

Pt 

°c. 

Pt 

Po 

°C. 

Pt 

Po 

-265. 

0.10 

.0092 

-252.9 

0.59 

.0298 

-200. 

34-8 

•314 

-252-9 

0.17 

.0218 

-253- 
-233- 
-'53- 
-  73- 

•'5 
7^2 

.014 
.049 
.378 
.708 

-203. 

-192.8 
-103. 
-  75-8 

4.42 
5-22 

n.8 
'3-95 

•223 
.264 
•598 
•705 

-150. 
-IOO. 

-  50. 

0. 

55-3 
75-6 
94-3 
110.7 

•499 
.683 
.852 

I.OO 

-200. 
-190.2 
-.83.1 
-139.2 

1.66 

2.OO 
2.22 
3.60 

•214 
.258 
.286 
•464 

o. 

1  1.05 

i.oo 

-  53- 

15-7 

.792 

"7- 

120.0 

1.083 

-IOO. 

A 

s, 

.619 

100. 

14.1 

1.28 

o. 

.9.8 

I.OO 

100. 

156.5 

'•4«3 

0. 

7-75 

I.OO 

200. 

17.9 

1.62 

100. 

27.8 

1.403 

200. 

214.5 

J-937 

300. 

16.50 

2.13 

400. 

800. 

?5  4 
40-3 

2.30 
3-65 

2OO. 

3'9- 

38.0 
50.0 

1.919 

2.52 

259. 
263. 

267.0 
127-5 

2.41  c 
1.150 

325. 
350. 

4-35 
4-33 

1000. 

47  -o 

4-25 

333- 

95  -° 

4.80 

300. 

128.9 

1.164 

400. 

?? 

?o 

4-35 

I2OO. 

52-7 

4-77 

400. 

98.3 

4.qb 

500. 

139-9 

1.263 

500. 

35 

12 

1400. 
1600. 

58.0 
63.0 

5-25 
5-7° 

600. 
800. 

107.2 
116.2 

5-41 

5-86 

700. 
750. 

150.8 
J53-5 

1.361 
1.386 

700. 

35-78 

4.62 

Tin. 

Carbon,  Graphite.* 

Fused  silica. 

Alundum  cement. 

P 

Pt 

Pt_ 
PO 

oC. 

p  in  ohms,  cm.  cube. 

°C.       p  =  megohms  cm. 

°c. 

p  in  ohms 
cm.  cube. 

-200. 

2.60 

.199 

Carbon 

Graphite 

15.          >2oo,ooo,ooo. 

20. 

>9X«o« 

-100. 

7-57 

.580 

O. 

0.0035 

0.00080 

230.                20,000,000. 

800. 

30800. 

o. 

13-05 

I.OO 

500. 

.0027 

.00083 

300.                                 200,000. 

900. 

13600. 

200. 

20.30 

i-55 

1000. 

.0021 

.00  .87 

350.                  30,000. 

1000. 

7600. 

225. 

22.00 

169 

1500. 

.0015 

.00090 

450.                      800. 

1  100. 

6500. 

235. 

47  .bo 

3-^3 

2000. 

.0011 

.ooioo 

700.                           30. 

1200. 

2300. 

750. 

dl.22 

4.69 

2500. 

.0009 

.001  1 

850.                   about  20. 

1600. 

190. 

Pt.  low,  Nernst,  1.  c.  high,  Pirrani,  Ber.  Dentsch.  Phvs.  Ges.  12,  p.  305,  Pb.  low,  Schimank,  Nernst,  1.  c.  high. 
Northrup,  see  Zn.  Bi.  low,  means,  high,  Northrup,  see  Zn.  Cd.  low,  Euchen,  Gehlhoff,  Verh.  Deutsch.  Phys.  Ges.  14, 
p.  169,  1912,  high,  Northrup,  see  Zn.  Sn.  low,  Dewar,  Fleming,  high,  Northrup,  see  Zn.  Carbon,  graphite,  Metallurg. 
Ch.  F.ng.  13,  p.  23,  1915.  Silica,  Campbell,  Nat.  Phys.  Lab.  n,  p.  207,  1914.  Alundum,  Metallurg.  Ch.  Eng.  12,  p. 
125,  1914. 

*  Diamond  1030°  C,  p  >io7;   1380°,  7.5  X  IC)5»  v-  Wartenberg,  1912. 

TABLE  404.— Volume  and  Surface  Resistivity  of  Solid  Dielectrics. 

The  resistance  between  two  conductors  insulated  by  a  solid  dielectric  depends  both  upon  the  surface  resistance  and 
the  volume  resistance  of  the  insulator.  The  volume  resistivity,  p,  is  the  resistance  between  two  opposite  faces  of  a  cen- 
timeter cube.  The  surface  resistivity,  <r,  is  the  resistance  between  two  opposite  edges  of  a  centimeter  square  of  the 
surface.  The  surface  resistivity  usually  varies  through  a  wide  range  with  the  humidity.  (Curtis,  Bui.  Bur.  Standards, 
IT,  359,  1915,  which  see  for  discussion  and  data  for  many  additional  materials.) 


Material. 

<r  ;  megohms 
50%  humidity. 

<r  ;  megohms 
70%  humidity. 

<r;  megohms 

90%  humidity. 

P 

Megohms-cms. 

Amber      

6  X  io8 

2  X  IO8 

i  X  io6 

S  X  io10 

Beeswax,  yellow   
Celluloid 

6  X  io8 
5  X  io* 

6X  io8 

2  X   IO4 

5X  io8 

2  X   IO8 

2  X  10* 

2  X   IO4 

Fiber   red 

2  X   IO* 

3  X  io3 

2  X  IO2 

Q  X  io8 

Glass  plate 

5  X  io4 

6  X  io 

2  X   IO 

2  X   10' 

"       Kavalier     
Hard  rubber,  new     
Ivory 

4  X  io6 
3  X  io9 
5  X  io8 

4  X  io8 
i  X  io8 
i  X  io8 

i  X  io8 

2X  IO8 

3  X  io 

8X  io9 
i  X  ioia 

2  X   IO2 

Khotinskv  cement     
Marble,  Italian      

7  X  io8 
3  X  io8 

3X  io8 

2  X   IOa 

5  X  to5 

2  X   10 

2  X   IO9 

i  X  io6 

Mica  colorless                           .     . 

2  X   IO7 

4XIO' 

8  X  io8 

2  X   I0» 

Paraffin  (pan  wax)     

9  X  io9 
6  X  io5 

7  X  io9 
7  X  io8 

6X  io9 
5  X  io 

i  X  io10 
3  X  io8 

3  X  io6 

2  X   IO8 

2  X  io2 

5  X  io12 

6X  io» 

3  X  io8 

2  X  IO8 

5  X  io10 

Sealing  wax                      .... 

2  X   IO9 

6  X  io8 

9  X  io7 

SX  io9 

Shellac          

6  X  io7 

3X10* 

7  X  io8 

i  X  io10 

Slate    

9  X  io 
7  X  10" 

3X  io 
4  X  io9 

i  X  io 
i  X  io8 

i  X  io2 
i  X  io11 

Wood,  parafined  mahogany  .     . 

4  X  io'- 

5  X  io5 

7  X  io8 

4  X  io7 

SMITHSONIAN   TABLES. 


332  TABLES  4O5,  405A 

TABLE  405.— Variation  of  Electrical  Kesistance  of  Glass  and  Porcelain  with  Temperature. 

The  following  table  gives  the  values  of  a,  b,  and  c  in  the  equation 

log  R  =  a  +  bt  +  cfl, 

where  R  is  the  specific  resistance  expressed  in  ohms,  that  is,  the  resistance  in  ohms  per  centimeter  of  a  rod  ona 
square  centimeter  in  cross  section.* 


No. 

Kind  of  glass. 

Density. 

a 

b 

c 

Range  of 
temp. 
Centigrade. 

I 

Test-tube  glass          .... 

- 

13.86 

—.044 

.000065 

0°-250° 

2 

3 
4 

«      ««        it 

2.458 

14.24 
1  6.2  1 
I3-I4 

—•055 
—•043 
—.031 

.0001 

.0000394 

—  .000021 

37-131 
60-174 
10-85 

Lime  glass  (Japanese  manufacture)  . 

2-55 

5 

«         «            ««                   «« 

2.499 

I4.OO2 

—.025 

—  .OOOO6 

35-95 

6 

Soda-lime  glass  (French  flask) 

2-533 

14.58 

—.049 

.000075 

45-120 

7 

Potash-soda  lime  glass 

2.58 

16.34 

—.0425 

.0000364 

66-193 

8 

Arsenic  enamel  flint  glass 

3-07 

18.17 

—•055 

.000088 

105-135 

9 

Flint  glass  (Thomson's  electrometer 
jar)         

3-I72 

18.021 

—.036 

—  .0000091 

100-200 

10 

Porcelain  (white  evaporating  dish)  . 

- 

*5-65 

—.042 

.OOOO5 

68-290 

COMPOSITION  OF  SOME  OF  THE  ABOVE  SPECIMENS  OF  GLASS. 

Number  of  specimen  — 

3 

4 

5 

7 

8 

9 

[    Sil 
Po 
So 
Le 

ica       
tash    

61.3 
22.9 
Lime,  etc. 
by  diff. 

57-2 

21.  1 

Lime,  etc. 
by  diff. 

70.05 
1.44 
14.32 
2.70 

75-65 
7.92 
6.92 

54-2 
10.5 
7.0 
23-9 

55-18 
13.28 

31.01 

da       

ad  oxide     .... 

Lime       

15.8 

16.7 

iQ-33 

8.48 

°-3 

0-35 

Magnesia        .... 

- 

-       • 

- 

0.36 

0.2 

0.06 

Arsenic  oxide 

- 

- 

- 

- 

3-5 

- 

Alumina,  iron  oxide,  etc. 

- 

- 

i-45 

0.70 

0.4 

0.67 

*  T.  Gray,  "  Phil.  Mag."  1880,  and  "  Proc.  Roy.  Soc."  1882. 
TABLE  405a.- Temperature  Resistance  Coefficients  of  Glass,  Porcelain  and  Quartz  dr/dt. 


Temperature. 

450° 

500° 

575° 

600° 

7oo° 

750° 

800° 

900° 

1000° 

Glass    .     .     . 

—32- 

—6. 

~l-S 

—.8 

—  0.17 

—O.I 

—0.06 

Porcelain  .     . 
Quartz.      .     . 

- 

-16. 

-9.8 

—2.8 

—1.6 

—  10. 

-•70 
—  6.40 

—0.30 
—2.60 

—  O.I  2 
—  1.  00 

Somerville,  Physical  Review,  31,  p.  261,  1910. 


SMITHSONIAN  TABLES. 


TABLE  4O6. 
TABULAR  COMPARISON  OF  WIRE  GAGES. 


333 


Gage 
No. 

American 
wire  gage 
(B.&SJ 
mils.t 

American 
wire  gage 
(B.&S.) 

mm.t 

Steel  wire 
gage* 
mils. 

Steel  wire 
gage* 

mm. 

Stubs' 
steel  wire 
gage 
mils. 

(British) 
standard 
wire  gage 
mils. 

Birming- 
lam  wire 

(S8uil>s') 
mils. 

Gage 
No. 

7-0 

490.0 

12.4 

500. 

7-0 

6-0 

461.5 

11.7 

464. 

6-0 

5-0 

430.5 

10.9 

432. 

S-o 

4-0 

460. 

TI.7 

393-8 

10.0 

400. 

454. 

4-0 

3-o 
•  2-0 

410. 
365. 

10.4 
9-3 

362.5 
33i.o 

9-2 
8.4 

372. 
348. 

425. 
380. 

3-o 

2-O 

o 
i 

2 

325. 
289. 
258. 

8.3 
7-3 
6-5 

306.5 
283.0 
262.5 

7-8 
7.2 
6-7 

227. 
219. 

324. 
300. 
276. 

340. 
300. 
284. 

0 
I 

2 

3 

229. 

5.8 

243-7 

6.2 

212. 

252. 

259. 

3 

4 

204. 

5-2 

225.3 

5-7 

207. 

232. 

238. 

4 

5 

182. 

4.6 

207.0 

5-3 

204. 

212. 

220. 

5 

6 

162. 

4-1 

192.0 

4-9 

2O  I. 

192. 

203. 

6 

7 

144- 

3-7 

177.0 

4-5 

199. 

176. 

I  80. 

7 

8 

128. 

3-3 

162.0 

4.1 

197. 

1  60. 

I6S. 

8 

9 

U4. 

2.91 

148.3 

3-77 

194- 

144- 

I48. 

9 

10 

102. 

2.59 

135.0 

3-43 

191. 

128. 

134. 

10 

II 

91. 

2.30 

120.5 

3-06 

188. 

116. 

120. 

II 

12 

81. 

2.05 

105.5 

2.68 

185. 

104. 

109. 

12 

13 

72. 

1.83 

9i.5 

2.32 

182. 

92. 

95. 

13 

14 

64. 

1.63 

80.0 

2.03 

180. 

80. 

83. 

14 

15 

57- 

1.45 

72.0 

1.83 

178. 

72. 

72. 

IS 

16 

Si- 

1.29 

62.5 

1-59 

175. 

64. 

65- 

16 

17 

45- 

US 

54-0 

1-37 

172. 

56. 

58. 

17 

18 

40. 

1.02 

47.5 

1.  21 

168. 

48. 

49* 

|| 

19 

36. 

0.91 

41.0 

1.04 

164. 

40. 

42. 

19 

20 

32. 

.81 

34-8 

0.88 

1  6  1. 

36. 

35- 

20 

21 

28.5 

.72 

31-7 

.81 

157- 

32. 

32. 

21 

22 

25-3 

.62 

28.6 

.73 

155. 

28. 

28. 

22 

33 

22.6 

•57 

25.8 

.66 

153- 

24- 

25. 

23 

24 

20.1 

•  Si 

23.0 

.58 

151. 

22. 

22. 

24 

25 

17.9 

•45 

20.4 

.52 

148. 

20. 

2O. 

75 

26 

IS.9 

.40 

18.1 

.46 

146. 

18. 

1  8. 

26 

27 

14.2 

•36 

17.3 

.439 

M3. 

16.4 

1  6. 

27 

28 

12.6 

•32 

16.2 

.411 

139. 

14.8 

14. 

28 

29 

11.3 

.29 

15-0 

.381 

134. 

13-6 

13- 

29 

30 

10.0 

.25 

14.0 

.356 

127. 

12.4 

12. 

3O 

31 

8.9 

.227 

13.2 

•335 

120. 

1  1.  6 

10. 

31 

32 

8.0 

.202 

12.8 

.325 

"5- 

10.8 

9- 

32 

33 

7-1 

.ISO 

11.8 

.300 

112. 

10.  0 

8. 

33 

34 

35 

6-3 
5.6 

.160 
.143 

10.4 
9.5 

.264 
.241 

no. 

1  08. 

§:: 

7- 
5- 

34 
35 

36 

S-o 

.127 

9.0 

.229 

106. 

7.6 

4* 

36 

37 

4-5 

.113 

8.5 

.216 

103. 

6.8 

37 

38 

4.0 

•1OI 

8.0 

.203 

101. 

6.0 

38 

39 

3-5 

.090 

7-5 

.191 

99. 

5-2 

39 

40 

3-1 

.080 

7.0 

.178 

97. 

4.8 

40 

4i 

6.6 

.168 

95- 

4-4 

41 

42 

6.2 

.157 

92. 

4.0 

42 

43 

6.0 

.152 

88. 

3-6 

43 

44 

5.8 

.147 

85. 

3-2 

44 

45 

5-5 

.140 

Si. 

2.8 

45 

46 

5.2 

.132 

79. 

2-4 

46 

47 

5-0 

.127 

77- 

2.0 

47 

48 

4.8 

.122 

75- 

1.6 

48 

49 

4.6 

.117 

72. 

1.2 

49 

50 

4-4 

.112 

69- 

I.O 

So 

*  The  Steel  Wire  Gage  is  the  same  gage  which  has  been  known  by  the  various  names:  "  Washburn  and  Moen,"  "  Roeb~ 
ling,"  "American  Steel  and  Wire  Co.'s."  Its  abbreviation  should  be  written  "Stl.  W.  G.r"  to  distinguish  it  from 
"  S.  W.  G.,"  the  usual  abbreviation  for  the  (British)  Standard  Wire  Gage. 

f  The  American  Wire  Gage  sizes  have  been  rounded  off  to  the  usual  limits  of  commercial  accuracy.  They  are  giren 
to  four  significant  figures  in  Tables  410  to  413.  They  can  be  calculated  with  any  desired  accuracy,  being  based  upon 
a  simple  mathematical  law.  The  diameter  of  No.  oooo  is  denned  as  0.4600  inch  and  of  No.  36  as  0.0050  inch.  The 


ratio  of  any  diameter  to  the  diameter  of  the  next  greater  number  \l =  1. 1229322. 

Taken  from  Circular  No.  31.    Copper  Wire  Tables,  U.S.  Bureau  of  Standards  which  contains  more  complete 
tables. 
SMITHSONIAN  TABLES. 


334  TABLES  4-07-413. 

WIRE   TABLES. 
TABLE  407  •  —  Introduction.    Mass  and  Volume  Resistivity  of  Copper  and  Aluminum. 

The  following  wire  tables  are  abridged  from  those  prepared  by  the  Bureau  of  Standards  at  the 
request  and  with  the  cooperation  of  the  Standards  Committee  of  the  American  Institute  of  Elec- 
trical Engineers  (Circular  No.  31  of  the  Bureau  of  Standards).  The  standard  of  copper  resist- 
ance used  is  "  The  Internationa!  Annealed  Copper  Standard  "as  adopted  Sept.  5,  1913,  by  the 
International  Electrotechnical  Commission  and  represents  the  average  commercial  high-conduc- 
tivity copper  for  the  purpose  of  electric  conductors.  This  standard  corresponds  to  a  conductivity 
of  58.  Xio-6  cgs.  units,  and  a  density  of  8.89,  at  20°  C. 

In  the  various  units  of  mass  resistivity  and  volume  resistivity  this  may  be  stated  as 

0.15328  ohm  (meter,  gram)  at  20°  C. 
875.20    ohms  (mile,  pound)  at  20°  C. 
1.7241    microhm-cm,  at  20°  C. 
0.67879  microhm-inch  at  20°  C. 
10.371    ohms  (mil,  foot)  at  20°  C. 

The  temperature  coefficient  for  this  particular  resistivity  is  020  =  0.00393  or  cto  =  0.00427. 
The  temperature  coefficient  of  copper  is  proportional  to  the  conductivity,  so  that  where  the  con- 
ductivity is  known  the  temperature  coefficient  may  be  calculated,  and  vice-versa.  Thus  the  next 
table  shows  the  temperature  coefficients  of  copper  having  various  percentages  of  the  standard  con- 
ductivity. A  consequence  of  this  relation  is  that  the  change  of  resistivity  per  degree  is  constant, 
independent  of  the  sample  of  copper  and  independent  of  the  temperature  of  reference.  This  re- 
sistivity-temperature constant,  for  volume  resistivity  and  Centigrade  degrees,  is  0.00681  michrom- 
cm.,  and  for  mass  resistivity  is  0.000597  ohm  (meter,  gram). 

The  density  of  8.89  grams  per  cubic  centimeter  at  20°  C.,  is  equivalent  to  0.32117  pounds  per 
cubic  inch. 

The  values  in  the  following  tables  are  for  annealed  copper  of  standard  resistivity.  The  user  of 
the  tables  must  apply  the  proper  correction  for  copper  of  other  resistivity.  Hard-drawn  copper 
may  be  taken  as  about  2.7  per  cent  higher  resistivity  than  annealed  copper. 

The  following  is  a  fair  average  of  the  chemical  content  of  commercial  high  conductivity  copper: 

Copper 99.91%  Sulphur 0.002% 

Silver.  .    03  Iron 002 

Oxygen 052  Nickel Trace 

Arsenic 002  Lead " 

Antimony 002  Zinc " 

The  following  values  are  consistent  with  the  data  above  : 

Conductivity  at  o°  C.,  in  c.g.s.  electromagnetic  units 62.969  X  io~& 

Resistivity  at  o°  C.,  in  michroms-cms 1.5881 

Density  at  o°  C 8.90 

Coefficient  of  linear  expansion  per  degree  C 0.000017 

"  Constant  mass  "  temperature  coefficient  of  resistance  at  o°  C 0.00427 

The  aluminum  tables  are  based  on  a  figure  for  the  conductivity  published  by  the  U.S.  Bureau 
of  Standards,  which  is  the  result  of  many  thousands  of  determinations  by  the  Aluminum  Company 
of  America.  A  volume  resistivity  of  2.828  michrom-cm.,  and  a  density  of  2.70  may  be  considered 
to  be  good  average  values  for  commercial  hard-drawn  aluminum.  These  values  give: 

Mass  resistivity,  in  ohms  (meter,  gram)  at  20°  C 0.0764 

"       "      (mile,  pound)  at  20°  C 436. 

Mass  per  cent  conductivity 200.7% 

Volume  resistivity,  in  michrom-cm.  at  20°  C 2.828 

in  microhm-inch  at  20°  C i.i  13 

Volume  per  cent  conductivity 61.0% 

Density,  in  grams  per  cubic  centimeter 2.70 

Density,  in  pounds  per  cubic  inch 0.0975 

The  average  chemical  content  of  commercial  aluminum  wire  is 

Aluminum 99-57% 

Silicon 0.29 

Iron 0.14 

SMITHSONIAN    TABLES. 


TABLES  408,  409. 
COPPER  WIRE   TABLES. 

TABLE  408.  -Temperature  Coefficients  of  Copper  for  Different  Initial  Temperatures  (Centtfrade) 

and  Different  Conductivities. 


335 


Ohms 

(meter,  gram) 
at  20°  C. 

Per  cent 
conductivity. 

a0 

«I5 

«20 

«2S 

a3o 

050 

0.161  34 
.ISQ66 

95% 
96% 

0.004  03 
.00408 

0.003  80 
.003  85 

0.003  73 
•00377 

0.003  67 
.00370 

0.003  60 
.00364 

0.003  36 
•00330 

.158  02 

•157  53 

97% 
97-3% 

.004  13 
.00414 

.00389 
.003  90 

.003  8  1 
.003  82 

•003  74 
•00375 

.00367 
.003  68 

.00342 
•003  43 

.15640 
.15482 

98% 

99% 

.004  17 

.004  22 

.00393 

.003  97 

.00385 
.00389 

.00378 
.003  82 

•OC3  71 
•003  74 

•00345 
.00348 

.153  28 

.151  76 

100% 
101% 

.004  27 
.00431 

.004  01 
.00405 

.003  93 

.00397 

.00385 
.003  89 

.00378 
.00382 

•003  5  * 
•00355 

NOTE.  — The  fundamental  relation  between  resistance  and  temperature  is  the  following: 

Rt  =  Rtl(i+ati[t-tJ), 

where  a^  is  the  "temperature  coefficient,"  and  t^  is  the  "initial  temperature"  or  "temperature  of  reference." 

The  values  of  a  in  the  above  table  exhibit  the  fact  that  the  temperature  coefficient  of  copper  is  proportional  to  the 
conductivity.  The  table  was  calculated  by  means  of  the  following  formula,  which  holds  for  any  per  cent  conductivity,  n, 
within  commercial  ranges,  and  for  centigrade  temperatures,  (n  is  considered  to  be  expressed  decimally:  e.g.,  il  percent 
conductivity  =:  99  per  cent,  n  =  0.99.) 


+  (/!  —  20) 


n  (0.00393) 
TABLE  409,  -Reduction  of  Observations  to  Standard  Temperature.  (Copper.) 


Temper- 
ature C. 

Corrections  to  reduce  Resistivity  to  20°  C. 

Factors  to  reduce  Resistance  to  20°  C. 

Temper- 
ature C. 

Ohm  (meter, 
gram). 

Microhm  — 
cm. 

Ohm  (mile, 
pound). 

Microhm  — 
inch. 

For  96  per 
cent  con- 
ductivity . 

For  98  per 
cent  con- 
ductivity. 

For  100  per 
cent  con- 
ductivity. 

o 
5 

10 

+0.011  94 
+  .008  96 
+  .005  97 

+0.1361 
+  .1021 
+  .0681 

+  68.20 
+  Si-iS 
+   M-io 

+0.053  58 
+  .040  1  8 
4-  .026  79 

ix4i6 

i.  0600 
1.0392 

1.0834 
1.0613 
1.0401 

X'2S2 
1.0626 

1.0409 

0 

5 
10 

ii 

12 

13 

+  .00537 
+  .004  78 
+  .004  18 

+  .0612 

+  -0544 
+  .0476 

+  30.69 
+  27.28 
+  23.87 

•f  .024  ii 
+  -021  43 
+  .01875 

1-0352 
1.0311 
1.0271 

1-0359 
1.0318 
1.0277 

1.0367 
1-0325 
1.0283 

ii 

12 

13 

14 

15 
16 

+  .003  58 
+  .002  99 
+  .002  39 

+  .0408 
+  -0340 
+  -0272 

+  20.46 
+   17-05 
+  13-64 

+  .016  07 
+  .013  40 
+  .010  72 

1.0232 
1.0192 
I-  oi  53 

1.0237 
1.0196 
1.0156 

1.0242 

1.0200 
I.OIOO 

14 

ii 

\\ 

19 

+  .001  79 
+  .001  19 
+  .000  60 

+  .0204 
+  -0136 
+  .0068 

+   10.23 
+     6.82 
+     3-41 

+  .00804 
+  -00536 
+  .00268 

1.0114 
1.0076 
1.0038 

1.0117 
1.0078 
1.0039 

I.OII9 
1.0079 
1.0039 

17 
18 
19 

20 
21 
22 

o 
—  .000  60 
—  .001  19 

0 

-  .0068 
—  .0136 

0 

—    3-41 
-    6.82 

o 
—   .002  68 
-   .00536 

1.  0000 

0.9962 
-9925 

1.  0000 

0.9962 
•9924 

1  .0000 

0.0961 
.9922 

20 

21 
22 

23 

24 
25 

-  .001  79 
—   .002  39 
-   .00299 

—  .0204 
—  .0272 
—  .0340 

—  10.23 
—  13.64 
—  17.05 

—  .008  04 
—   .010  72 
—  .013  40 

.9888 
.9851 
•9815 

.9886 
.9848 

.9811 

.9883 

.9845 

.9807 

23 

24 
25 

26 

11 

-   .003  58 
—   .004  18 
—   .004  78 

—  .0408 
—  .0476 
-   -0544 

—  20.46 

-  23.87 
—  27.28 

—  .016  07 
—   .018  75 
-  .021  43 

•9779 
•9743 
.9707 

•9774 
•9737 
.9701 

.9770 
•9732 
.9695 

26 

27 
28 

29 

30 

35 

-   -00537 
—   -005  97 
—   .008  96 

—   .0612 
'     -   .0681 
—  .1021 

—  30.69 
-  34.10 
—  51-15 

—  .024  ii 
—   .026  79 
—   .040  1  8 

.9672 
.9636 
.9464 

.9665 
.9629 
•9454 

.9658 

.9622 
•9443 

29 

30 

35 

40 
45 
50 

—   .on  94 
—   -014  93 
-   .017  92 

—  .1361 
—  .1701 
—   .2042 

-  68.20 
-  85.25 
—  102.30 

-   -053  58 
•-   .06698 
-   .08037 

.9298 
.9138 
.8983 

.9285 
.9122 
.8964 

.9271 
•9105 
.8945 

40 
45 
50 

55 
60 
65 

—    .020  OO 
—    .023  89 
—    .02687 

-   .2382 
-   .2722 
—  .3062 

-119-35 
-136.40 
-153-45 

-   -093  ?6 
—   .107  16 
—  .120  56 

.8833 
.8689 

•8549 

.8812 
.8665 
.8523 

.8791 
.8642 
.8497 

g 

65 

70 

75 

—  .029  86 
-  .03285 

-   -3403 
—   -3743 

-170.50 
-187-55 

—  -133  95 
—  -147  34 

.8413 
.8281 

•8385 
.8252 

.8358 
.8223 

70 
75 

SMITHSONIAN  TABLES. 


336 


TABLE  410. 
WIRE  TABLE,  STANDARD  ANNEALED  COPPER, 

American  Wire  Gage  (B.  A  S.)-   English  Units. 


ENGLISH. 


Gage 
No. 

Diameter 

in  Mils. 
at  20°  C. 

Cross-Section  at  20°  C. 

Ohms  per  1000  Feet.* 

Circular  Mils. 

Square  Inches. 

o°C 
(  =  3*°F) 

20°  C 

(  =  68°F) 

50°  C 

(=i23°F) 

75°  C 
(  =  1670  F) 

oooo 
ooo 

00 

460.0 
409.6 
364.8 

211  600. 
167800. 

133  loo. 

0.1662 
.1318 
.1045 

0.045  J6 
.056  95 
.071  81 

0.049  01 

.061  80 
•077  93 

0.054  79 
.06909 
.087  12 

0.059  61 
.075  16 
.09478 

o 
I 

2 

324-9 
289.3 
257.6 

105  500. 
83690. 
66370. 

.08289 

•065  73       . 
.052  13 

•09055 
.1142 
.1440 

.09827 
.1239 
•1563 

.1099 
•1385 
•1747 

.1195 

•i507 
.1900 

3 
4 

5 

229.4 
204.3 
181.9 

52  640. 
41  740. 

33100. 

.041  34 
.032  78 
.02600 

.1816 
.2289 
.2887 

.1970 
.2485 
•3*33 

.2203 
.2778 
.3502 

.2396 
.3022 
.3810 

6 

8 

162.0 

144-3 
128.5 

26250. 

20  820. 

16  510. 

.020  62 
-01635 
.01297 

.3640 
-4590 
.5788 

•3951 
.4982 
.6282 

.4416 

•5569 
.7023 

.4805 
.6059 
.7640 

9 

10 

ii 

114.4 
101.9 
90.74 

13090. 
10  380. 

8234. 

.01028 
.008155 
.006  467 

.7299 
.9203 
1.161 

.7921 
.9989 
1.260 

.8855 
I.II7 
1.408 

•9633 
1.215 

1-532 

12 
13 
14 

80.8  1 
71.96 
64.08 

6530. 

5*78. 
4107. 

.005  129 
.004  067 
.003225 

1.463 
1.845 
2.327 

1-588 
2.003 

2.525 

1-775 
2.239 
2.823 

I-931 

2.436 
3.071 

3 

17 

57-07 
50.82 
45.26 

32$7. 
2583. 
2048. 

.002  558 
.002  028 
.001  609 

2-934 
3.700 
4.666 

3.184 
4.016 
5.064 

3-560 
4.489 
5.660 

3-873 
4.884 
6.158 

18 

'9 

20 

40.30 

35-»9 
31.96 

1624. 
1288. 

IO22. 

.001  276 

.OOI  OI2 

.000  802  3 

5.883 
7.418 
9-355 

6.385 
8-051 
10.15 

7-138 
9.001 

IJ-35 

7765 
9.792 

12.35 

21 

22 
23 

28.45 

25-35 
22-57 

SlO.I 
642.4 
509-5 

.000  636  3 
.000  504  6 
.0004002 

11.80 

14.87 
18.76 

12.80 
16.14 
20.36 

14-31 
18.05 
22.76 

15-57 
19.63 
24.76 

24 

3 

20.10 
17.90 
15.94 

404.0 
320.4 
254-1 

•0003173 
.000251  7 
.000  199  6 

23-65 
29.82 
37.61 

25.67 

32-37 
40.81 

28.70 
36.18 
45-63 

31.22 
39-36 
49.64 

27 
28 
29 

14.20 
12.64 
11.26 

2OI.5 
159.8 
126.7 

.0001583 
.000  125  5 
.00009953 

47-42 
59.80 
75-40 

5M7 
64.90 
81.83 

57-53 
72-55 
91.48 

62.59 

78.93 
99-52 

30 
31 
32 

10.03 
8.928 

7-95° 

IOO-5 
79.70 
63.21 

.000  078  94 
.000  062  60 
.000  049  64 

95.08 
119.9 
151.2 

103.2 
130.1 
164.1 

"5-4 
145-5 
183.4 

123.5 
158.2 
199-5 

33 
34 

35 

7.080 
6-305 
5-615 

50.13 
39-75 
3I-52 

.000  039  37 

.000  031  22 
.OOO  O24  76 

190.6 
240.4 
3°3-  1 

206.9 
260.9 
329.0 

231-3 
291.7 
367.8 

251.6 

3I7-3 
400.1 

36 

^ 

5.000 
4-453 
3-965 

25.00 
19.83 
1572 

.00001964 
.00001557 

.000012  35 

382.2 
482.0 
607.8- 

414.8 
659.6 

463-7 
584.8 

737-4 

504-5 
636.2 
802.2 

39 
40 

3-531 
3-145 

12.47 
9-888 

.000009793 

.000  007  766 

766.4 
966.5 

831.8 
1049. 

929.8 
"73- 

IOI2. 
1276. 

*  Resistance  at  the  stated  temperatures  of  a  wire  whose  length  is  1000  feet  at  20°  C. 
SMITHSONIAN  TABLES. 


ENGLISH.  TABLE  41O  (continued}. 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER 

American  Wire  Gage  (B.  &  a.).    English  Units  (confined). 


337 


% 

Diameter 
in  Mils, 
at  20°  C. 

Pounds 
per 
1000  Feet. 

Feet 
per 
Pound. 

Feet  per  Ohm.* 

o°  C 
(=32°  F) 

20°  C 

(=68°  F) 

50°  C 

(=I22°F) 

75°  C 
(=.67  F) 

0000 

ooo 

00 

460.0 
409.6 
364.8 

640.5 

507-9 
402.8 

1.561 

1.968 
2.482 

22  140. 
17  560. 
13  930. 

2O  400. 

16  180. 

12  830. 

18  250. 
14  470. 
ii  480. 

16  780. 
13  300. 
10  550. 

0 

I 

2 

324.9 
289.3 
257-6 

3'9-S 

253-3 
200.9 

3-130 
3-947 
4-977 

II  040. 
8758. 
6946. 

10  180. 

8070. 

6400. 

9103. 
7219. 

5725. 

8367. 
6636. 
5262. 

3 
4 

5 

229.4 
204.3 
I8I.9 

159-3 
126.4 

100.2 

6.276 
7.914 
9.980 

5508. 
4368. 
3464. 

5075- 
4025. 
3192. 

4540- 
3600. 

2855- 

4I73- 
3309. 
2625. 

6 

162.0 

M4-3 
128.5 

79.46 
63.02 
49.98 

12.58 

15-87 

2O.OI 

2747. 
2179. 
1728. 

2531. 

2007. 

1592. 

2264. 
1796. 
1424. 

2081. 
1651. 
1309. 

9 

10 

ii 

114.4 
IOI-9 
90.74 

39.63 
31-43 
24.92 

25-23 
31.82 
4O.I2 

1370. 
I087. 
861.7 

1262. 

1001. 

794.0 

1129. 
895-6 
710.2 

1038. 
823.2 
652.8 

12 

J3 
14 

80.81 
71.96 
64.08 

19.77 
15.68 
12.43 

50-59 
63.80 
80.44 

683.3 
541-9 
429.8 

629.6 

499-3 
396.0 

563-2 
446.7 
354-2 

5177 
410.6 

325-6 

II 

i? 

57-07 
50.82 
45.26 

9.858 
7.8l8 
6.200 

IOI-4 
127.9 
161.3 

340.8 
270.3 
214-3 

314.0 
249.0 
J97-5 

280.9 

222.8 
176.7 

258.2 
204.8 
162.4 

18 
19 

20 

40.30 

35.89 
31.96 

4.917 

3-899 
3.092 

203.4 
256.5 
3234 

I7O.O 
134.8 
106.9 

156.6 
124.2 
98.50 

I4O.I 
III.  I 

88.ii 

128.8 

I02.I 
80.99 

21 
22 
23 

28.46 

25-35 
22.57 

2.452 

1-945 

1.542 

407.8 
514.2 
648.4 

84.78 
67.23 
53-32 

78.11 
61.95 
49-13 

69.87 
55-41 
43-94 

64-23 
50-94 
40.39 

24 

3 

20.  i  o 
17.90 
'5-94 

1.223 
0.9699 
.7692 

817.7 
1031. 
I3OO. 

42.28 

33-53 
26.59 

38.96 
30.90 
24.50 

34.85 
27.64 
21.92 

32.03 
25.40 
20.15 

27 
28 
29 

14.20 
12.64 
11.26 

.6100 
.4837 
•3836 

1639. 
2067. 
2607. 

21.09 
16.72 
13.26 

'9-43 
I5-4I 

12.22 

I7-38 
I3-78 
10.93 

15.98 
12.67 
IO.O5 

30 
31 
32 

10.03 
8.928 
7-95° 

.3042 
.2413 
•1913 

3287. 
4I45- 

5227. 

10.52 
8.341 
6.614 

9.691 
7.685 
6.095 

8.669 
6-875 
5-452 

7.968' 
6.319 
5.0II  j 

33 
34 
35 

7.080 
6-305 
5-6i5 

.1517 
.1203 
.095  42 

6591. 
8310. 

10  480. 

5-245 
4.160 

3-299 

4-833 
3-833 
3.040 

4.323 
3-429 
2.719 

3-974  i 
3-I52  : 
2-499 

36 

9 

5.000 
4-453 
3-965 

.075  68 
.060  01 
.047  59 

13  210. 

16  660. 

21  OIO. 

2.616 

2.075 
1.645 

2.4II 
I.9I2 
I.5l6 

2.156 
1.710 
1.356 

1.982 

*-572  i 
1.247 

39 
40 

3-53' 
3-M5 

.037  74 
.029  93 

26  5OO. 

33  4io. 

1-305 
1-035 

I.2O2 
0-9534 

1-075 
0.8529 

0.9886 

.7840 

•  Length  at  20°  C.  of  a  wire  whose  resistance  is  i  ohm  at  the  stated  temperature*. 
SMITHSONIAN  TABLES. 


33  O  TABLE  410    (continued). 

WIRE   TABLE,  STANDARD  ANNEALED  COPPER  (continued). 
American  Wire  Gage  (B.  A  S.  >.    English  Units  (continued). 


ENGLISH, 


Gage 
No. 

Diameter 

in  Mils 
at 

20°  C. 

Ohms  per  Pound. 

Pounds  per  Ohm. 

o°C. 
(  =  32°F.) 

20°  C. 

(  =  6S°F.) 

50°  C. 

(=.22°F.) 

20°  C. 

(  =  68°  F.) 

oooo 

000 
00 

460.0 
409.6 
364.8 

o.ooo  070  51 

.OOO  II2I 

.000  1783 

o.ooo  076  52 
.000  1217 
.000  1935 

o.ooo  085  54 
.000  1360 
.000  2163 

13070. 
8219. 
5169. 

O 

I 

2 

324.9 
289.3 
257.6 

.000  2835 
.000  4507 
.000  7166 

.000  3076 
.000  4891 
.000  7778 

.000  3439 
.000  5468 
.000  8695 

325L 
2044. 
1286. 

3 
4 

5 

229.4 
204.3 
181.9 

.001  140 
.001  812 
.002  881 

.001  237 
.001  966 

.003  127 

.001  383 
.002  198 
•003  495 

808.6 
508.5 
319.8 

6 

i 

162.0 

144-3 
128.5 

.004  581 
.007  284 
.on  58 

.004  972 
.007  905 

.012  57 

•005  558 
.008838 
.014  05 

2OI.I 
126.5 

79-55 

9 
10 
ii 

114.4 
101.9 
90.74 

.018  42 
.029  28 
.046  56 

.01999 
.031  78 

•05°  53 

.022  34 

•035  53 
.056  49 

50-03 
3'-47 
19.79 

12 
13 
14 

80.8  1 
71.96 
64.08 

.074  04 
.1177 

.1872 

.080  35 
.1278 
.2032 

.08983 
.1428 
.2271 

12.45 
7.827 
4.922 

;i 

17 

57-07 
50.82 
45.26 

.2976 

•4733 
•7525 

-323° 
-5136 
.8167 

.3611 

•5742 
.9130 

3.096 
1.947 
1.224 

18 
19 

20 

40.30 

35*9 
31.96 

1.197 
1.903 

3-025 

1.299 
2.065 
3-283 

1.452 
2.308 
3.670 

0.7700 

•4843 
.3046 

21 

22 

23 

28.46 

25-35 
22.57 

4.810 
7.649 

12.  l6 

5.221 
8.301 
13.20 

5.836 
9.280 
14.76 

•J9i5 
.1205 

•075  76 

24 

3 

2O.  I  O 

17.90 
15-94 

19-34 

30.75 
48.89 

20.99 

33-37 
53.06 

23.46 
37-31 
59-32 

.047  65 
.029  97 
.01885 

3 

29 

14.20 
12.64 
11.26 

77-74 
123.6 
196.6 

84.37 
134.2 

213-3 

94.32 
150.0 

238-5 

.on  85 
.007  454 
.004  688 

30 
3i 

32 

10.03 
8.928 
7.950 

312.5 

497-0 
790.2 

339-2 

539-3 
857.6 

379-2 
602.9 
958.7 

.002  948 
.001  854 
.001  166 

33 
34 
35 

7.080 
6-305 
5-615 

1256. 
1998. 

3*77- 

1364. 
2168. 
3448. 

iSH 

2424. 

3854. 

•ooo  7333 
.000  4612 
.000  2901 

36 

!      % 

5.000 
4-453 
3-965 

5051- 
8032. 

12  770. 

5482. 
8717. 
13860. 

6128. 

9744. 
15490. 

.000  1824 
.000  1147 
.000072  15 

39 
40 

3-531 
3-145 

20  310. 
32  290. 

22  040. 

35  040- 

24  640. 
39  170- 

.000  045  38 
.000  028  54 

SMITHSONIAN  TABLES. 


METRIC.  TABLE  411. 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER. 

American  Wire  Gage  (B.  &  S.)  Metric  Units. 


339 


Diameter 

Cross  Section 

Ohms  per   ] 

Uloroeter." 

Gage 
No. 

in   mm. 
at  20°  C. 

in  mm.1 
at  20°  C. 

o°C. 

20°  C. 

50°  C. 

75°  C. 

0000 

11.68 

107.2 

0.1482 

0.1608 

0.1798 

0.1956 

OOO 

10.40 

85.03 

.1868 

.2028 

.2267 

.2466 

oo 

9.266 

6743 

•2356 

•2557 

.2858 

.3110 

o 

8.252 

53-48 

.2971 

.3224 

.3604 

.3921 

I 

7.348 

42.41 

•3746 

.4066 

•4545 

•4944 

2 

6-544 

.4724 

•5127 

.6235 

3 

5.827 

26.67 

•5956 

.6465 

.7227 

.7862 

4 

5 

5.189 
4.621 

21.15 
16.77 

•75" 
.9471 

.8152 
1.028 

•91  1  3 
1.149 

.9914 
1.250 

6 

4.115 

I3-3° 

1.194 

I.2Q6 

1.449 

1-576 

7 

3-665 

1.506 

1.634 

1.827 

1.988 

8 

3.264 

8.366 

1.899 

2.o6l 

2.304 

2.506 

9 

2.906 

6.634 

2-395 

2-599 

2.905 

3.161 

10 

2.588 

5.261 

3.020 

3-277 

3-663 

3.985 

ii 

2.305 

4.172 

3.807 

4.132 

4.619 

5-025 

12 

2-053 

3-309 

4.801 

|.2I  I 

5-825 

6-337 

\4 

.828 
.628 

2.624 
2.081 

6.054 
7-634 

6-571 
8.285 

7-345 
9.262 

7.991 
10.08 

15 

.450 

1.650 

9.627 

10.45 

n.68 

12.71 

16 

.291 

1.309 

12.14 

13.17 

14-73 

16.02 

.150 

1.038 

1  6.6  1 

18.57 

20.20 

18 

1.024 

0.8231 

19.30 

20.95 

23.42 

25.48 

19 

0.9116 

•6527 

24-34 

26.42 

29-53 

32.12 

20 

.8ll8 

•5X76 

30.69 

33-31 

37-24 

40.51 

21 

.7230 

.4105 

38.70 

42.00 

46.95 

51.08 

22 
23 

•6438 

•5733 

•32^5 
.2582 

48.80 
61.54 

52-96 
66.79 

59-21 
74.66 

6441 
81.22 

24 

25 

.5106 
•4547 

.2047 
.1624 

77.60 
97.85 

84.21 
106.2 

94.14 
118.7 

IO2.4 
I29.I 

26 

.4049 

.1288 

123.4 

133-9 

149.7 

162.9 

27 

.3606 

.1021 

155-6 

168.9 

188.8 

203.4 

28 

.3211 

.080  98 

196.2 

212.9 

238.0 

258.9 

29 

.2859 

.064    22 

247.4 

268.5 

300.1 

326.5 

3° 

•2546 

.050  93 

3"-9 

338.6 

378.5 

4II.7 

32 

.2268 
.2019 

.040  39 
.032  03 

393-4 
496.0 

426.9 
538.3 

477-2 
601.8 

519.2 
654.7 

33 
34 

'I&ol 

.025  40 

.020    14 

625.5 
788.7 

678.8 
856.0 

758.8 
956.9 

825.5 
IO4I. 

35 

:!426 

•015  97 

994-5 

1079. 

1207. 

I313- 

36 

.1270 

.012  67 

1254- 

1361- 

1522. 

I655- 

3 

.1131 

.1007 

.010  05 
.007  967 

1581. 
1994. 

1716. 
2164. 

1919. 
2419. 

2087. 
2632. 

39 
40 

.089  69 
.079  87 

.006  318 
.005  oio 

2514- 

2729. 
3441- 

3847. 

33*9- 
4185. 

•Resistance  at  the  stated  temperatures  of  a  wire  whose  length  is  i  kilometer  a 

SMITHSONIAN    TABLES, 


340  TABLE  411  (continued). 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued). 
American  Wire  Gage  (B.  &  S.)    Metric  Units  (continued). 


METRIC, 


Gage 
No. 

Diameter 
in  mm. 
at  20°  C. 

Kilograms 
per 
Kilometer. 

Meters 
per 
Gram. 

Meters  per  Ohm.* 

o°C. 

20°  C. 

50°  C. 

75°  C. 

oooo 

000 
00 

11.68 

10.40 
9.266 

953-2 

755-9 
599-5 

o.ooi  049 
.001  323 
.001  668 

6749. 
5352. 
4245- 

6219. 
4932. 
39II- 

5563. 

4412. 
3499. 

5"3. 
4055. 
3216. 

o 
I 

2 

8.252 
7.348 
6-544 

475-4 
377-0 
299.0 

.002  103 

.002  652 

•003  345 

2117. 

3102. 
2460. 
1951' 

2774. 

2200. 
1745. 

2550. 
2O22. 
1604. 

3 
4 
5 

5.827 
5.189 
4.621 

237.1 
188.0 

149.1 

.004  217 
.005  318 
.006  706 

1679. 

I33J. 
1056. 

1547- 
1227. 
972.9 

1384. 
1097. 
870.2 

1272. 
1009. 

799-9 

6 

I 

4-IIS 
3.665 
3.264 

118.2 

93-78 
74.37 

.008  457 
.010  66 
-013  45 

^7'3 
664.0 

526.6 

771-3 
611.8 

485.2 

690.1 

547-3 
434-0 

634-4 

5°3-  i 
399-o 

9 
10 
ii 

2.906 
2.588 
2.305 

58.98 

46.77 
37.09 

.016  96 

.021   38 
.026  96 

417.6 
33L2 
262.6 

384-8 

305-1 
242.0 

344-2 
273.0 
216.5 

316.4 
250.9 
199.0 

12 
U 
M 

2.053 
1.828 
1.628 

29.42 

23-33 
18.50 

.03400 
.042  87 
.054  O6 

208.3 
165.2 
131.0 

191.9 

152.2 
120.7 

171.7 
136.1 
1  08.0 

157.8 
125.1 
99.24 

\l 

I? 

1.450 
1.291 
1.150 

14.67 

11.63 
9.226 

.068  16 

•085  95 
.1084 

103.9 
82.38 
65.33 

95-71 

75-90 
60.20 

85.62 
67.90 
53-85 

78.70 
62.41 
49.50 

18 
19 

20 

I.O24 
0.9116 
.8ll8 

7.317 

5-803 

4.602 

•1367 
•1723 
.2173 

51.81 
41.09 
32.58 

47-74 
37-86 
30.02 

42.70 
33-86 
26.86 

39.25 
31-13 
24.69 

21 
22 
23 

.7230 
.6438 

•5733 

3-649 
2.894 
2.295 

.2740 
•3455 
•4357 

25.84 
20.49 
16.25 

23.81 
1  8.88 
14.97 

21.30 
16.89 
13-39 

19.58 

15-53 
12.31 

24 
25 
26 

.5106 

4547 
.4049 

1.820 
1.443 
1.145 

.5494 
.6928 
.8736 

I2.89 
10.22 
8.105 

11.87 
9.417 
7.468 

10.62 
8.424 
6.680 

9-764 
7-743 
6.141 

11 

29 

.3606 
.3211 
.2859 

0.9078 

.7199 
.5709 

1.  102 
1.389 

1.752 

6.428 

5-°97 
4.042 

5.922 
4.697 
3-725 

5.298 
4.201 
3-332 

4.870 
3.862 
3.063 

30 
31 
32 

:22^6 
.2019 

.4527 
•3590 
.2847 

2.2O9 
2.785 
3-512 

3.206 
2.542 
2.OI6 

2-954 
2.342 
1.858 

2.642 
2.095 
1.662 

2.429 
1.926 

i.527 

33 
34 
35 

.1798 
.1601 
.1426 

.2258 
.1791 

.1420 

4.429 

5.584 
7.042 

1.  006 

1.473 
1.168 
0.9265 

1.318 

1.045 
0.8288 

1.  211 
0.9606 
.7618 

36 
% 

.1270 
.u3i 

.1007 

.1126 
.08931 

.070  83 

8.879 
1  1.  2O 
14.12 

0.7974 
.6324 
•5015 

•7347 
.5827 
.4621 

.6572 
.5212 
.4133 

.6041 
.4791 

-3799 

39 

40 

.08969 
.079  87 

.056  17 

.044  54 

17.80 
22.45 

•3977 
•3'54 

.3664 
.2906 

.3278 
.2600 

•3OI3 
.2390 

*  Length  at  20°  C.  of  a  wire  whose  resistance  is  i  ohm  at  the  stated  temperatures. 
SMITHSONIAN  TABLES. 


METRIC.  TABLE   411  {continued). 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued). 
American  Wire  Gage  (B.  &  S.).    Metric  Units  (continued). 


Gage 
No. 

Diameter 
in  mm. 
at  20°  C. 

Ohms  per  Kilogram. 

Grams  per  Ohm. 

o°C. 

20°  C. 

50°  C. 

20°  C. 

oooo 
ooo 

00 

11.68 

10.40 
9.266 

o.ooo  155  4 

.OOO  247  2 

.000  393  o 

o.ooo  168  7 
.000  268  2 
.000  426  5 

o.ooo  188  6 
.000  299  9 
.000  476  8 

5  928  ooo. 
3  728  ooo. 

2  344000. 

0 

2 

8.252 
7-348 
6-544 

.000  624  9 

.000  993  6 
.001  580 

.OOO  678  2 

.001  078 
.001  715 

.000  758  2 
.001  206 
.001  917 

i  474  ooo. 
927  300. 
583  200. 

3 
4 
5 

5.827 
5.189 
4.621 

.002  512 
•003  995 
.006352 

.002  726 
•004  335 
.006  893 

.003  048 
.004  846 
.007  706 

366800. 
230  700. 
145  100. 

6 
8 

4-ii5 
3.665 
3.264 

.010  10 

.016  06 
-025  53 

.010  96 

•017  43 
.027  71 

.012  25 
.019  48 
.030  98 

91  230. 
57380. 

36080. 

9 
10 
ii 

2.906 
2.588 
2-305 

.04060 
.064  56 
.1026 

.044  06 
.070  07 
.1114 

.049  26 

•078  33 
.1245 

22  690. 
I4  270. 
8976. 

12 
!3 
14 

2-053 
1.828 
1.628 

.1632 

•2595 
.4127 

.1771 
.2817 
•4479 

.1980 

•3M9 
.5007 

56.45 
355°- 
2233- 

11 

17 

1.450 
1.291 
1.150 

.6562 
1.043 
1.659 

.7122 
1.132 
1.801 

•7961 
1.266 
2.013 

1404. 
883.1 

555-4 

18 

!9 

20 

1.024 
0.9116 
.8118 

2.638 
4.194 
6.670 

2.863 

$ 

3-201 

3.089 

8.092 

349-3 
219.7 

138-2 

21 

22 
23 

.7230 
.6438 
-5733 

1  0.60 
16.86 
26.81 

11.51 

18.30 
29.10 

12.87 

20.46 

32.53 

86.88 
54.64 
34.36 

24 

S 

.5106 

•4547 
.4049 

42.63 
67.79 
107.8 

46.27 

73-57 
117.0 

51.73 
82.25 
130.8 

21.61 

13-59 
8.548 

27 
28 
29 

.3606 
.3211 
.2859 

171.4 

272.5 
433-3 

1  86.0 
295.8 
470.3 

207.9 
33°-6 
525-7 

5-376 
3-381 
2.126 

3° 
31 
32 

.2546 
.2268 
.2019 

689.0 
1096. 
1742. 

747-8 
1189. 
1891. 

836.0 
1329. 
2114. 

1-337 
0.8410 
.5289 

33 
34 
35 

•'S8 
..i6oi 

.1426 

2770. 
4404. 
7003. 

3006. 
4780. 
7601. 

336i- 
«44- 
8497- 

.3326 
.2092 
.1316 

36 
% 

.1270 
.1131 
.1007 

11140. 
17710. 
28150. 

1  2090. 
19220. 
30560. 

i35io. 
21480. 
34i6a 

.08274 
.052  04 
•032  73 

39 

40 

.08969 
.079  87 

44770. 
71180. 

48590. 
77260. 

54310' 
86360. 

.020  58 
.01294 

SMITHSONIAN  TABLES. 


342 


TABLE   412. -ALUMINUM  WIRE  TABLE, 

Hard-Drawn  Aluminum  Wire  at  20°  C.  (or,  68°  F.). 
American  Wire  Gage  (B.  &  S.).    English  Units. 


ENGLISH. 


Gage 
No. 

Diameter 
in  Mils. 

Cross  Section. 

Ohms 
per 
1000  Feet. 

Pounds 
per 
looo  Feet. 

Pounds 
per  Ohm. 

Feet 
per  Ohm. 

Circular 

Mils. 

Square 
Inches. 

oooo 

460. 

212  OOO. 

0.166 

0.0804 

195- 

2420. 

12  400. 

OOO 

410. 

168  ooo. 

.132 

.IOI 

154- 

1520. 

9860. 

00 

365. 

133000. 

.105 

.128 

122. 

957- 

7820. 

0 

325. 

106000. 

.0829 

.l6l 

97-o 

602. 

62OO. 

2 

2!: 

83700. 
66400. 

.0657 
.0521 

3 

76.9 

61.0 

379- 
238. 

4920. 
3900. 

3 
4 

229. 
204. 

52  600. 

41-700. 

.0413 
.0328 

.408 

48.4 
38-4 

150. 
94.2 

3090. 
2450. 

5 

182. 

33  I0°- 

.0200 

.514 

30-4 

59-2 

I950- 

6 

162. 

26  300. 

.O2O6 

.648 

24.1 

37-2 

1540. 

7 

144. 

20  800. 

.0164 

.817 

19.1 

23-4 

I22O. 

8 

128. 

1  6  500. 

.0130 

1.03 

15.2 

14.7 

970. 

9 

114. 

13  100. 

.0103 

1.30 

I2.O 

9.26 

770. 

10 

102. 

10  400. 

.008  15 

1.64 

9-55 

5-83 

610. 

ii 

91. 

8230. 

.00647 

2.07 

7-57 

3-66 

484. 

12 

81. 

6530. 

.005  I3 

2.61 

6.00 

2.30 

384- 

13 

72. 

5180. 

.004  07 

3-29 

4.76 

i.45 

3°4- 

64. 

4110. 

.003  23 

4.14 

378 

0.911 

241. 

I5 

57- 

3260. 

.002  56 

5.22 

2.99 

•573 

191. 

16 

51- 

2580. 

.002  03 

6.59 

2-37 

.360 

152. 

17 

45- 

2050. 

.001  61 

8.31 

1.88 

.227 

1  20. 

18 

40. 

1620. 

.001   28 

10.5 

1.49 

•  143 

95-5 

19 
20 

36. 
32. 

1290. 

IO2O. 

.001  01 
.000  802 

13.2 
16.7 

1.18 

0-939 

.0897 
.0564 

75-7 
60.0 

21 

28.5 

810. 

.000  636 

2I.O 

•745 

•°355 

47.6 

22 

25-3 

642. 

.000  505 

26.5 

•591 

.0223 

37-8 

23 

22.6 

509- 

.000400 

33-4 

.468 

.0140 

29.9 

24 

20.1 

404. 

.000  317 

42.1 

•371 

.008  82 

23-7 

11 

17.9 
15.9 

320. 
254- 

.000  252 

.000  200 

I3'1 
67.0 

•295 
•234 

•005  55 
.003  49 

1  8.8 
14.9 

27 

14.2 

202. 

.000  158 

84.4 

.185 

.002  19 

11.8 

28 

12.6 

1  60. 

.000  126 

1  06. 

.147 

.001  38 

9-39 

29 

"•3 

127. 

.000  099  5 

134- 

.117 

.000868 

745 

30 

1  0.0 

101. 

.000  078  9 

169. 

.0924 

.000  546 

5-91 

31 
32 

8.9 

8.0 

79.7 
63.2 

.000  062  6 
.000  049  6 

213. 
269. 

•0733 
.0581 

.000  343 
.000  216 

4.68 
3-72 

33 

7.1 

50.1 

.000  039  4 

339- 

.0461 

.000  136 

2-95 

34 

6-3 

39-8 

.OOO  031    2 

428. 

•°365 

.000  085  4 

2-34 

35 

5.6 

3r-5 

.000  024  8 

540. 

.0290 

.000  053  7 

1.85 

36 

5-o 
4-5 

25.0 
19.8 

.000  019  6 
.000  015  6 

681. 
858. 

.0230 
.0182 

.000  033  8 

.OOO  O2  I  2 

1.47 
1.17 

38 

4.0 

iS-7 

.000  012  3 

1080. 

•0145 

.000  013  4 

0.924 

39 

3-5 

12.5 

.000009  79 

1360. 

.0115 

.000  008  40 

.733 

40 

3-i 

9-9. 

.000  007  77 

1720.  ' 

.0091 

.000  005  28 

.581 

SMITHSONIAN  TABLES. 


METRIC. 


TABLE  413. -ALUMINUM  WIRE  TABLE. 

Hard-Drawn  Aluminum  Wire  at  20°  0. 
American  Wire  Gage  (B.  &  S.)    Metric  Units. 


343 


Gage 
No. 

Diameter 
in  mm. 

Cross  Section 
in  mm.2 

Ohms  per 
Kilometer. 

Kilograms  per 
Kilometer. 

Grams  per 
Ohm. 

Meters  per 
Ohm. 

0000 

II.7 

107. 

0.264 

289. 

I    100  000. 

3790. 

ooo 

10.4 

85.0 

•333 

230. 

690  ooo. 

3010. 

oo 

9-3 

67.4 

.419 

182. 

434  ooo. 

2380. 

0 

8-3 

53-5 

.529 

144. 

273  ooo. 

1890. 

I 

7-3 

42.4 

.667 

114. 

172  ooo. 

1500. 

2 

6.5 

33-6 

.841 

90.8 

108  ooo. 

1190. 

3 

5-8 

26.7 

1.  06 

72.0 

67  900. 

943. 

4 

5-2 

21.2 

i-34 

57-1 

42  700. 

748. 

5 

4-6 

1  6.8 

1.69 

45-3 

26  900. 

593- 

6 

4.1 

13-3 

2.13 

35-9 

1  6  900. 

470. 

7 

3-7 

10.5 

2.68 

28.5 

10  600. 

373- 

8 

3-3 

8-37 

3.38 

22.6 

6680. 

296. 

9 

10 
n 

2.91 

2-59 
2.30 

S3 

4.17 

4.26 
& 

17.9 
14.2 
"•3 

4200. 
2640. 

1660. 

X 

148. 

12 

2.05 

3-31 

8-<55 

8.93 

1050. 

117. 

IT 

1.83 

2.62 

10.8 

7.08 

657. 

92.8 

14 

1.63 

2.08 

13.6 

5.62 

413- 

73-6 

I5 

i.45 

1.65 

17.1 

446 

260. 

584 

16 

1.29 

I-31 

21.6 

3-53 

164. 

46-3 

17 

'•IS 

1.04 

27-3 

2.80 

103. 

36-7 

18 

1.02 

0.823 

344 

2.22 

64.7 

29.1 

19 

O.gi 

•653 

43-3 

1.76 

40.7 

23-1 

20 

.81 

.518 

54-6 

I.4O 

25.6 

18.3 

21 

.72 

.411 

68.9 

I.  II 

16.1 

14.5 

22 
23 

.64 

•57 

.326 
.258 

86.9 
no. 

0.879 
.697 

IO.I 

6.36 

11.5 

24 

•51 

.205 

138. 

•553 

4.00 

7.24 

25 

•45 

.162 

174. 

438 

2.52 

5-74 

26 

^  3 

.40 

.129 

220. 

•348 

1.58 

4-55 

3 

•36 

•32 

.102 
.0810 

277. 
349- 

.276 
.219 

*§3 

3.61 
2.86 

29 

.29 

.0642 

440. 

•173 

•394 

30 

3' 

32 

•25 
.227 

.202 

.0509 
.0404 
.0320 

555- 
700. 
883. 

•138 
.109 
.0865 

.248 
.156 
.0979 

i.  80 
143 

'•13 

33 

34 
35 

.ISO 
.160 
•143 

.0254 
.O20I 
.Ol6o 

i  no. 
1400. 

1770. 

.0686 

•0544 
.0431 

.0616 
.0387 
.0-44 

0.899 
•712 
•565 

36 

.127 

.0127                2230. 

•0342 

•°T53 

448 

•TI3 

.0100           2820. 

.0271 

.00903 

•355 

38 

.101 

.0080 

355°- 

.0215 

.00606 

.2    2 

39 
40 

.090 
.080 

.0063 
.0050 

4480. 
5640. 

. 

.0171 

. 

.00381 
.002  40 

— 

.223 
•  177 

^•^•"•i^"""* 

SMITHSONIAN   TABLES. 


344  TABLES  414-415. 

TABLE  414.  —  Ratio  of  Alternating  to  Direct  Current  Resistances  for  Copper  Wires. 

This  table  gives  the  ratio  of  the  resistance  of  straight  copper  wires  with  alternating  currents  of  different  frequencies 
to  the  value  of  the  resistance  with  direct  currents. 


Diameter  of 

Frequency/  = 

wire  in 

millimeters. 

00 

100 

IOOO 

10,000 

100,000 

1,000,000 

0.05 

_ 

_ 

_ 

_ 

*I.OOI 

O.I 

— 

— 

— 

— 

*    .001 

1.008 

0.25 

— 

— 

— 

— 

.003 

1.247 

o-S 

— 

— 

— 

*    .001 

.047 

2.240 

I.O 

— 

— 

— 

.008 

.503 

4.19 

2.O 

— 

— 

.001 

.120 

.756 

8.10 

3- 

— 

— 

.006 

•  437 

4.00 

12.0 

4- 

— 

— 

.021 

.842 

5.24 

17.4 

5- 

— 

*    .001 

.047 

.  240 

6.49 

19.7 

7-5 

.001 

.002 

.210 

3-22 

7.50 

29.7 

10. 

.003 

.008 

.503 

4.IQ 

12.7 

39-1 

IS- 

.016 

.038 

.136 

6.14 

18.8 

20. 

.044 

.120 

.756 

8.10 

25.2 

—  . 

25- 

•  105 

.247 

3.38 

10.  I 

28.3 

— 

40. 

•474 

.842 

5.24 

17.4 

— 

100. 

3-31 

4.19 

13.7 

39-i 

Values  between  i.oop  and  i.ooi  are  indicated  by  *i.poi. 

The  values  are  for  wires  having  an  assumed  conductivity  of  1.60  microhm-cms;  for  copper  wires  at  room  tempera- 
tures the  values  are  slightly  less  than  as  given  in  table. 

The  change  of  resistance  of  wire_other  than  copper  (iron  wires  excepted)  may  be  calculated  from  the  above  table 
by  taking  it  as  proportional  to  d^///p  where  d  —  diameter,/  the  frequency  and  p  the  resistivity. 

If  a  given  wire  be  wound  into  a  solenoid,  its  resistance,  at  a  given  frequency,  will  be  greater  than  the  values  in  the 
table,  which  apply  to  straight  wires  only.  The  resistance  in  this  case  is  a  complicated  function  of  the  pitch  and  radius 
of  the  winding,  the  frequency,  and  the  diameter  of  the  wire,  and  is  found  by  experiment  to  be  sometimes  as  much  as 
twice  the  value  for  a  straight  wire. 


TABLE  415.  — Maximum  Diameter  of  Wires  for   High-frequency  Alternating-to-direct-current 

Resistance  Ratio  of  1.01. 


Frequency  -f-  io6.  .  .  . 

O.I 

O.2 

0-4 

0.6 

0.8 

I.O 

1.2 

1-5 

2.0 

3-0 

Wave-length,  meters 

3000 

I5OO 

750 

500 

375 

300 

250 

200 

150 

IOO 

Material. 

Diameter  in  centimeters. 

Copper 

o  006 

bilver  

.0345 

o  C)o8o 

Gold 

Platinum  

.1120 

0.0793 

0.0560 

0.0457 

0.0396 

0-0354 

0.0323 

0.0290 

.0250 

0.0205 

Mercury  

.264 

0.187 

0.132 

.1080 

0.0936 

0.0836 

0.0763 

0.0683 

.0591 

0.0483 

Manganin  
Constantan  
German  silver  

.1784 
.1892 
1942 

0.1261 
0.1337 
0.1372 

0.0892 
0.0946 
0.0970 

.0729 
.0772 
.0792 

.0631 
.0664 
.0692 

0.0564 
0598 

.0515 
.0546 
.0560 

0.0488 
0.0500 

•  0399 
•  0423 
•  0434 

0.0325 

0.0345 
0.0354 

Graphite  

765 

0-541 

0.383 

312 

.271 

242 

221 

0.197 

•  171 

0.140 

Carbon 

60 

o  801 

t-66 

r06 

,c« 

Iron  n  *=  1000  

.     y 

00263 

0.00186 

0.00131 

00108 

0.00094 

0.00083 

0.00076 

0.  00p68 

0.00059 

0.00048 

/x  =  500  

00373 

0.00264 

0.00187 

00152 

0.00132 

o.  00118 

O.OOIOS 

0.00096 

o  .  00084 

0.00068 

p.  =  loo  

00838 

0.00590 

0.00418 

00340 

0.00295 

0.00264 

O.O024I 

0.00215 

0.00186 

0.00152 

Bureau  of  Standards  Circular  74,  Radio  Instruments  and  Measurements,  1918. 
SMITHSONIAN  TABLES. 


TABLE  416. 
ELECTROCHEMICAL   EQUIVALENTS- 


345 


Every  gram-ion  involved  in  an  electrolytic  change  requires  the  same  number  of  coulombs  or  ampere-hours  of  elec- 
tricity per  unit  change  of  valency.  This  constant  is  96.404  coulombs  or  26.804  ampere-hours  per  gram-hour  (a  Fara- 
day) corresponding  to  an  electrochemical  equivalent  for  silver  of  o.ooi  11800  gram  sec"1  amp"1.  It  is  to  be  noted  that 
the  change  of  valence  of  the  element  from  its  state  before  to  that  after  the  electrolytic  action  should  be  considered. 
The  valence  of  a  free,  uncombined  element  is  to  be  considered  as  o.  The  same  current  will  electrolyze  "chemically 
equivalent"  quantities  per  unit  time.  The  valence  is  then  included  in  the  "chemically  equivalent"  quantity.  The  fol- 
lowing table  is  based  on  the  atomic  weights  of  1917. 


Element. 

II 

CJ  > 

Mg 

coulomb. 

Coulombs 
per 
mg 

Grams 
per  amp.- 
hour. 

Element. 

Change  of  1  1 
valency.  | 

Mg 
per 
coulomb. 

Coulombs 
per 
mg 

Grams 
per  amp.- 
hour. 

10  682 

Nickel  

o  6081 

Chlorine.    .    . 
Copper  .'.      '.'. 

I 
3 
5 
7 

.'3675 
.1225 
•0735 
.0525 
.6588 
.3294 

2.721 
8.164 
13.606 
19-05 
1.518 
3.036 

1.3229 
0.4410 
o  .  2646 
0.1890 
2.3717 
i  1858 

Oxygen  .    . 
Platinum  . 

2 
3 

2 

4 
2 

0.3041 
0.2027 
0.08291 
0.04145 
1.0115 
o  5057 

3.289 
4-933 
12.062 
24.123 
0.0887 

.0946 
.7208 
2085 
.1492 
.641 
821 

Gold  

.044 

0.4893 

7-357 

it 

6 

0.3372 

2.966 

214 

Hydrogen  
Lead  

.6812 
.010459 

•  *473 

1.468 
5-728 
o.  4657 

2.452 
0.037607 
7  .  7302 

Potassium  .    . 
Silver  
Sodium  

I 
i 

0.4052 
1.1180 
o  .  2384 

2.468 
0.89445 
4  195 

-459 
.0248 
8581 

07  }6 

o  9314 

3  8651 

Tin 

2 

o  6151 

I   626 

u 

.5368 

1.8628 

I  .9326 

4 

0.3075 

3.252 

.  IO7 

Mercury  

.0789 
•  0394 

0.4810 
0.9620 

7.484 
3-742 

Zinc  

2 

0.3387 

2-952 

.2IQ4 

The  electrochemical  equivalent  for  silver  is  p.ooi  11800  g  sec"1  amp"1.     (See  p.  xxxvii.) 

For  other  elements  the  electrochemical  equivalent  =  (atomic  weight  divided  by  change  oi  valency)  times  1/96494 
g/sec/amp.  or  g/coulomb.    The  equivalent  for  iodine  has  been  determined  at  the  Bureau  of  Standards  as  0.0013150 

For  a  unit  change  of  valency  for  the  diatomic  gases  Brs,  Cb,  Fz,  Hj,  Nz  and  Oz  there  are  required 
8.619  coulombs/cm3  o°  C,  76  cm  (0.1160  cm3/coulomb) 
2.394  ampere-hours//,  o°  C,  76  cm  (0.4177  //ampere-hour). 

NOTE.  —  The  change  of  valency  for  Oa  is  usually  2,  etc. 
SMITHSONIAN  TABLES. 


346  TABLES  417,  418. 

CONDUCTIVITY   OF    ELECTROLYTIC 'SOLUTIONS. 

This  subject  has  occupied  the  attention  of  a  considerable  number  of  eminent  workers  in 
molecular  physics,  and  a  few  results  are  here  tabulated.  It  has  seemed  better  to  confine  the 
examples  to  the  work  of  one  experimenter,  and  the  tables  are  quoted  from  a  paper  by  F.  Kohl- 
rausch,*  who  has  been  one  of  the  most  reliable  and  successful  workers  in  this  field. 

The  study  of  electrolytic  conductivity,  especially  in  the  case  of  very  dilute  solutions,  has  fur- 
nished material  for  generalizations,  which  may  to  some  extent  help  in  the  formation  of  a  sound 
theory  of  the  mechanism  of  such  conduction.  If  the  solutions  are  made  such  that  per  unit 
volume  of  the  solvent  medium  there  are  contained  amounts  of  the  salt  proportional  to  its  electro- 
chemical equivalent,  some  simple  relations  become  apparent.  The  solutions  used  by  Kohlrausch 
were  therefore  made  by  taking  numbers  of  grams  of  the  pure  salts  proportional  to  their  elec- 
trochemical equivalent,  and  using  a  liter  of  water  as  the  standard  of  quantity  of  the  solvent.  Tak- 
ing the  electrochemical  equivalent  number  as  the  chemical  equivalent  or  atomic  weight  divided 
by  the  valence,  and  using  this  number  of  grams  to  the  liter  of  water,  we  get  what  is  called 
the  normal  or  gram  molecule  per  liter  solution.  In  the  table,  m  is  'used  to  represent  the 
number  of  gram^ molecules  to  the  liter  of  water  in  the  solution  for  which  the  conductivities 
are  tabulated.  The  conductivities  were  obtained  by  measuring  the  resistance  of  a  cell  filled  with 
the  solution  by  means  of  a  Wheatstone  bridge  alternating  current  and  telephone  arrangement. 
The  results  are  for  18°  C.,  and  relative  to  mercury  at  o°  C.,  the  cell  having  been  standardized  by 
filling  with  mercury  and  measuring  the  resistance.  They  are  supposed  to  be  accurate  to  within 
one  per  cent  of  the  true  value. 

The  tabular  numbers  were  obtained  from  the  measurements  in  the  following  manner  :  — 

Let  KI 8  =  conductivity  of  the  solution  at  18°  C.  relative  to  mercury  at  o°  C. 

A78  =  conductivity  of  the  solvent  water  at  18°  C.  relative  to  mercury  at  o°  C. 

Then  K^ — J£™^  =  k1(t  =  conductivity  of  the  electrolyte  in  the  solution  measured. 

-±±  =  ^  =  conductivity  of  the  electrolyte  in  the  solution  per  molecule,  or  the  "  specific 

0V 

molecular  conductivity." 

TABLE  417.  —Value  of  A-IH  for  a  few  Electrolytes. 

This  short  table  illustrates  the  apparent  law  that  the  conductivity  in  very  dilute  solutions  is  proportional  to  the 

amount  of  salt  dissolved. 


«l 

KC1 

NaCl 

AgN03 

KC2H302 

K2S04 

MgS04 

0.0000  1 

1.2*6 

I.O24 

1.080 

0-939 

T-275 

1.056 

O.OOOO2 

2.434 

2.056 

2.146 

1.886 

2-532 

2.104 

0.00006 

7.272 

6.162 

6.462 

5.610 

7-524 

6.216 

O.OOOI 

12.09 

10.29 

10.78 

9-34 

12.49 

10.34 

TABLE  418.  —Electro-Chemical  Equivalents  and  Normal  Solutions. 

The  following  table  of  the  electro-chemical  equivalent  numbers  and  the  densities  of  approximately  normal  solutions 
of  the  salts  quoted  in  Table  419  may  be  convenient.  They  represent  grams  per  cubic  centimeter  of  the  solution 
at  the  temperature  given. 


Salt  dissolved. 

Grams 
per  liter. 

m 

Temp. 
C. 

Density. 

Salt  dissolved. 

Grams 
per  liter. 

m 

Temp. 

Density. 

KC1    . 

74-59 

I.O 

15.2 

1-0457 

£K2S04 

87.16 

I.O 

18.9 

1.0658 

NH4C1    .     . 
NaCl  .     .     . 

53-55 
58.50 

I.OOO9 
I.O 

18.6 
18.4 

1.0152 
.0391 

|Li2SO4     . 

71.09 
55-09 

I.OOO3 
1.0007 

18.6 
18.6 

1.  0602 
1.0445 

LiCl    .     .     . 

42.48 

I.O 

18.4 

.0227 

|MgSO4    . 

60.17 

1.0023 

18.6 

1-0573 

iBaCl2    .     . 

104.0 

I.O 

1  8.6 

.0888 

^ZnSO4 

80.58 

I.O 

5-3 

1.0794 

|ZnCl2    .     . 
KI.     .     .     . 

68.0 
165.9 

I.OI2 
I.O 

15.0 
1  8.6 

.0592 
.1183 

£CuS04     . 

79-9 
69.17 

I.OOI 

1.  0006 

18.3 

1.0776 
1.0576 

KNO8     .     . 

101.17 

I.O 

1  8.6 

.0001 

^NagCOs  . 

53-04 

I.O 

17.9 

1.0517 

NaNO8    .     . 

85.08 

I.O 

18.7 

1.0542 

KOH    .     . 

56.27 

1.0025 

1  8.8 

1.0477 

AgNO8    .     . 

169.9 
65.28 

I.O 

HC1       .     . 
HN08  .     . 

36-51 
63-13 

1.0041 
1.0014 

18.6 
18.6 

I.Ol6l 

1.0318 

KCTOj, 

61.29 

°-5 

18.3 

1.0367 

iH2S04     . 

49.06 

1.  0006 

18.9 

1.0300 

KC2H8O2     . 

98.18 

1.0005 

1  8.6 

1  .0467 

SMITHSONIAN  TABLE*. 


*  "  Wied.  Ann."  vol.  26,  pp.  161-226,  1885. 


TABLE  419. 


347 


SPECIFIC    MOLECULAR    CONDUCTIVITY  /x  :   MERCURY  =  1O8. 


Salt  dissolved. 

w  —  10 

5 

3 

I 

0.5 

O.I 

.05 

.03 

.01 

£K2S04   .        . 

_ 

_ 

_ 

_ 

672 

736 

897 

959 

1098 

KC1 

— 

— 

827              919 

958 

1047 

1083 

1107 

"47 

KI  .          ... 

— 

7/0 

900             968 

997 

1069 

IIO2 

1123 

1161 

NH4C1     . 

- 

752 

825 

907 

948 

1035 

1078 

IIOI 

1142 

KNO3      . 

— 

— 

572 

752 

839 

983 

1037 

1067 

1122 

|BaCl2     . 

- 

- 

487 

658 

725 

86  1 

904 

939 

IOO6 

KC1O3     . 

— 

— 

— 

— 

799 

927 

(976) 

1006 

I053 

^BaN2Oe 

— 

— 

— 

— 

531 

755 

828 

(870) 

951 

|CuS04  . 
AgN08    .        .        . 

- 

35i 

150 
448 

24I 
635 

288 
728 

424 
886 

479 
936 

(966! 

675 
1017 

±ZnSO4   . 

- 

82 

I46 

249 

302 

43  i 

500 

51:6 

685 

j;MgS04  . 

- 

82 

270 

330 

474 

532 

587 

715 

vNa2SO4          .         . 

-     i      - 

— 

475 

559 

734 

784 

828 

906 

NaCl2     !        .'        ! 

60 

180 
398 

280 
528 

$ 

757 

865 

817 
897 

(920) 

9'5 
962 

NaNO3    . 
KC2H302 

3° 

240 

381 

617 
594 

694 
671 

817 

784 

855 
820 

841 

879 

I     |Na2C03 

660 

1270 

2|4 
1560 

427 
1820 

1899 

682 
2084 

2343 

799 

2515 

899 
2855 

C2H4O     . 

o-5 

2.6 

5-2 

12 

19 

43 

62 

79 

132 

HC1         ... 

600 

1420 

2010 

2780 

3OI7 

3244 

3330 

3369 

34i6 

HNO3      . 

610 

1470 

2O7O 

2770 

2991 

3225 

3289 

3328 

3395 

1H3P04  .        .        . 
KOH       . 

148 
423 

160 
990 

170 

2OO 
I7l8 

250 
1841 

43° 
1986 

540 
2045 

620 
2078 

790 
2124 

NH3 

2.4 

3-3 

8.4 

12 

31 

43 

50 

92 

Salt  dissolved. 

.006 

.002 

.001 

.0006 

.0002 

.0001 

.00006 

.00002 

.00001 

iK2S04  . 

1130 

n8r 

1207 

1220 

1241 

1249 

1254 

1266 

1275 

KC1          ".        .        '. 

1162 

1185 

"93 

"99 

1209 

1209 

1212 

I2I7 

1216 

KI   . 

1176 

"97 

1203 

1209 

1214 

1216 

1216 

1216 

1207 

NH4C1     . 

"57 

1180 

1190 

"97 

I2O4 

I2O9 

1215 

1209 

1205 

KN03      . 

1140 

"73 

1180 

1190 

"99 

I2O7 

I22O 

1198 

1215 

|BaCl2     . 

1031 

1074 

1092 

IIO2 

1118 

1126 

"33 

"44 

1142 

KClOg     . 

1068 

1091 

IIOI 

IIO9 

1119 

1122 

1126 

"35 

1141 

^BaN2O« 

982 

1033 

1054 

1066 

1084 

1096 

IIOO 

1114 

1114 

|CuS04  . 

740 

873 

95° 

987 

1039 

1062 

1074 

1084 

1086 

AgN03    . 

I033 

1068 

1069 

1077 

1078 

1077 

1073 

1080 

!£nSO4 

744 

861 

919 

953 

IOOI 

1023 

1032 

1047 

1060 

^IgSO4  . 

773 

88  1 

935 

967 

1015 

1034 

1036 

1052 

1056 

^a2SO4 

933 

980 

998 

1009 

1026 

1034 

1038 

1056 

1054 

aCl2     '. 

939 
976 

979 
998 

994 
1008 

1004 
1014 

1020 

1018 

IO29 
1029 

1031 
1027 

1033 
1028 

1036 
1024 

NaN03    . 

921 

942 

952 

956 

966 

975 

970 

972 

975 

KC2H3O2 

891 

913 

919 

923 

933 

934 

935 

943 

*Na2CO3 

956 

1010 

1037 

1046 

988 

874 

790 

715 

697* 

|H2S04  . 

3001 

3240 

3316 

3342 

3280 

3"8 

2927 

2077 

M'3* 

C2H40     . 

170 

283 

380 

470 

796 

995 

"33 

1304* 

HC1 

3438 

3455 

3455 

3440 

3340 

3i7o 

2968 

2057 

1254* 

HN03      . 

342i 
858 

3448 
945 

968 

3408 
977 

3285 
920 

3088 
837 

2863 
746 

1904 
497 

"44* 
402* 

ko8H  4  .'      .'      ! 

2141 

2140 

2110 

2074 

1892 

1689 

M74 

845 

747* 

NH3 

116 

190 

260 

330 

500 

610 

690 

700 

560* 

*  Acids  and  alkaline  salts  show  peculiar  irregularities. 


SMITHSONIAN  TABLES. 


34-8  TABLES  420,  421. 

LIMITING  VALUES  OF  JJL.    TEMPERATURE  COEFFICIENTS. 

TABLE  420.-  Limiting  Values  of  p. 
This  table  shows  limiting  values  of  /*  =:  —  .10*  for  infinite  dilution  for  neutral  salts,  calculated  from  Table  271. 


Salt. 

P 

Salt. 

pi 

Salt. 

M 

Salt. 

M 

iK2S04     . 

1280 

|BaCl2      . 

1150 

iMgS04    . 

1080 

iH2S04     . 

3700 

KC1  .    .    . 

1220 

iKClO8     . 

1150 

iNa2SO4  . 

1060 

HC1      .    . 

3500 

KI    .    .    . 

I22O 

£BaN206  . 

1  1  20 

iZnCl    .     . 

1040 

HNO3  .     . 

35°° 

NH4C1  .    . 

I2IO 

iCuSO4     . 

IIOO 

NaCl     .     . 

1030 

£H3P04    . 

IIOO 

KN08  .     . 

I2IO 

AgNO3     . 

1090 

NaN08      . 

980 

KOH   ,    . 

2200 

- 

- 

iZnSO4     . 

1080 

K2C2H8O2 

940 

iNa2CO8  . 

I4OO 

If  the  quantities  in  Table  420  be  represented  by  curves,  it  appears  that  the  values  of  the 
specific  molecular  conductivities  tend  toward  a  limiting  value  as  the  solution  is  made 
more  and  more  dilute.  Although  these  values  are  of  the  same  order  of  magnitude,  they 
are  not  equal,  but  depend  on  the  nature  of  both  the  ions  forming  the  electrolyte. 

When  the  numbers  in  Table  421  are  multiplied  by  Hittorf's  constant,  or  o.oooii,  quan- 
tities ranging  between  0.14  and  o.io  are  obtained  which  represent  the  velocities  in  milli- 
metres per  second  of  the  ions  when  the  electromotive  force  gradient  is  one  volt  per 
millimetre. 

Specific  molecular  conductivities  in  general  become  less  as  the  concentration  is  in- 
creased, which  may  be  due  to  mutual  interference.  The  decrease  is  not  the  same  for 
different  salts,  but  becomes  much  more  rapid  in  salts  of  high  valence. 

Salts  having  acid  or  alkaline  reactions  show  marked  differences.  They  have  small 
specific  molecular  conductivity  in  very  dilute  solutions,  but  as  the  concentration  is  in- 
creased the  conductivity  rises,  reaches  a  maximum  and  again  falls  off.  Kohlrausch  does 
not  believe  that  this  can  be  explained  by  impurities.  H3PO4  in  dilute  solution  seems  to 
approach  a  monobasic  acid,  while  H2SO4  shows  two  maxima,  and  like  HsPO4  approaches 
in  very  weak  solution  to  a  monobasic  acid. 

Kohlrausch  concludes  that  the  law  of  independent  migration  of  the  ions  in  media  like 
water  is  sustained. 


TABLE  421. -Temperature  Coefficients. 

The  temperature  coefficient  in  general  diminishes  with  dilution,  and  for  very  dilute  solutions  appears  to  approach  a 
common  value.  The  following  table  gives  the  temperature  coefficient  for  solutions  containing  o.oi  gram  mole- 
cule of  the  salt. 


Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

KC1  .     .     . 

O.O22I 

KI     .    .    . 

0.0219 

iK2S04      . 

0.0223 

1K2C08     .     . 

0.0249 

NH4C1  .     . 
NaCl     .    . 
LiCl.    .    . 
*BaCl2  .    . 
|ZnCl2  .     . 
*MgCl2      . 

0.0226 
0.0238 
0.0232 
0.0234 
0.0239 
O.O24I 

KN08   .    . 
NaNO8  .     . 
AgN08.     . 
|Ba(NOa)2 
KC1O3  .     . 
KC2H8O2  . 

0.0216 

0.0226 
0.0221 
0.0224 
O.O2I9 
0.0229 

!Na2S04    . 
iLi2S04     . 
iMgS04     . 
IZnSOs      • 
iCuS04     . 

0.0240 
0.0242 
0.0236 
0.0234 
0.0229 

4Na2CO3  .     . 

0.0265 

KOH    .     , 
HC1       .     .    . 
HNO8  .    .     . 
*H2S04     .    . 

0.0194 
0.0159 
0.0162 
0.0125 

*H2S04          ) 
for  m  =  .001  f 

0.0159 

SMITHSONIAN  TABLES. 


TABLE  422, 


349 


THE    EQUIVALENT     CONDUCTIVITY     OF    SALTS,    ACIDS  AND    BASES     IN 

AQUEOUS  SOLUTIONS. 

In  the  following  table  the  equivalent  conductance  is  expressed  in  reciprocal  ohms.  The  con- 
centration is  expressed  in  milli-equivalents  of  solute  per  litre  of  solution  at  the  temperature  to  which 
the  conductance  refers.  (In  the  cases  of  potassium  hydrogen  sulphate  and  phosphoric  acid  the 
concentration  is  expressed  in  milli-formula-weights  of  solute,  KHS(  )4  or  I  I:!l'(  )4,  per  liter  of  solu- 
tion, and  the  values  are  correspondingly  the  modal,  or  "formal,"  conductances.)  Except  in  the 
cases  of  the  strong  acids  the  conductance  of  the  water  was  subtracted,  and  for  sodium  acetate, 
ammonium  acetate  and  ammonium  chloride  the  values  have  been  corrected  for  the  hydrolysis  of 
the  salts.  The  atomic  weights  used  were  those  of  the  International  Commission  for  1905,  referred 
to  oxygen  as  16.00.  Temperatures  are  on  the  hydrogen  gas  scale. 

Concentration  in  gram  equivalents, 
looo  liter 

reciprocal  ohms  per  centimeter  cube 

Equivalent  conductance  in  —         — : — ;  — 

gram  equivalents  per  cubic  centimeter 


Substance. 

Concen-  1 
tration.  1 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

218° 

281° 

306° 

Potassium  chloride  . 

0 

130.1 

(152.1) 

(232.5) 

(321-5) 

414 

(519) 

625 

825 

1005 

1  1  20 

«                <« 

2 

126.3 

146.4 

393 

— 

588 

779 

930 

I008 

«                « 

10 

122.4 

141-5 

215.2 

295.2 

377 

470 

560 

741 

874 

9IO 

(4                               <( 

80 

"3-5 

342 

— 

498 

638 

723 

720 

((                               «( 

IOO 

II2.O 

129.0 

194-5 

264.6 

336 

415 

490 

Sodium  chloride  .     . 

0 

109.0 

- 

- 

362 

555 

760 

970 

I080 

"             " 

2 

105.6 

— 

- 

— 

349 

— 

534 

722 

895 

955 

"             " 

IO 

102.0 

_ 

— 

— 

336 

— 

511 

685 

820 

860 

"             "        .    . 

80 

935 

- 

- 

- 

301 

- 

450 

500 

674 

680 

"             " 

IOO 

92.0 

- 

— 

— 

296 

— 

442 

Silver  nitrate  .     .     . 

0 

115.8 

- 

- 

- 

367 

- 

570 

780 

965 

1065 

"          "        ... 

2 

II2.2 

— 

- 

- 

353 

- 

539 

727 

877 

935 

«          «< 

IO 

108.0 

_ 

.  — 

— 

337 

— 

5°7 

673 

790 

818 

«          « 

2O 

I05.I 

_ 

_ 

- 

326 

- 

488 

639 

«          «< 

40 

IOI-3 

_ 

_ 

— 

312 

— 

462 

599 

680 

680 

«          « 

80 

96.5 

_ 

- 

- 

294 

- 

432 

552 

614 

604 

"          " 

IOO 

94.6 

_ 

— 

— 

289 

Sodium  acetate    .     . 

0 

78.1 

- 

- 

- 

285 

450 

660 

- 

024 

«             u 

2 

74-5 

— 

— 

— 

268 

421 

578 

— 

801 

a            a 

10 

71.2 

— 

— 

— 

253 

396 

542 

— 

702 

Magnesium  sulphate 

80 
O 

63-4 
114.1 

„ 

_ 

_ 

221 

426 

- 

340 
690 

1080 

^_ 

«                 « 

2 

94-3 

- 

— 

- 

302 

— 

377 

260 

««                 «« 

10 

76.1 

— 

— 

- 

234 

— 

241 

'43 

U                                 « 

20 

67.5 

— 

- 

— 

190 

— 

195 

no 

"                 " 

40 

59-3 

- 

- 

- 

160 

- 

158 

88 

"                 " 

80 

52.0  !     - 

- 

- 

136 

- 

'33 

75 

"                    " 

IOO 

49.8 

— 

- 

'3° 

- 

126 

Ammonium  chloride 

2OO 
0 

152.0 

_ 

_ 

no 

(415) 

_ 

(fe§) 

(841) 

_ 

(1176) 

2 

126.5 

146.5 

- 

- 

399 

- 

601 

801 

— 

1031 

<4                                    «           \               I0 

122.5 

T  T  Q     r 

141.7 

- 

— 

382 

~ 

573 

758 

"™ 

92? 
828 

Ammonium  acetate  . 

i     3° 
o 

II5.I 

(99.8) 

_ 

- 

- 

(338) 

- 

(523) 

"                " 

10 

9T.7 

— 

— 

- 

300 

— 

456 

-   . 

25 

88.2 

286 

426 

From  the  investigations  of  Noyes,  Melcher,  Cooper,  Eastman  and  Kato;  Journal  of  the  American  Chemical  Society, 

30,  p.  335.  1908- 
SMITHSONIAN  TABLES. 


35°  TABLE 

THE    EQUIVALENT    CONDUCTIVITY    OF    SALTS,     ACIDS    AND    BASES    IN 

AQUEOUS    SOLUTIONS. 


Substance. 

C   c 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

218° 

281° 

306° 

Barium  nitrate  .    .     . 

O 

116.9 

_ 

— 

_ 

385 

_ 

600 

840 

II2O 

1300 

tt        .  tt 

2 

109.7 

- 

— 

— 

352 

— 

536 

7i5 

828 

824 

"           "... 

10 

IOI.O 

— 

— 

— 

322 

— 

481 

618 

658 

615 

tt           it 

40 

88.7 

- 

_ 

- 

280 

- 

412 

5°7 

5°3 

448 

"           "... 

80 

81.6 

- 

- 

- 

258 

- 

372 

449 

430 

it           it 

IOO 

79.1 

— 

— 

— 

249 

Potassium  sulphate  . 

0 

132-8 

- 

- 

- 

455 

- 

715 

1065 

1460 

1725 

" 

2 

124.8 

- 

— 

— 

402 

- 

605 

806 

893 

867 

"                "     .     . 

IO 

115.7 

- 

- 

- 

365 

- 

537 

672 

687 

637 

ii                it 

104.2 

- 

- 

- 

455 

545 

.6- 

A  A% 

466 

tr>f\ 

ft                it 

80 
so 

IOO 

97-2 
95-o 

_ 

.  _ 

_ 

286 

4*5 

402 

440 

39° 

Hydrochloric  acid     . 

o 

379-o 

- 

- 

- 

850!     - 

1085 

1265 

1380 

1424 

"               "  .     . 

2 

373-6 

— 

— 

— 

826       -       1048 

I2I7 

X332 

'337 

"              " 

IO 

368.1 

_ 

_ 

— 

807 

-       1016 

1168 

1226 

1162 

"               "  .     . 

80 

353-o 

- 

- 

- 

762 

- 

946 

1044 

1046 

862 

ii               ii 

IOO 

35°-6 

— 

_ 

— 

754 

_ 

929 

1006 

Nitric  acid    ....        o 

377-o 

421.0    570     706 

826 

945  !  1047  (1230) 

- 

(1380) 

"      .     .     .     .        2 

371-2 

413.7      559       690     806 

919     1012    1166 

— 

1156 

"         ....         10 

406.0     548 

676       786 

893       978 

"        "      •     •    •    •      5° 

353-7 

393-3     528 

649       750 

845 

917 

"        ....      IOO 

346.4 

385.0     516 

632 

728 

817 

880 

— 

— 

454* 

Sulphuric  acid  ...        o 

383-0 

(429)     (590 

(746) 

891  (1041) 

1176 

1505 

- 

(2030) 

"...           2 

353-9 

390.8     501 

561 

571     551 

536 

563 

— 

637 

"...         10 

309.0 

337.0     406      435 

446  j  460 

481 

533 

"...         50 

253-5 

273-0     323      356 

384  i  417 

448 

502 

'      .      .      .      IOO 

233-3 

251.2     300      336 

369 

404 

435 

483 

- 

474* 

(             2 

Potassium  hydrogen  \ 
sulphate    ...},£ 

Phosphoric  acid    .     .  i      o 

455-3 
295-5 
263.7 

338.3 

506.0 
318.3 
283.1 
376 

661.0     754 
374.4     403 

329-1     354 
510      631 

784 
422 

375 
73° 

773 
446 
402 

754 
477 
435 
93° 

"          •    " 

2 

283.1 

3TI-9 

401       464 

498 

508 

489 

"             " 

'   10 

203.0 

222.0 

273    ;   3°° 

308 

298 

2/4 

"             "       .     . 

50 

I  2  °  7 

132.6 

157.8  \  1  68.6 

168 

158 

142 

ti                           « 

IOO 

96-5 

104.0   122.7  !  129.9 

128  I     120 

108 

Acetic  acid  .... 

0 

(347-0) 

- 

- 

(773)!     - 

(980) 

("65) 

- 

(1268) 

"         " 

IO 

14.50 

— 

- 

— 

25-1       - 

22.2 

14.7 

if         it 

3° 

8.50 

— 

— 

— 

14.7  1     - 

13.0 

8-65 

tt         (i 

80 

5.22 

— 

_ 

— 

9-°5      ~ 

8.00 

5-34 

it         ii 

IOO 

4-67 

_ 

_ 

_ 

8.10!     - 

4.82       - 

1.57 

Sodium  hydroxide     . 

0 

.,   ' 

216.5 

- 

- 

594       -        835 

1060 

"                 ' 

2 

212.  1 

— 

- 

— 

814 

.      .  1      20 

205.8 

- 

559 

771      930 

it                       i 

Barium  hydroxide 

50 
0 

200.6 
222 

256      389 

-       540       -        738      873 
(520)    645    (760)     847 

'     .     .     .        2 

215 

359 

4 

591 

'       ...  j      10 

207 

235        342 

449 

548     664      722 

'     .     .     .      50 

Igl.I 

215.1     308 

399 

478 

549  i    593 

"...      IOO 

iSo.I 

204.2      291        373      443 

503  i    53i 

f       o 
Ammonium  hydrox-j       10 

(238) 
9-66 

(271) 

(404) 

(526)  (647) 
-       23.2 

(764) 

(908) 
22.3 

(1141) 
15.6 

— 

(1406) 

ide                  .     .    1 

IO 

c  66 

mm 

17  6 

IOO 

3.io 

3-62     5-35      6.70, 

1  j.U 

7-47 

- 

7.17 

4.82 

- 

i-33 

*  These  values  are  at  the  concentration  80.0. 


SMITHSONIAN  TABLES. 


TABLE  423. 


351 

THE     EQUIVALENT     CONDUCTIVITY    OF     SOME     ADDITIONAL     SALTS     IN 

AQUEOUS  SOLUTION. 

Conditions  similar  to  those  of  the  preceding  table  except  that  the  atomic  weights  for  1908  were  used. 


Substance. 

Concen- 

Equivalent conductance  at  the  following  °  C  temperature. 

tration. 

0° 

18° 

*5° 

5°° 

75° 

100° 

.280 

i56P 

Potassium  nitrate  .     .     . 

0 

80.8 

126.3 

I45-1 

219 

299 

384 

485 

580 

. 

2 

78.6 

122.5 

140.7 

212.7 

289.9 

370.3 

460.7 

551 

Potassium  oxalate  .     .     . 

12.5 

5° 

IOO 
0 

75-3 
70.7 
67.2 
79-4 

II7.2 
109.7 
104.5 

134-9 
126.3 
120.3 
M7.5 

202.9 
189.5 
180.2 
230 

276.4 

257-4 
244.1 
322 

351.5 

326.1 

308.5 
419 

435-4 
402.9 

379-5 

520.4 
476.1 

447-3 
653 

.     .     . 

2 

74-9 

119.9 

139.2     215.9 

300.2 

389.3 

489.1 

587 

. 

I2.5 

69.3     1  1  1.  1 

129.2 

199.1 

275-1 

354.1 

438.8 

.     .     . 

50 

63 

101 

116.5 

178.6 

244.9 

312.2 

383-8 

449-5 

. 

IOO 

59-3 

94.6 

109.5 

167 

227.5 

288.9 

353-2 

4097 

Calcium  nitrate     .     .     . 

200 
O 

55-8 
70.4 

II2.7 

102.3 
130.6 

'55 

202 

210.9 
282 

265.1 

369 

321.9 
474 

372.1 

575 

.'     '.     ! 

2 
I2.5 

5° 

66.5 
61.6 
55-6 

I07.I 

H4.J 

IO2.6 

191.9 
176.2 
157.2 

266.7 

244 
216.2 

346.5 

314.6 
276.8 

438.4 
394-5 
343 

529.8 

473-7 
405.1 

. 

IOO 

51-9 

82.6 

95.8 

146.1 

199.9 

255-5 

3'S-i 

369-1 

Potassium  ferrocyanide  . 

2OO 
0 

48.3 
98.4 

76.7 
159.6 

88.8 
185-5 

2^'4 

184.7 
403 

234.4 
527 

288 

334-7 

it                                       if 

°"5 

91.6 

— 

171.1 

"                    " 

2. 

84.8 

137 

158.9 

243.8 

335.2 

427.6 

. 

I2-5 

71 

II3-4 

131.6 

2OO.3 

271 

340 

«                            a 

50 

58.2 

93-7 

108.6 

163.3 

219.5 

272.4 

. 

IOO 

53 

84.9 

98.4 

I48.I 

198.1 

245 

" 

200 

48.8 

77-8 

90.1 

'35-7 

180.6 

222.3 

. 

400 

45-4 

72.1 

83.3 

124.8 

1657 

203.1 

Barium  ferrocyanide  .     . 
Calcium  ferrocyanide     . 

O 
2 
I2.5 
O 

46.9 

150 

4^.8 
146 

176 
86.2 
56.5 
171 

277 
127.5 
83.1 
271 

393 
166.2 
107 
386 

521 

202.3 

129.8 
512 

"                 " 

2 

47.1 

75.5 

86.2 

130 

. 

I2-5 

31.2 

49-9 

57-4 

" 

24.1 

38.5 

44-4 

64.6 

81.9 

"    .*  ; 

IOO 
2OO 

21.0 

2O.6 

35-1 
32-9 

40.2 
37-8 

58.4 

55 

m 

84.3 

77-5 

u                          « 

4OO 

20.2 

32-2 

54 

67.5 

76.2 

Potassium  citrate  .     .     . 

0 

76.4 

124.6 

144-5 

228 

320 

420 

"       ... 

o-5 

— 

1  20.  i 

«               n 

2 

5 

67.6 

"5-4 
109.9 

134.5 
128.2 

2IO.I 
198.7 

293.8 
276.5 

381-2 
357-2 

"              "... 

I2-5 

62.9 

101.8 

118.7 

183.6 

254.2 

326 

"       ... 

50 

54-4 

87.8 

1  02.  i 

157-5 

215-5 

273 

"       ... 

IOO 

50.2 

80.8 

93-9 

143-7 

196.5 

247-5 

"               "... 

300 

43-5 

69.8 

I23-5 

167 

209.5 

Lanthanum  nitrate     .     . 

O 

122.7 

142.6 

223 

3*3 

534 

651 

"                "          .     . 

2 

68.9 

1  1  0.8 

128.9 

200.5 

279.8 

363-5 

549 

" 

I2-5 

61.4 

98.5 

114.4 

176.7 

243-4 

311.2 

353.4 

447-8 

"                " 

5° 

54 

86.1 

99-7 

'52-5 

207.6 

261.4 

3I5-8 

357-7 

«                       it 

IOO 

200 

49.9 
46 

79-4 
72.1 

91.8 
83-5 

139-5 
126.4 

189.1 

170.2 

236.7 

210.8 

282.5 
249.6 

316.3 
276.2 

From  the  investigations  of  Noyes  and  Johnston,  Journal  of  the  American  Chemical  Society,  31,  p.  287,  1909. 
SMITHSONIAN  TABLES. 


352  TABLES  424,  425. 

CONDUCTANCE  OF  IONS.  -  HYDROLYSIS  OF  AMMONIUM  ACETATE. 

TABLE   424.  -The  Equivalent  Conductance  of  the  Separate  Ions. 


Ion. 

0° 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

K.    . 

4O  4 

646 

74.  c 

lie 

I  CQ 

206 

263 

-117 

Na    

40.4 
26 

47.  c 

50.9 

82 

116 

155 

203 

249 

NH4      

40.  2 

64.  S 

74.  c 

115 

159 

207 

26^ 

319 

Ac 

-12  Q 

C4.-2 

03.5 

IOI 

143 

1  88 

24? 

299 

£Ba  .    .    . 

•77 

552 

65 

1  04 

149 

200 

767 

•122 

*Ca  

10 

Si' 

66 

08 

142 

191 

252 

312 

Jla  

TC 

61 

72 

119 

173 

2^C, 

312 

388 

Cl 

4I.I 

65.5 

7C.C, 

116 

160 

207 

264 

3l8 

NO8  

4O.4 

61.7 

70.6 

104 

140 

178 

222 

263 

C2H802     .... 
£SO4     

20.3 

41 

34-6 
682 

40.8 
70 

67 

I2C. 

96 

177 

I30 

274 

171 
7Q-? 

211 

77O 

*C204    
|C6H607    .... 
}Fe(CN)6  .... 

H 

39 
36 

58 

240 

632 
60 

95 

•?I4 

73 
70 
in 

•5  CQ 

»s 

"3 

i73 

465 

u 
'63 

161 

244 

565 

213 

214 

32I 

644 

275 
722 

336 

777 

OH  .    . 

IOC 

172 

102 

o"> 
204 

j^j 
760 

4-10 

C2C 

CQ2 

From  Johnson,  Journ.  Amer.  Chem.  Soc.,  31,  p.  1010,  1909. 


TABLE  425.  —Hydrolysis  of  Ammonium  Acetate  and  lonlzatlon  of  Water. 


Temperature. 

Percentage 
hydrolysis. 

lonization  constant 
of  water. 

Hydrogen-ion  concen- 
tration in  pure  water. 
Equivalents  per  liter. 

t 

I00h 

KwXio" 

CHXio' 

0 

- 

0.089 

0.30 

18 

(0-35) 

0.46 

0.68 

25 

- 

0.82 

0.91 

IOO 

4.8 

48. 

6.9 

156 

18.6 

223. 

14.9 

218 

52-7 

461. 

21.5 

306 

9i-5 

168. 

13.0 

Noyes,  Kato,  Kanolt,  Sosman,  No.  63  Publ.  Carnegie  Inst.,  Washington. 
SMITHSONIAN  TABLES. 


TABLES  426,  427.  353 

DIELECTRIC   STRENGTH. 

TABLE  426.  —  Steady  Potential  Difference  in  Volts  required  to  produce  a  Spark  In  Air  with  Ball  Electrodes. 


Spark 
length, 
cm. 

J?  =  o. 
Points. 

/e  =  o.25 

cm. 

/?  =  o.5 

cm. 

K=i  cm. 

R  =  2  cm. 

R  —  3  cm. 

*-«. 

Plates. 

O.O2 

_ 

_ 

1560 

1530 

0.04 

- 

- 

2460 

2430 

2340 

0.06 

- 

— 

33°° 

3240 

3060 

0.08 

— 

— 

4050 

3990 

3810 

O.I 
O.2 

3720 
4680 

5010 
8610 

4740 
8490 

4560 
8490 

4560 
8370 

4500 
7770 

4350 
7590 

o-3 

S310 

III4O 

11460 

11340 

III90 

10560 

10650 

0.4 
0.5 

0.6 

5970 
6300 
6840 

14040 

IS990 
17130 

14310 
16950 
19740 

14340 
17220 
20070 

14250 
16650 
20070 

13140 
16470 
19380 

16320 
I9IIO 

0.8 

8070 

18960 

23790 

24780 

25830 

26220 

24960 

I.O 

8670 

20670 

26190 

27810 

29850 

32760 

30840 

i-5 

9960 

22770 

29970 

37260 

2.0 

10140 

2t57° 

33060 

45480 

3-° 

11250 

28380 

4.0 

I22IO 

29580 

5.0 

13050 

Based  on  the  results  of  Bailie,  Bichat-Blondot,  Freyburg,  Liebig,  Macfarlane,  Orgler,  Paschen,  Quincke,  de  la  Rue, 
Wolff.  For  spark  lengths  from  i  to  200  wave-lengths  of  sodium  light,  see  Earhart,  Phys.  Rev.  15,  p.  163;  Hobbs, 
Phil.  Mag.  10,  p.  607,  1905. 


TABLE  427,  —  Alternating  Current  Potentials  required  to  produce  a  Spark  in  Air  with  various  Ball  Elec- 
trodes. 

The  potentials  given  are  the  maxima  of  the  alternating  waves  used.     Frequency,  33  cycles  per 

second. 


Spark  length. 
cm. 

K=i  cm. 

R  =  i  .92 

... 

.-« 

R  =10 

,-„ 

0.08 

3770 

.10 

4400 

4380 

433° 

4290 

4245 

4230 

•IS 

5990 

5940 

5790 

5800 

57»o 

.20 

7510 

7440 

734° 

7250 

7320 

733° 

•25 

9045 

8970 

8850 

8710 

8760 

8760 

0.30 

10480 

10400 

10270 

10130 

IOl8o 

10150 

•35 

11980 

11890 

11670 

11570 

Il6lO 

11590 

.40 

13360 

13300 

13100 

12930 

12980 

12970 

•45 

14770 

14700 

14400 

14290 

I433° 

14320 

•50 

16140 

16070 

15890 

15640 

15690 

15690 

0.6 

18700 

18730 

18550 

18300 

18350 

18400 

•7 

21  35° 

21380 

21140 

20980 

20990 

2IOOO 

.8 
0.9 

23820 
26190 

24070 
26640 

23740 
26400 

23490 
26130 

23540 
26110 

23550 
26090 

I.O 

28380 

29170 

28950 

28770 

28680 

28610 

1.2 
1.4 

32400 

34100 
38850 

33790 
38850 

38580 

33640 
38620 

33620 
3»580 

1.6 

38750 

43400 

43570 

43250 

43520 

1.8 

40900 

- 

48300 

47900 

2.0 

42950 

52400 

Based  upon  the  results  of  Kawalski,  Phil.  Mag.  18,  p.  699,  1909. 


SMITHSONIAN  TABLES. 


354  TABLES  428.  429. 

DIELECTRIC  STRENGTH. 

TABLE  428.  —Potential  Necessary  to  produce  a  Spark  In  Air  between  more  widely  Separated  Electrodes. 


§ 

I, 

Steady  potentials. 

§ 

t 

<  c 

i      Steady  potentials. 

§ 

«S 

Ball  electrodes. 

Cup  electrodes. 

.c 

to 

c 

(/.   3 

Ball  electrodes. 

JJ 

s  ° 

li 

^ 

if 

Projection. 

EL 

C/3 

2s 

R=i  cm. 

R-=2.scm. 

& 

3  c 

R.=  i  cm. 

R=2.scm. 

• 

4.5  mm. 

i.  5  mm. 

°-3 

_ 

_ 

_ 

_ 

II280 

6.0 

61000 

_ 

86830 

o-5 

_ 

17610 

17620 

- 

17420 

7.0 

- 

52000 

0.7 

- 

- 

23050 

- 

22950 

8.0 

67000 

52400 

9O2OO 

I.O 
1.2 

I2OOO 

30240 
33800 

31390 
36810 

31400 

31260 
36700 

IO.O 
12.0 

73000 
82600 

74300 

9!93° 
933oo 

!-5 

— 

37930 

443  10 

- 

445  10 

14.0 

92000 

— 

94400 

2.0 

292OO 

42320 

56000 

56500 

56530 

I5.0 

— 

— 

94700 

2-5 

3-o 

40000 

45000 
46710 

65180 
71200 

80400 

68720 
81140 

1  6.0 

2O.O 

IOIOOO 

119000 

~ 

IOIOOO 

3-5 

— 

753°° 

— 

92400 

25.0 

140600 

4.0 

48500 

49100 

78600 

IOI700 

103800 

30.0 

165700 

4-5 

— 

— 

81540 

— 

114600 

35-o 

190900 

S-o 

56500 

50310 

83800 

- 

126500 

5-5 

135700 

This  table  for  longer  spark  lengths  contains  the  results  of  Voege,  Ann.  der  Phys.  14,  1904,  using  alternating  current 
it"  electrodes,  and  the  results  with  steady  potential  found  in  the  recent  very  careful  work  of  C.  Miit- 


and  "dull  point 

ler,  Ann.  d.  Phys.  28,  p.  585,  1909. 


The  specially  constructed  elec- 
trodes lor  the  columns  headed 
"  cup  electrodes  "  had  the  form  of 
a  projecting  knob  3  cm.  in  diame- 
ter and  having  a  height  of  4.5  mm. 
and  1.5  mm.  respectively,  attached 
to  the  plane  face  of  the  electrodes. 
These  electrodes  give  a  very  satis- 
?en  the 
voltage 
iroughout  the  range  studied. 


<3cm.>       V  ihese  electrodes  give  a  very  s£ 
J  factory  linear  relation  between 
I  spark    lengths     and    the    volt 
'  throughout  the  range  studied. 


TABLE  429,  -  Effect  of  the  Pressure  of  the  Gas  on  the  Dielectric  Strength. 

Voltages  are  given  for  different  spark  lengths  /. 


Pressure, 
cm.  Hg. 

7=0.04 

/=o.o6 

7=o.o8 

7=0.10 

7=0.20 

l=o  30 

7=0.40 

7=0.50 

2 

_ 

_ 

_ 

_ 

744 

939 

IIIO 

1266 

4 

- 

483 

567 

648 

1015 

'35° 

1645 

J9i5 

6 

— 

582 

690 

795 

1290 

1740 

2140 

25°5 

10 

— 

771 

933 

1090 

1840 

245° 

3015 

358o 

15 

- 

IO6O 

1280 

1490 

2460 

3300 

4080 

4850 

25 

IIIO 

1420 

1725 

2040 

35°o 

4800 

6000 

7120 

35 
45 

1375 
1640 

1820 
2150 

222O 
2660 

2615 
3120 

45°5 
5475 

.6270 
7650 

7870 

9620 

9340 
11420 

55 

1820 

2420 

3025 

36*0 

6375 

8950 

11290 

'3455 

65 

2040 

2720 

3400 

4060 

7245 

I02IO 

12950 

15470 

75 

2255 

3035 

3805 

4565 

8200 

II570 

14650 

1745° 

This  table  is  based  upon  the  results  of  Orgler,  1899.  See  this  paper  for  work  on  other  gases  (or  Landolt-Bornstein- 
Meyerhoffer). 

For  long  spark  lengths  in  various  gases  see  Voege,  Electrotechn.  Z.  28,  1907.  For  dielectric  strength  of  air  and  CO2 
in  cylindrical  air  condensers,  see  Wien,  Ann.  d.  Phys.  29,  p.  679,  1909. 

SMITHSONIAN  TABLES, 


TABLES  430,  431. 
DIELECTRIC  STRENGTH. 

TABLE  430.  —  Dielectric  Strength  of  Materials. 
Potential  necessary  for  puncture  expressed  in  kilovolts  per  centimeter  thickness  of  the  dielectric. 


Substance. 

Kilovolts 
per  cm, 

Substance. 

l§ 

2* 
*«• 

Substance. 

Kilovolts 
per  cm. 

Ebonite    .... 

300-1100 

Oils  :                           Thickness. 

Papers  : 

Empire  cloth     .     . 

80-300 

Castor                 0.2  mm. 

190 

Beeswaxed  .     . 

770 

paper   .     . 
Fibre    . 

45° 
20 

I.O      " 

Cottonseed 

130 

*7O 

Blotting   .     .     . 

ISO 

Fuller  board      .     . 

200-300 

Lard                     0.2     " 

/U 
140 

iVl  3.11  1  1  1  3     .       .       . 

Paraffined     .     . 

2S 
500 

Glass    
Granite  (fused) 

300-1500 
90 

1.0      " 

Linseed,  raw       0.2     " 

40 
'85 

Varnished    .     . 
Paraffine  : 

100-250 

Guttapercha  .     .     . 

80-200 

I.O      " 

9° 

Melted     .     .     . 

75 

Impregnated  jute  . 

20 

boiled  0.2     « 

190 

Melt,  point. 

Leatheroid    .     .     . 
Linen,  varnished   . 

30-60 

100-200 

"          I.O      " 

Lubricating  

80 
5° 

Solid        43° 
47° 

350 
400 

Liquid  air     ... 

40-90 

Neatsfoot            0.2     " 

200 

52° 

230 

Mica  :           Thickness. 

1.0      " 

9° 

70° 

450 

Madras  o.i  mm. 

1600 

Olive                   0.2     " 

170 

Presspaper  .     .     . 

45-75 

1.0      " 

300 

I.O      " 

75 

Rubber   .... 

160-500 

Bengal    o.i     " 

22OO 

Paraffin                0.2     " 

215 

Vaseline.     .    .     . 

90-130 

1.0      " 

700 

1.0      " 

160 

Thickness. 

Canada  o.i     " 

1500 

Sperm,  mineral  0.2     " 

1  80 

Xylenc     0.2  mm. 

140 

"           1.0      " 

500 

1.0      " 

85 

1.0      " 

80 

South  America  . 

I5OO 

"       natural   0.2     " 

'95 

Micanite    .     .     . 

400 

I.O      " 

90 

Turpentine         0.2    " 

160 

1.0      " 

no 

TABLE  431.      Potentials  in  Volts  to  Produce  a  Spark  In  Kerosene. 


Electrodes  Balls  of  Diam.  d. 

Spark  length. 

mm. 

0.5  cm. 

i  cm. 

2  cm. 

3  cm. 

0.1 

3800 

3400 

2750 

2200 

.2 

7500 

6450 

4800 

3500 

•3 

10250 

9450 

7450 

4600 

•4 

11750 

10750 

9100 

5600 

i 

I3050 
14000 

12400 

!355° 

IIOOO 

12250 

8250 

.8 

15500 

15100 

13850 

10450 

I.O 

16750 

16400 

15250 

12350 

Determinations  of  the  dielectric  strength  of  the  same  substance  by  different  observers  do  not  agree  well  For  a  dis- 
cussion of  the  sources  of  error  see  Mos'cicki,  Electrotechn.  Z.  25,  1904. 

For  more  detailed  information  on  the  dependence  of  the  sparking  distance  in  oils  as  a  function  of  the  nature  of  the 
electrodes,  see  Edmondson,  Phys.  Review  6,  p.  65,  1898. 

SMITHSONIAN  TABLES. 


356  TABLES  432,  433. 

DIELECTRIC   CONSTANTS. 

TABLE  432.  -  Dielectric  Constant  (Specific  Inductive  Capacity)  of  Gases. 
Atmospheric  Pressure. 

Wave-lengths  of  the  measuring  current  greater  than  10000  cm. 


Gas. 

Temp. 

°c 

Dielectric  constant 
referred  to 

Authority. 

Vacuum=i 

Air=i 

Air  

M 

0 

20 

0 
100 

o 

0 

0 

o 

0 
0 

ICO 

o 
o 

0 

o 

0 
0 

0 

0 

145 

1.000590 
1.000586 

1.00718 

1.00290 
1.00239 

1.000946 
1.000985 

I.000600 
1.000695 

I.OOI3I 
1.00146 

1.00258 

1.000264 
1  .000264 

1.000944 
1.000953 

I.OOII6 
1.00099 

1.00993 
1.00905 

1.00705 

I.OOOOOO 
I.OOOOOO 

1  .00659 

1.00231 
1.00180 

1.000356 

1.000399 

I.OOOIOO 

1.000109 

1.00072 
1.00087 

1.00199 

0.999674 
0.999678 

1.000354 

1.000367 

1.00057 

1.00041 

1.00934 
1.00846 

1  .00646 

Boltzmann,  1875. 
KlemenCiC,  1885. 

Badeker,  1901. 

KlemenCic". 
Badeker. 

Boltzmann. 
KlemenCic". 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCic". 

Badeker. 

Boltzmann. 
KlemenclC. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCiC. 

Badeker. 
KlemenCic'. 

Badeker. 

Ammonia                         . 

Carbon  bisulphide     .    .    . 

Carbon  dioxide      .... 
«            « 

Carbon  monoxide  .... 

«              « 

Ethylene        

Hydrochloric  acid      .     .     . 
Hydrogen      

Methane  

Nitrous  oxide  (N2O)      .     . 

«                          «                          (4 

Sulphur  dioxide     .... 
<«             « 

Water  vapor,  4  atmospheres 

TABLE  433,—  Variation  of  the  Dielectric  Constant  with  the  Temperature. 

For  variation  with  the  pressure  see  next  table. 

If  Z>0  =  the  dielectric  constant  at  the  temperature  6°  C.,  Dt  at  the  tempera- 
ture /°  C.,  and  a  and  0  are  quantities  given  in  the  following  table,  then 


D9  =  Dt  [i  —  a(/—  0)  +  0(/  — 
The  temperature  coefficients  are  due  to  Badeker. 


Gas. 

a 

/3 

Range  of 
temp.  °  C. 

Ammonia     .     . 

5-45  X  io-« 

2.59  X  icr7 

10  —  no 

Sulphur  dioxide 

6.19  X  lo-6 

i.  86XIQ-7 

0  —  IIO 

Water  vapor     . 

1.4X10-* 

- 

US 

The  dielectric  constant  of  air  at  atmospheric  pressure  but  with  varying  tem- 
perature may  also  be  calculated  from  the  fact  that  D  —  i  is  approximately  pro- 
portional to  the  density. 
SMITHSONIAN  TABLES. 


TABLES  434,  435, 

DIELECTRIC   CONSTANTS  (continued). 
TABLE  434.  —Change  of  the  Dielectric  Constant  of  Oases  with  the  Pressure. 


357 


Gas. 

Temper- 
ature,0 C. 

Pressure 
atmos. 

Dielectric 
constant. 

Authority. 

Air   

19 

II 

15 

15 

2O 
40 
60 
80 
IOO 
2O 

£ 
60 

so 

IOO 

120 
I4O 

160 
180 

10 
20 
40 
IO 

20 

40 

I.OIOS 

1.0218 

1.0330 
1.0439 
1.0548 
I.OIOI 
1.0196 
1.0294 
1.0387 
1.0482 

1-0579 
1.0674 
1.0760 
1.0845 
1.008 
1.020 
1.  060 
I.OIO 
1.025 
1.070 

Tangl,  1907. 
«            « 

Occhialini,  1905. 

«             « 

«             « 
««             it 
«             « 
«<             « 
Unde,  1895. 

« 
«« 
«« 

« 

H 

«, 

a 

;; 

» 

M 

« 

M 

« 

It 

Carbon  dioxide  .     . 

Nitrous  oxide,  NgO 
«           «         « 

TABLE  435.  —Dielectric  Constants  of  Liquids. 
A  wave-length  greater  than  10000  centimeters  is  denoted  by  oo . 


Substance  . 

Temp. 

Wave- 
length, 
cm. 

Dielectric 
constant. 

o   . 

Substance. 

Temp. 

Wave- 
length, 
cm. 

Dielectric 
constant. 

j* 

Alcohol  : 

Alcohol  : 

Amyl  .     .     . 

frozen 

00 

2.4 

I 

Methyl      .     . 

—50 

00 

45-3 

'        ... 

—  IOO 

" 

30.1 

I 

"      .  •. 

o 

" 

35-° 

'        ... 

—  50 

" 

23.0 

I 

"... 

+  20 

" 

31.2 

'        ... 

O 

" 

17.4 

I 

"... 

17 

75 

33-2 

, 

+  20 

18 

200 

1  6.0 
10.8 

I 

2 

Propyl      .     . 

—  120 
—60 

oo 

46.2 
33-7 

'        ... 

18 

73 

4-7 

2 

"... 

O 

" 

24.8 

Ethyl  .    .     . 

frozen 

oo 

2.7 

"... 

+  20 

" 

22.2 

"      ... 

—  1  2O 

1C 

54.6 

"... 

15 

75 

12.7 

2 

"      ... 

—80 

" 

44-3 

Acetone  .     .    . 

—80 

00 

33-8 

5 

it 

—40 
0 

« 

35-3 
28.4 

"         '.'.', 

O 
15 

I2OO 

2O.6 
'    21.85 

1 

« 
(i 

+20 
17 

200 

25.8 
24.4 

2 

Acetic  acid 

17 

18 

73 

00 

20.7 

97 

I 

"      ... 

75 

23.0 

2 

"         "     .     . 

'5 

I2OO 

10.3 

6 

M 

" 

53 

2O.6 

3 

"         " 

17 

2OO 

7.07 

2 

« 

tt 

4 

8.8 

3 

"         " 

19 

75 

6.29 

2 

« 

f* 

0.4 

5-0 

4 

Amyl  acetate    . 

00 

4.81 

9 

Methyl'    .'    .' 

frozen 
—  IOO 

00 

58.0 

i 

Amylene       .     . 

2.  2O 

10 

References  on  page  358. 


SMITHSONIAN  TABLES. 


TABLE  435  (continued}. 
DIELECTRIC  CONSTANTS  OF  LIQUIDS. 

A  wave-length  greater  than  10000  centimeters  is  designated  by  oo 


Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 
const. 

0 

~  >, 

Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 
const. 

"5  >* 

!a.~ 

(frozen) 

Aniline     .... 

18 

00 

7-3l6 

|| 

Nitrobenzol  .     .     . 

—  10 

00 

9-9 

I 

Benzol  (benzene)  . 

18 

" 

2.288 

" 

. 

-5 

" 

42.0 

" 

"              " 

19 

73 

2.26 

2 

. 

o 

" 

41.0 

" 

Bromine  .... 

23 

84 

3.18 

12 

. 

+*s 

" 

37-8 

" 

Carbon  bisulphide 

20 
17 

oo 
73 

2.626 
2.64 

13 
2 

.     .     . 

30 

18 

y 

36.45 

II 

Chloroform  .     .    . 

18 

00 

5-2 

II 

"           ... 

17 

73 

34-o 

2 

"          ... 

17 

73 

4-95 

2 

Octane      .... 

17 

00 

1.949 

16 

Decane    ....        14 

00 

1.97 

IO 

Oils: 

Decylene      .     .     .        17 

2.24 

«« 

Almond     .    .     . 

20 

00 

2.83 

18 

Ethyl  ether       .     .    —  80 

00 

7-05 

5 

Castor  .... 

ii 

14 

4-67 

19 

".     .     .     .  :  —40 

5-67 

« 

Colza    .... 

20 

" 

3-11 

20 

0 

4.68 

u 

Cottonseed    .     . 

14 

M 

3.10 

21 

«                (4 

18 

4.368 

ii 

Lemon  .... 

21 

*« 

2.25 

22 

44                41 

20 

4-30 

13 

Linseed 

13 

" 

3-35 

21 

44                 4« 

60 

3-65 

Neatsfoot  .     .     . 

- 

U 

3.02 

2O 

"                 "... 

100 

3.12 

" 

Olive     .... 

20 

" 

3-n 

23 

44                  44 

140 

M 

2.66 

" 

Peanut  .     .     .     .  !    11.4 

" 

3-°3 

21 

44                 44 

180 

44 

2.12 

«< 

Petroleum      .     . 

_ 

2OOO 

2-13 

24 

Crit. 

Petroleum  ether 

20 

oo 

1.92 

2O 

44                 44 

temp. 

|| 

». 

Rape  seed     .     . 

16 

" 

2.85 

21 

192 

1  53 

Sesame      .     .     . 

134 

•« 

3.02 

M 

Formic  acid      .    . 

44                  <« 

Glycerine      .     .     . 

18 

+2 
(frozen) 

II 

15 

83 

73 
1  200 

73 

1200 

4-35 
19.0 

62.0 
58.5 
56.2 

14 

2 

6 

2 

6 

Sperm  .... 
Turpentine    .     . 
Vaseline    .     .     . 
Phenol      .... 
Toluene        .     .     . 

20 
20 

Js 

4-i6 

44 

73 

00 
(I 

•*  17 
2.23 
2.17 
9.68 

2-51 
2.T.T, 

20 

25 
2 

5 

**                •         •        •        • 

15 

2OO 

39.1 

2 

• 

|     »V 

JJ 

« 

u 

•         •         • 

IQ 

73 

2.31 

2 

M 

X5 

87? 

25-4 

I  C 

Meta-xylena  .     .     . 

18 

00 

II 

ii 

_ 

0.4 

2^6 

J 

4 

.    .    . 

17 

73 

2-37 

2 

TT 

T  *7 

OQ 

I  ICAdilC         •          •          •          • 

Hydrogen  perox-  ) 
ide46%inH2o} 

I7 
18 

oo 

75 

84.7 

i? 

Water       .... 
for  temp,  coeff. 

18 

17 

oo 
200 

81.07 
80.6 

II 

2 

see  Table  344. 

17 

74 

8l.7 

" 

17 

38 

83.6 

i  Abegg-Seitz,  1899.             10  Landolt-Jahn,  ^892.                  18  Hasenohrl,  1896. 

2  Drude,  1896.                        ii  Turner,  1900.                              19  Arons-Rubens,  1892. 

3  Marx,  1898.                          12  Schlundt.                                     20  Hopkinson,  1881. 

4  Lampa,  1896.                       13  Tangl,  1903.                                21  Salvioni,  1888. 
5  Abegg,  1897.                       14  Coolidge,  1899.                          22  Tomaszewski,  1888. 
6  Thwing,  1894.                      15  v.  Lang,  1896.                             23  Heinke,  1896. 
7  Drude,  1898.                        16  Nernst,  1894.                              24  Marx. 

8  Francke,  1893.                    J7  Calvert,  1900.                           25  Fuchs. 

9  Lowe,  i'898. 

Addenda  to  Table  440,  p.  361,  Dielectric  Constant  of  Rochelle  Salt: 

The  polarization  of  the  Rochelle  salt  dielectric  in  an  electric  field  is  somewhat  analagous  to  the  behavior  of  the  mag- 
netization of  iron  in  a  magnetic  field,  showing  both  saturation  and  hysteresis.  The  dielectric  constant  D  depends  on 
the  initial  and  final  fields  and  the  hysteresis. 

Initial  field,  765  v/cm.;  Final  field,  690  v/cm.;  Average  D  (23°  C),    40 

765  —153  205 

765  -765  157 

o  880  86 

The  last  value  may  be  fair  value  for  ordinary  purposes.  The  electrodes  were  tinfoil  attached  with  shellac.  The  fieJd 
was  applied  perpendicular  to  the  a  axis.  Like  piezoelectric  properties,  the  dielectric  constant  varies  with  different 
crystals.  It  depends  on  the  temperature  as  follows :  (field  o  to  880  v/cm) 

-70°  C,  D  =  12;  -40°,  14;  -20°,  48;  o°,  174  ;  +20°,  88;  +30°,  52. 
(Data  from  Valesek,  University  of  Minnesota,  1921.) 
SMITHSONIAN  TABLES. 


TABLES  436,  437. 

DIELECTRIC  CONSTANTS  OF   LIQUIDS  {continued). 
TABLE  436.  —  Temperature  Coefficients  of  the  Formula : 


359 


Substance. 

a 

0 

Temp, 
range,  °  C. 

Authority. 

Amyl  acetate  .     .     . 
Aniline   .     .     . 

0.0024 
0.00351 
O.OO106 
0.000966 
O.OOO922 
0.00410 
0.00459 
O.OO57 
0.00163 
0.01067 
0.00364 
0.000738 
O.OOO92  1 
0.000977 
0.004474 
0.004583 
0.00436 
0.0008l7 

0.0000087 

O.OOOOOO6O 
O.OOOOI5 

0.000026 

0.0000072 
O.OOOOOO46 
O.OOOOII7 

10-40 

20-181 

22-l8l 
0-13 

20-181 
5-20 

0-76 

4-2£ 
20-181 

Lowe. 
Katz. 
Hasenohrl. 
Rate. 

Tangl. 

Ratz. 
Drude. 
Hasenohrl. 
Heinke,  1896. 

Hasenohrl. 
Ratz. 
Tangl. 
Heerwagen. 
Drude. 
Coolidge. 
Tangl. 

Benzene 

Carbon  bisulphide  . 
<i             «< 

Chloroform     .     .     . 
Ethyl  ether     .     .     . 
Methyl  alcohol    .     . 
Oils  :   Almond     .     . 
Castor  .     ,     . 
Olive    .     .     . 
Paraffine   .     . 
Toluene  

ii 

Water         .     .    . 

Meta-xylene  .     .     . 

(See  Table  433  for  the  signification  of  the  letters.) 


TABLE  437.—  Dielectric  Constants  of  Liquefied  Gases. 

A  wave-length  greater  than  10000  centimeters  is  designated  by  oo. 


r 

Substance. 

Temp. 

ii 

Dial, 
constant. 

& 

o 

JZ 
3 

Substance. 

Temp. 

°c 

ii 

Dial, 
constant. 

t>s 

3 

< 

j 

1 

1 

Air          .     . 

—  IQI 

oo    !       i.Aio 

I 

Nitrous  oxide 

y 

75 

1.47-1.50 

2 

N2O 

—88 

00 

i-93« 

8 

Ammonia  .     .     . 

—34 

75 

21-23 

3 

ii           ii 

—5 

" 

1.630 

5 

U 

130 

16.2 

4 

ii           ii 

+  5 

" 

i.  57s 

ii 

Carbon  dioxide  . 

—5 

0 

00 

i-6o8 
1-583 

5 

ii           ii 
Oxygen      .     .     . 

+  '5 
—182 

II 

1-520 
1-491 

it 
9 

'              " 

4-iQ 

II 

1-540 

" 

ii 

" 

•' 

1-465 

8 

Chlorine         .     . 

II 

1-526 
2.150 

" 

Sulphur  dioxide. 

14.5 
20 

1  20 

BO 

1375 
14.0 

j 

. 

—  20 

II 

2.030 

it 

u              .. 

40 

" 

12.5 

. 

0 

II 

i-97o 

" 

ii              ii 

60 

" 

10.8 

. 

+  10 

" 

i-94o 

u 

ii              ii 

80 

" 

9-2 

. 

0 

II 

2.08 

6 

ii              ii 

IOO 

4i 

7.8 

, 

+  14 

IOO 

1.88 

4 

ii              ii 

1  20 

II 

6.4 

Cyanogen       .     . 
Hydrocyanic  acid 

23 

21 

84 

2.52 
about  95 

7 

Critical.     .     .     . 

140 
154-2 

II 

4.8 

2.1 

« 

Hydrogen  sulph. 

IO            CO 

5-93 

6 

U              ii 

50  i  " 

4.92 

ii 

. 

90 

376 

i  v.  Pirani,  1903.                                 4  Coolidge,  1899.                 7  Schlundt  1901. 

2  Bahn-Kiebitz,  1904.                         5  Linde,  1895.                      8  Hasenohrl,  1900. 

3  Goodwin-Thompson,  1899.            6  Eversheim,  1904.             9  Fleming-Dewar,  1896. 

SMITHSONIAN  TABLES. 


360  TABLES438,  439- DIELECTRIC    CONSTANTS   (continued). 

TABLE  438.  -Standard  Solutions  for  the  Calibration  of  Apparatus  for  the  Measuring  of  Dielectric  Constants. 


Turner. 

Drude. 

Nernst. 

Substance. 

Diel.  const, 
at  1  8°. 
A=  oo. 

Acetone  in  benzene  at  19°.     A  =  75  cm. 

Ethyl  alcohol  in 
water  at  19.5°. 
A=  oo. 

Per  cent 
by  weight. 

Density  16°. 

Dielectric 
constant. 

Temp, 
coefficient. 

2.288 
2.376 
4.36' 
7.298 
10.90 
27.71 

36.45 
81.07 

Per  cent 
by  weight. 

Dielectric 
constant. 

Meta-xylene  .... 
Ethyl  ether    .... 
Aniline      
Ethyl  chloride  .     .     . 
O-nitro  toluene      .     . 
Nitrobenzene    .     .     . 
Water  (conduct.  lo"6) 

0 
20 
40 
60 
80 
100 

0.885 
0.866 
0.847 
0.830 
0.813 
0.797 

2.26 
5.10 
8-43 

I2.I 
1  6.2 

20.5 

0.1% 
0.4 

0.6 

100 
90 
80 
70 
00 

26.0 
29-3 

Water  in  acetone  at  19°.     A  =  75  cm. 

O 
20 
40 
60 
80 
100 

0-797 
0.856 
0.903 
0.940 

0-973 
0.999 

20.5 
31-5 

43-5 
57-0 
70.6 
80.9 

vo  10  LO  vo  LO  TJ- 

d  d  d  o  d  d 

TABLE  439.  -Dielectric  Constants  of  Solids. 


Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Dielectric 
constant. 

1* 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Dielectric 
constant. 

1* 

Asphalt      .     . 

_ 

00 

2.68 

, 

Temp. 

Barium      sul- 

Iodine (cryst.)  . 

23 

75 

4.00 

2 

phate      .     . 

_ 

75 

IO.2 

2 

Lead  chloride  . 

Caoutchouc    . 

_ 

oo 

2.22 

3 

(powder) 

_ 

« 

42 

2 

Diamond    .     . 

- 

" 

I6.5 

i 

"      nitrate 

_ 

u 

16 

2 

" 

- 

75 

5-5° 

2 

"      sulphate  . 

_ 

" 

28 

2 

Ebonite      .    . 

- 

oo 

2.72 

4 

"      molybde- 

ii 

— 

it 

2.86 

5 

nate   .     . 

— 

M 

24 

2 

" 

— 

1000 

2-55 

6 

Marble 

Glass  * 

Density. 

(Carrara) 

_ 

« 

8-3 

2 

Flint  (extra 
heavy) 

4-5 

00 

9.90 

7 

Mica    .... 

- 

00 
u 

5.80-6.62 

5 
15 

Flint    (very 

Madras,  brown 

_ 

ii 

2.5-3.4 

16 

light)  .     . 
Hard  crown 
Mirror    .     . 

2.87 
2.48 

« 

6.61 
6.96 
6.44-7.46 

7 
7 

5 

green 
ruby  . 
Bengal,  yellow 

- 

„ 

3-9-5-5 

£3 

16 
16 
16 

. 

_ 

" 

5-37-5-90 

8 

"       white  . 

— 

M 

4.2 

16 

Lead  (Pow- 

"* 

600 

5.42-6.20 

8 

"       ruby    . 
Canadian    am- 

— 

i« 

4-2-4-7 

16 

ell).     .     . 

3-0-3-5 

00 

5-4-8-0 

9 

ber.     .     .     . 

_ 

" 

3-° 

16 

Jena 

South  America 

_ 

« 

5-9 

16 

Boron 
Barium    . 

_ 

I 

5-5-8-1 
7.8-8.5 

10 

TO 

Ozokerite  (raw) 
Paper         (tele- 

- 

" 

2.21 

i 

Borosili- 

phone) 

- 

u 

2.0 

17 

cate 

— 

6.4-7.7 

i 

"      (cable)    . 

_ 

ii 

2.0-2.5 

i 

Gutta  percha  . 

- 

- 

3-3-4-9 

ii 

Paraffine       .     . 

Melting 

" 

2.46 

18 

Temp. 

"              . 

point. 

" 

2.32 

19 

Ice    .... 

-5 

I2OO 

2.85 

12 

"              .     . 

44-46 

ii 

2.IO 

20 

"      .'!.'! 

—  18 
—190 

5000 

75 

3.16 
1.76-1.88 

13 

"      ;  ; 

54-56 
74-76 

M 

ii 

2.14 
2.l6 

20 
20 

References  on  p.  361, 

*  For  the  effect  of  temperature,  see  Gray-Dobbie,  Pr.  Roy.  Soc.  63,  i8c 
"  waye-length,  see  K.  F.  Lowe,  Wied.  Ann.  66,  1898.' 

SMITHSONIAN  TABLES. 


67,  1900. 


TABLES  439,  440. 

DIELECTRIC  CONSTANTS  (continued). 
TABLE  439.  —  Dielectric  Constanta  of  Solids  (continued). 


36i 


Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Diel. 
constant. 

f 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Did. 

constant. 

JU 

r 

Paraffine    .     . 

47-°6 

6l 

2.16 

21 

Sulphur 

« 

56.°2 

61 

2.25 

21 

Amorphous 

- 

00 

3-98 

i 

Phosphorus: 

" 

— 

75 

2 

Yellow     .     . 

- 

75 

3-60 

2 

Cast,  fresh 

_ 

oo           4.22 

I 

Solid   .     .     . 

_ 

80 

4.1 

22 

<«        (i 

— 

u 

4-05 

IS 

Liquid      .     . 

_ 

80 

3-85 

22 

"         " 

_ 

75 

3-95 

2 

Porcelain: 

Cast,  old     . 

_ 

oo 

3.60 

18 

Hard 

"        " 

_ 

75 

3-9° 

2 

(Royal  B'l'n) 

- 

00 

5-73 

15 

( 

near 

) 

Seger   "  "     . 

- 

" 

6.6  1 

'5 

Liquid     .   ) 

melting- 

oo 

3-42 

I 

Figure  "  "     . 

— 

II 

6.84 

15 

I 

point 

) 

Selenium   .     . 

_ 

" 

7-44 

i 

Strontium 

"           .     . 

- 

75 

6.60 

2 

sulphate 

_ 

75 

"-3 

2 

" 

|      oo 

6.13 

23 

Thallium 

" 

1000 

6.14 

23 

carbonate 

_ 

75 

17 

2 

Shellac  .     .     . 

— 

00 

3.10 

4 

"  nitrate     . 

_ 

75 

16.5 

2 

"      ... 

_ 

" 

2-95-3-73 

24 

Wood 

dried 

"      ... 

- 

" 

25  ; 

Red  beech  . 

||  fibres 

oo 

4.83-2.51 

- 

Amber  .     .     . 

_ 

— 

2.86 

18 

(i                 ii 

Oak  .     .     ! 

J_    " 

ii 

7-73-3-63 
4.22-2.46 

: 

.     .     . 

-L    " 

H 

6.84-3-64 

— 

i  v.  Pirani,  1903.                          10  Lowe,  1898.                               18  Fallinger,  1902. 

2  Schmidt,  1903.                          n   (submarine-data).                      19  Boltzmann,  1875. 

3  Gordon,  1879.                           I2  Thwing,  1894.                           20  Zietkowski,  1900. 

4  Winklemann,  1889,                 13  Abegg,  1897.                             21   Hormell,  1902. 

5  Elsas,  1891.                               14  Behn-Kiebitz,  1904.                 22  Schlundt,  1904. 

6  Ferry,  1897.                               15  Starke,  1897.                             23  Vonwiller-Mason,  1907. 
7  Hopkinson,  1891.                     16  E.  Wilson.                                 24  Wullner,  1887. 

8  Arons-Rubens,  1891.               17  Campbell,  1906.                        25  Donle. 

9  Gray-Dobbie,  1898. 

TABLE  440.  -Dielectric  Constants  of  Crystals. 
Do,  D/3,  D-y  are  the  dielectric  constants  along  the  brachy,  macro  and  vertical  axes  respectively. 


Wave- 

Diel.  const. 

Wave- 

Diel.  const. 

O      L. 

2  ,£ 

C    U   * 

-e  x 

cm. 

_i_Axis. 

I  Axis. 

1* 

cm. 

Da 

DP 

Dy 

UNIAXIAL  : 

RHOMBIC  : 

Apatite     .... 
Beryl                  .     . 

75 

OO 

9.50 

7.8; 

7.40 
7  44 

2 

Aragonite  .     .     . 

00 

75 

9.14 
9.80 

7-68 

6.55 

4 
I 

7.IO 

6.O; 

7 

Barite     .... 

00 

6-97 

10.09 

7.00 

4 

M 

7C 

C.C2 

I 

75 

7.6S 

I  2.  2O 

7.70 

i 

Calcite     .... 

oo 

8.49 

7J-S6 

4 

Celestite     .     .     . 

75 

7.70 

I8.5 

8.30 

i 

Dolomite      .     .     . 
Iceland  spar      .     . 
Quartz     .... 

75 
75 

oo 

8.78 
7.80 
8.50 

4.38 

8.29 
6.80 
8.00 
5.06 
4.40 

5 
i 
i 

4 
6 

Cerussite    .     .     . 
MgSO4+7lU> 
K2SO4    .... 
Rochelle  salt*     . 
Sulphur 

75 

00 
n 

it 

6.70 
>St 

23-2 
6.05 
5-08 
6.92 

192 

8.28 
4.48 
8.89 
4-77 

i 
7 
7 

I 

,« 

IOOO 

4.27 

4.74 

6 

M 

3.65 

3  85 

4.66 

7 

Ruby  (Siam)     .     . 
Rutile  (TiO2)  .     . 
Tourmaline  .     .     . 

75 

00 

"•3 

'•73 
6-S4 

4 

i 

4 

Topaz     .... 
"       colorless  . 

75 
75 

3.62 
6.65 
6.25 

3-85 
6.70 

6.54 

4-66 
6.30 
644 

i 
i 
4 

"          ... 

75 

6-75 

5-65 

i 

Zircon      .... 

75 

12.8 

12.6 

i 

»  See  page  358. 

i  Schmidt,  1903.                   4  Fallinger,  1902,  1919.                7  Borel,  1893. 
2  Starke,  1897.                      5  v.  Pirani,  1903.                           8  Bolztmann,  1875. 

3  Curie,  1889.                         6  Ferry,  1897. 

SMITHSONIAN  TABLES. 


32  TABLE  441. 

WIRELESS   TELEGRAPHY. 

Wave-Length  in  Meters,  Frequency  in  periods  per  second,  and  Oscillation  Constant  LG  in 
Microhenries  and  Microfarads. 

The  relation  between  ihe  free  wave-length  in  meters,  the  frequency  in  cycles  per  second,  and 
the  capacity-inductance  product  in  microfarads  and  microhenries  are  given  for  circuits  between 
1000  and  10,000  meters.  For  values  between  100  and  1000  meters,  multiply  the  columns  for  n 
by  10  and  move  the  decimal  point  of  the  corresponding  LC  column  two  places  to  the  left  (divid- 
ing by  100);  for  values  between  10,000  and  100,000,  divide  the  n  column  by  10  and  multiply  the 
LC  column  by  100.  The  relation  between  wave-length  and  capacity-inductance  may  be  relied 
upon  throughout  the  table  to  within  one  part  in  200. 

Example  i  :  What  is  the  natural  wave-length  of  a  circuit  containing  a  capacity  of  o.ooi  micro- 
farad, and  an  inductance  of  454  microhenries  ?  The  product  of  the  inductance  and  capacity  is 
454  X  o.ooi  =0.454.  Find  0.454  under  LC ;  opposite  under  meters  is  1270  meters,  the  natural 
wave-length  of  the  circuit. 

Example  2  :  What  capacity  must  be  associated  with  an  inductance  of  880  microhenries  in  order 
to  tune  the  circuit  to  3500  meters  ?  Find  opposite  3500  meters  the  LC  value  3.45  ;  divide  this  by 
880,  and  the  quotient,  0.00397,  is  the  desired  capacity  in  microfarads. 

Example  3  :  A  condenser  has  the  capacity  of  0.004  microfarad.  What  inductance  must  be  placed 
in  series  with  this  condenser  in  order  that  the  circuit  shall  have  a  wave-length  of  600  meters  ? 
From  the  table,  the  LC  value  corresponding  to  600  meters  is  o.ioi.  Divide  this  by  0.004,  the 
capacity  of  the  condenser,  and  the  desired  inductance  is  25.2  microhenries. 


Meters. 

n 

LC 

Meters. 

n 

LC 

Meters. 

n 

LC 

1000 

3OO,OOO 

0.281 

1300 

230,800 

0.476 

1600 

187,500 

0.721 

IOIO 

297,000     0.287 

1310 

229,000 

0.483 

1610 

186,300 

0.730 

1020 

294,100  !  0.293 

1320 

227,300 

0.490 

1620 

185,200 

0-739 

1030 

291,300   0.299 

'33° 

225,600 

0.498 

1630 

184,100 

0.748 

IO4O 

288,400    0.305 

1340 

223,900 

0-505 

1640 

182,900 

0.757 

IO5O     285,700     0.310 

J350 

222,200 

0-5*3 

1650 

181,800 

0.766 

IO6O     283,600     0.316 

1360    220,600 

0.521 

1660 

180,700 

0.776 

1070 

280,400   0.322 

1370 

218,900 

0.529 

1670 

179,600 

0.785 

1080 

277,800   0.328 

1380 

217,400 

0-536 

1680 

178,600 

0-794 

logo 

275,200 

°-335 

1390 

215,800 

0.544 

1690 

177,500 

0.804 

IIOO 

272,700 

0.341 

1400 

214,300 

0.552 

1700 

176,500 

0.813 

IIIO 

270,300 

0-347 

1410 

212,800 

0-559 

1710 

175,400 

0-823 

1  120 

267,900 

°-353 

1420 

2II,3OO 

0.567 

1720 

174,400 

0-833 

1130 

265,500 

°-359 

143° 

2O9,8OO 

0.576 

1730 

173,400 

0.842 

1140 

263,100 

0.366 

1440 

208,300 

0.584 

1740 

172,400 

0.852 

1150 

260,900 

0.372 

1450 

2O6,9OO 

0.592 

1750 

171,400 

0.862 

1160 

258,600 

o-379 

1460 

205,500 

0.600 

1760 

170,500 

0.872 

1170    256,400 

0.385 

1470 

2O4,IOO 

0.608 

1770 

169,400 

0.882 

1180    254,200 

0.392 

1480 

2O2,7OO 

0.617 

1780 

168,500 

0.892 

1190 

252,100 

0-399 

1490 

2OI,3OO 

0.625 

1790 

167,600 

0.902 

1200 

250,000 

0.405 

1500 

200,000 

0-633 

1800 

166,700 

0.912 

I2IO 

247,900 

0.412 

1510 

198,700 

0.642 

1810 

165,700 

0.923 

I22O 

245,900 

0.419 

1520 

197,400 

0.650 

1820 

164,800 

o-933 

1230     243,900 

0.426 

1530 

196,100 

0.659 

1830 

163,900 

0-943 

1240     241,900 

o-433 

1540 

194,800 

0.668 

1840 

163,000 

o-953 

1250 

240,000 

0.440 

J55o 

193,600 

0.676 

1850 

l62,2OO 

0.963 

1200 

238,100 

0.447 

1560 

192,300 

0.685 

1860 

161,300 

o-974 

1270 

236,200 

0-454 

1570 

I9I,IOO 

0.694 

1870 

160,400 

0.985 

1280 

234,400 

0.461 

1580 

189,900 

0.703 

1880 

159,600 

0-995 

I20X) 

232,600 

0.468 

i59o 

188,700 

0.712 

1890 

158,700 

1.  000 

Adapted  from  table  prepared  by  Greenleaf  W.  Picard  ;  copyright  by  Wireless  Specialty  Apparatus  Company,  New 
jrk.     Computed  on  basis  of  300,000  kilometers  per  second  for  the  velocity  of  propagation  of  electromagnetic  waves. 


Yo 


SMITHSONIAN  TABLES. 


TABLE  441    (concluded). 
WIRELESS  TELEGRAPHY. 

Wave  Length,  Frequency  and  Oscillation  Constant. 


363 


Meters. 

n 

LC 

Meters. 

n 

LC 

Metere. 

n 

LC 

I9OO 

157,900  i  1.016  1 

2800 

IO7,IOO 

2.21 

7000 

42,860 

13-8 

1910 

157,100 

1.026 

2820 

106,400 

2.24 

7100 

42,250 

14.2 

1920 

156,300 

1-037 

2840 

105,600 

2.27 

7200 

41,670 

14.6 

193° 

155,400 

1.048 

2860 

104,900 

2.30 

73°° 

41,100 

15.0 

I940 

1  54,600 

1.059 

2880 

IO4,2OO 

2-33 

7400 

40,540 

15.4 

!95° 

153,800 

1.070 

2900 

103,400 

2.37 

75°° 

4O,OOO 

I5.8 

1960 

153,100 

I.oSl 

2920 

IO2,7OO 

2.40 

7600 

39470 

16.3 

1970 

152,300 

1.092 

2940 

102,000 

2-43 

7700 

38,960 

16.7 

1980 

151,500 

1.103 

2960 

101,300 

2.47 

7800 

38,460 

17.1 

1990 

1  50,800 

I.1I4 

2980 

100,700 

2.50 

7900 

37,980 

I7.6 

2OOO 

150,000 

I.I26  ' 

3000 

IOO,OOO 

2-53 

8000 

37,5°° 

1  8.0 

2020 

148,500 

1.148 

3100 

96,770 

2.70 

8100 

37,040 

18.5 

2040 

147,100 

I.I7I 

3200 

93,75° 

2.88 

8200 

36,59° 

18.9 

2000 

145,600 

1.194 

33°° 

90,910 

3-°7 

8300 

36,140 

19.4 

2080 

144,200 

1.218 

3400 

88,240 

3-26 

8400 

35,7i° 

19.9 

2IOO 

142,900 

1.241 

35°° 

85,910 

3-45 

8500 

35,29° 

20.7 

2120 

141,500 

1.265  ! 

3600 

83,330 

3-65 

8600 

34,880 

20.8 

2140 

140,200 

1.289  ! 

3700 

8  1  ,080 

3-85 

8700 

34,480 

21.3 

2l6o 

138,900 

I-3I3  1 

3800 

78,950 

s 

4.06 

8800 

34,090 

21.8 

2180 

137,600 

1-338 

39°° 

76,920 

4.28 

8900 

33,71° 

22.3 

2200 

136,400 

1.362 

4000 

75,000 

4-5° 

9000 

33,33° 

22.8 

2220 

135,100 

1-387 

4100 

73,  1  7° 

4.73 

9100 

32,970 

23.3 

224O 

133,900  i  1.412 

4200 

7i,43° 

4.96 

9200 

32,610 

23.8 

2200 
2280 

132,700 

131,600 

1.438 
1.463 

43°° 
4400 

69,770 
68.180 

5.20 
545 

93°° 
9400 

32,260 

24-3 
24.9 

2300 
2320 
2340 

130,400 
129,300 
128,200 

1.489 

'•5*5 

1.541 

45°° 
4600 

47°° 

66,670 
65,220 
63,83° 

5-7° 
5.96 

6.22 

95°° 
9600 
9700 

3^59° 
3I»25° 
3°,93° 

25.4 

25-9 
26.5 

^T 

2360 

127,100 

1.568 

4800 

62,500 

6.49 

9800 

30,610    27.0 

2380 

126,000 

1-594 

4900 

61,220 

6.76 

9900 

3°,310 

27.6 

24OO 

125,000 

1.621 

5000 

60,000    7.04 

10000 

30,000 

28.1 

2420 

124,000 

1.648 

5100 

58,820 

7-32 

2440 

129,000 

1.676 

5200 

57,69° 

7.6l 

2460 

121,900 

1.703 

53°° 

56,600 

7-91 

2480 

121,000 

1.731 

54°° 

55,560 

8.21 

2500 

120,000 

1-759 

55°° 

54,55° 

8.51 

2520 

119,000    1.787 

5600 

53,57° 

0.03 

2540   :   IlS.IOO 

1.816 

57°° 

52,630 

9.15 

2560      117,200 

1.845 

5600 

51,720 

947 

2580 

116,300 

1.874 

59°° 

50,850 

9.81 

j 

26OO 

1  1  5,400 

1.903 

6000 

50,000 

IO.I 

262O 

II4,5OO 

1.932 

6100 

49,180 

KM 

2640 

1  1  3,6OO 

1.962 

6200 

48,550 

10.8 

2660 

II2,8OO 

1.991 

6300 

47,620 

I  I.I 

2680 

111,900 

2.02 

6400 

46,870 

"-5 

27OO 

111,100 

2.05 

6500 

46,150 

11.9 

2720 

1  10,300 

2.08 

6600 

45,45° 

12.3 

2740 

IO9,5OO     2.  1  1 

6700 

44,780 

12.6 

2760 

108,700 

2.14 

6800 

44,120 

13.0 

2780 

107,900 

2.18 

6900 

43,480 

134 

2800 

107,100 

2.21 

7000 

42,860 

13-8 

SMITHSONIAN  TABLES. 


^64  TABLES  442-443. 

TABLE  442. 
WIRELESS  TELEGRAPHY. 

Radiation  Resistances  lor  Various  Wave-Lengths  and  Antenna  Heights. 

The  radiation  theory  of  Hertz  shows  that  the  radiated  energy  of  an  oscillator  may  be  repre- 
sented by  E=  constant  (h'/A2)  I2,  where  h  is  the  length  of  the  oscillator,  A,  the  wave-length  and 
I  the  current  at  its  center.  For  a  flat-top  antenna  E  ==  1600  (h2/  A2)  I2  watts ;  1600  h2/ A2  is  called 
the  radiation  resistance. 

(h  =  height  to  center  of  capacity  of  conducting  system.) 


\^= 

40  Ft. 

60  Ft. 

80  Ft. 

100  Ft. 

120  Ft. 

160  Ft. 

200  Ft. 

300  Ft. 

450  Ft. 

600  Ft. 

1200  Ft. 

Length  A 

m 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

200 

6.0 

134 

24.0 

37.0 

S4-o 

95.0 

300 

2-7 

6.0       10.6 

I6.5 

23.8 

42.4 

400 
600 

a66 

34 
1.5 

6.0 
2.7 

9-3 

4.1 

134 
6.0 

23.8 

10.6 

I6.4 

374 

84.0 

149.0 

800 

o-37 

0.84 

2-3 

34 

6.0 

9.2 

21.0 

47-o 

84.0 

1000 
I2OO 

0.24 
0.17 

0.54 
o-37 

H 

1.03 

2.1 

3i 

2.6 

6.0 
4.1 

13-5 

9-3 

30.0 

21.0 

54-0 

37-o 

215.0 
149.0 

I5OO 

O.I  I 

0.24 

0.42 

0.66 

o-9S 

1.7 

2.6 

6.0 

134 

24.0 

95-o 

2000 

0.13 

0.24 

0.37 

0-54 

o>95 

1.5 

34 

7-5 

134 

54-0 

2500 
3OOO 

0.15 

O.I  I 

0.24 
0.17 

o.34 
0.24 

0.61 
0.42 

S33 

2.2 

'•5 

4.8 
34 

8.6 
6.0 

34-0 
24.0 

4OOO 

0.06 

0.09 

0.13 

0.24 

0.37 

0.84 

1.9 

34 

'34 

5OOO 

0.24 

°-53 

1.20 

2.2 

8.6 

6000 

0.16 

0-37 

0.84 

"•5 

6.0 

7000 

O.I  2          O.27 

0.61 

I.I 

44 

Austin,  Jour.  Wash.  Acad.  of  Sci.  i,  p.  190,  1911. 


TABLE  443. 
THE  DIELECTRIC   PROPERTIES  OF   NON-CONDUCTORS. 

Phillips   Thomas,   J.  Franklin  Inst.  176,  283,  1913. 


Results  of  tests  at  unit  area  and  unit  thickness  of  dielectric. 

At  1000  cycles. 

Mica. 

Paper. 

Celluloid. 

Ice. 

Max.  breakdown  volts  per  cm. 

i  o6Xio6 

O.7IXIO6 

I  .O5XIO6 

onXio6 

Specific  indue,  capacity            .... 

4.00 

4.OO 

13.26 

8640 

Max.  absorbable  energy,  watts-sec/cm3 

0.198 

0.108 

0.640 

.00040 

9O°-angle  of  lead      

o°  57' 
3-Qi 

2°   10' 
9.84 

3°  40' 
48.3 

I3e  39' 
1400 

Equiv.  resistance  ohms/cm3  Xio11     . 

Conductivity  per  cm.  cubeXicr10      .     . 

2.56 

1.02 

0.207 

.00722 

Percent  change  in  cap.  per  cycleXio4    . 

2.18 

14.31 

30.7 

70.0 

Percent  change  in  resistance  per  cycle  . 

0.258 

0.146 

0.106 

0.127 

At  15  cycles. 

Specific  inductive  capacity      .... 

4.09 

5-77 

18.60 

429.0 

Max.  absorbable  energy,  watt-sec/cm3. 

0.203 

0.126 

0.90 

O.OO2 

Percent  change  in  capacity  per  cycle     . 

o.oo 

0.306 

1.74 

i-59 

On  direct  current. 

Conductivity  per  cm3     .... 

2   42XIO"17 

2.2/XIO-1- 

7I.5XIO-14 

163.  lo-11 

SMITHSONIAN  TABLES. 


TABLE  444. 

MAGNETIC    PROPERTIES. 

Unit  pole  is  a  quantity  of  magnetism  repelling  another  unit  pole  with  a  force  of  one  dyne; 
47T  lines  of  force  radiate  from  it.  M,  pole  strength;  ^irM  lines  of  force  radiate  from  pole  of 
strength  M . 

H,  field  strength,  =  no.  of  lines  of  force  crossing  unit  area  in  normal  direction;  unit  =-  gauss  — 
one  line  per  unit  area. 

M,  magnetic  moment,  =  Ml,  where  /  is  length  between  poles  of  magnet. 

/,  intensity  of  magnetization  or  pole  strength  per  unit  area,  =  M/K  =  M/A  where  A  is  cross 
section  of  uniformly  magnetized  pole  face,  and  V  is  the  volume  of  the  magnet.  ^irM/A  -  4717  = 
no.  lines  of  force  leaving  unit  area  of  pole. 

/,  specific  intensity  of  magnetism,  =  // p  where  p  =  density,  g/cm3. 

</>,  magnetic  flux,  =  4irM  +  HA  for  magnet  placed  in  field  of  strength  H  (axis  parallel  to  field). 
Unit,  the  maxwell. 

B,  flux  density  (magnetic)  induction,  =  <f>/A  =  4?r/  +  H;   unit  the  gauss,  maxwell  per  cm. 

IA,  magnetic  permeability,  =  B/H.  Strength  of  field  in  air-filled  solenoid  =  H  =  UTT/IO)  ni 
in  gausses,  *  in  amperes,  w,  number  of  turns  per  cm  length.  If  iron  filled,  induction  increased, 
i.e.,  no.  of  lines  of  force  per  unit  area,  B,  passing  through  coil  is  greater  than  H;  fj.  =  B/H. 

K,  susceptibility;  permeability  relates  to  effect  of  iron  core  on  magnetic  field  strength  of  coil; 
if  effect  be  considered  on  iron  core,  which  becomes  a  magnet  of  pole  strength  M  and  intensity 
of  magnetism  /,  then  the  ratio  I/H  =  (fj.  —  i)/4  iris  the  magnetic  susceptibility  per  unit  volume 
and  is  a  measure  of  the  magnetizing  effect  of  a  magnetic  field  on  the  material  placed  in  the  field. 

fj.  =  47TK  +1. 

X,  specific  susceptibility  (per  unit  mass)  =  K/p  =  J/H. 

XA>  atomic  susceptibility,  =  X  X  (atomic  weight) ;  XM  =  molecular  susceptibility. 

/A,  /M,  similarly  atomic  and  molecular  intensity  of  magnetization. 

Hysteresis  is  work  done  in  taking  a  cm3  of  the  magnetic  material  through  a  magnetic  cycle 
=  flldl  =  (i/4ir)J*H  dB.  Steinmetz's  empirical' formula  gives  a  close  approximation  to  the 
hysteresis  loss;  it  is  aB1'6  where  B  is  the  max.  induction  and  a  is  a  constant  (see  Table  472).  The 
retentivity  (B  r)  is  the  value  of  B  when  the  magnetizing  force  is  reduced  to  zero.  The  reversed 
field  necessary  to  reduce  the  magnetism  to  zero  is  called  the  coercive  force  (He). 

Ferromagnetic  substances,  ju  very  large,  K  very  large:  Fe,  Ni,  Co,  Heusler's  alloy  (Cu  62.5, 
Mn  23.5,  Al  14.  See  Stephenson,  Phys.  Rev.  1910),  magnetite  and  a  few  alloys  of  Mn.  n  for 
Heusler's  alloy,  90  to  100  for  B  =  2200;  for  Si  sheet  steel  350  to  5300. 

Paramagnetic  substances,  fJi>i,  very  small  but  positive,  K  =  io~3  to  io~*:  oxygen,  especially 
at  low  temperatures,  salts  of  Fe,  Ni,  Mn,  many  metallic  elements.  (See  Table  474.) 

Diamagnetic  substances,  ji<i,  K  negative.  Most  diamagnetic  substance  known  is  Bi,  -14 
X  ic.-6.  (See  Table  474.) 

Paramagnetic  substances  show  no  retentivity  or  hysteresis  effect.  Susceptibility  independent 
of  field  strength.  The  specific  susceptibility  for  both  para-  and  diamagnetic  substances  is  in- 
dependent of  field  strength. 

For  Hall  effect  (galvanomagnetic  difference  of  potential),  Ettinghausen  effect  (galvanomagnetic 
difference  of  temperature),  Nernst  effect  (thermomagnetic  difference  of  potential)  and  the  Leduc 
effect  (thermomagnetic  difference  of  temperature),  see  Tables  487  and  488. 

Magneto-strictive  phenomena: 

Joule  effect:  Mechanical  change  in  length  when  specimen  is  subjected  to  a  magnetic  field. 
With  increasing  field  strength,  iron  and  some  iron  alloys  show  first  a  small  increment  A///  = 
(7  to  35)  X  io~7,  then  a  decrement,  and  for  H  =  1600,  A///  may  amount  to  -(6  to  8)  x  io~*. 
Cast  cobalt  with  increasing  field  first  decreases,  A///  =  -8  Xio"6,  H  -  150,  then  increases  in 
length,  A///  =  +  5  X  iQ"6,  H  =  2000;  annealed  cobalt  steadily  contracts,  A///  =  -25  X  lo"6,  H 
=  2000.  Ni  rapidly  then  slowly  contracts,  A///  =  -30  X  lo"6,  H  =  100;  -35  X  10"*,  H  =  300; 
-36  X  iQ-6,  H  =  2000  (Williams,  Phys.  Rev.  34,  44,  1912).  A  transverse  field  generally  gives 
a  reciprocal  effect. 

Wiedemann  effect:  The  lower  end  of  a  vertical  wire,  magnetized  longitudinally,  when  a  current 
is  passed  through  it,  if  free,  twists  in  a  certain  direction,  depending  upon  circumstances  (see 
Williams,  Phys.  Rev.  32,  281,  1911).  A  reciprocal  effect  is  observed  in  that  when  a  rod  of  soft 
iron,  exposed  to  longitudinal  magnetizing  force,  is  twisted,  its  magnetism  is  reduced. 

Villari  effect;  really  a  reciprocal  Joule  effect.  The  susceptibility  of  an  iron  wire  is  increased 
by  stretching  when  the  magnetism  is  below  a  certain  value,  but  diminished  when  above  that 
value. 

SMITHSONIAN  TABLES. 


366 


TABLE  445. 


COMPOSITION    AND    MAGNETIC 

This  table  and  Table  456  below  are  taken  from  a  paper  by  Dr.  Hopkinson  *  on  the  magnetic  properties  of  iron  and  steel, 
which  is  stated  in  the  paper  to  have  been  240.  The  maximum  magnetization  is  not  tabulated ;  but  as  stated  in  the 
by  4».  "  Coercive  force  "  is  the  magnetizing  force  required  to  reduce  the  magnetization  to  zero.  The  '"demag- 
previous  magnetization  in  the  opposite  direction  to  the  "  maximum  induction  "  stated  in  the  table.  The  "energy 
which,  however,  was  only  found  to  agree  roughly  with  the  results  of  experiment. 


No. 
of 
Test 

Description  of 
specimen. 

Temper. 

Chemical  analysis. 

Total 
Carbon. 

Manga- 
nese. 

Sulphur. 

Silicon. 

Phos- 
phorus. 

Other 
substances. 

I 

Wrought  iron    . 

Annealed 

_ 

_ 

_ 

2 

Malleable  cast  iron    . 

« 

_ 

_ 

_ 

_ 

_ 

_ 

3 

Gray  cast  iron   . 

- 

- 

- 

- 

_ 

_ 

_ 

4 

Bessemer  steel  . 

_ 

0.045 

0.200 

0.030 

None. 

0.040 

_ 

5 

Whitworth  mild  steel 

Annealed 

0.090 

0.153 

0.016 

" 

0.042 

_ 

6 

"                « 

u 

0.320 

0.438 

0.017 

0.042 

0-035 

- 

u 

(  Oil-hard- 

tt 

M 

7 

• 

(    ened 

•~ 

8 

a                « 

Annealed 

0.890 

0.165 

0.005 

0.081 

0.019 

_ 

t( 

j  Oil-hard- 

u 

(( 

u 

« 

9 

• 

|    ened 

"*• 

10 

Hadfield's  manganese  ) 
steel                            f    ' 

-       , 

I.OO5 

12.360 

0.038 

0.204 

0.070 

- 

ii 

12 

Manganese  steel 

As  forged 
Annealed 

0.674 

4-73° 

0.023 

u 

0.608 

0.078 

- 

«                 u 

(  Oil-hard- 

lt 

(t 

u 

tt 

t< 

*3 

\    ened 

14 

"           " 

As  forged 

1.298 

8740 

0.024 

0.094 

0.072 

_ 

15 

"              "             . 

Annealed 

" 

" 

" 

" 

" 

«                 « 

(  Oil-hard- 

u 

<4 

M 

tt 

ID 

(    ened 

™* 

'I 

Silicon  steel 

As  forged 

0.685 

0.694 

" 

3438 

0.123 

- 

18 

"         "... 

Annealed 

M 

u 

'< 

" 

_ 

(  Oil-hard- 

lt 

19 

. 

\    ened 

— 

20 

Chrome  steel     . 

As  forged 

0-532 

0.393 

O.O2O 

O.22O 

0.041 

0.621  Cr. 

21 

"         "... 

Annealed 

u 

M 

M 

« 

M 

(  Oil-hard- 

<4 

22 

. 

(    ened 

" 

23 

"         "... 

As  forged 

0.687 

0.028 

U 

0.134 

0.043 

I.I95   Cr- 

24 

"         "... 

Annealed 

" 

M 

" 

(i 

(  Oil-hard- 

u 

(( 

t( 

|| 

25 

... 

(    ened 

26 

Tungsten  steel  . 

As  forged 

i-357 

O.O36 

None. 

0.043 

0.047 

4.649  W. 

27 

"             .        . 

Annealed 

" 

" 

u 

"  ' 

" 

» 

(  Hardened 

28 

"            "... 

<    in  cold 

M 

(t 

« 

« 

" 

« 

(    water 

(  Hardened 

29 

"            "... 

<    in  tepid 

u 

" 

• 

« 

M 

" 

(    water 

30 

"    (French)   . 

(  Oil-hard- 
\    ened 

0.511 

0.625 

None. 

0.021 

O.O28 

3-444  W. 

31 
32 
33 
34 
35 

Gray  cast  iron    . 
Mottled  cast  iron 
White       "                  . 
Spiegeleisen 

Very  hard 

0.855 

3455 
2.581 
2.036 
4.510 

0.312 

0.173 

0.610 
0.386 
7.970 

0.042 
0.105 
0.467 
Trace. 

O.I5I 
2.044 
1.476 
0.764 
0.502 

0.089 
O.I5I 

0-435 
0.458 
0.128 

2.353  w. 

2.064  C.t 
1-477  C.t 

*  Phil.  Trans.  Roy.  Soc.  vol.  176. 
SMITHSONIAN  TABLES. 


t  Graphitic  carbon. 


TABLE  445  (continued"). 
PROPERTIES    OF    IRON    AND    STEEL. 


367 


The  numbers  in  the  columns  headed  "  magnetic  properties  "  give  the  results  for  the  highest  magnetizing  force  used, 
paper,  it  may  be  obtained  by  subtracting  the  magnetizing  force  (240)  from  the  maximum  induction  and  then  dividing 
netizing  force  "  is  the  magnetizing  force  which  had  to  be  applied  in  order  to  leave  no  residual  magnetization  after 
dissipated"  was  calculated  from  the  formula :— Energy  dissipated  =  coercive  force  X  maximum  induction  —  w 


No. 
of 
Test 

Description  of 
specimen. 

Temper. 

Specific 
electri- 
cal resis- 
tance. 

Magnetic  properties. 

Energy  dis- 
sipated per 
cycle. 

Maxi- 
mum  in- 
duction. 

Residual 
induc- 
tion. 

Coer- 
cive 
force. 

Demag- 
netizive 
force. 

2 

3 

4 

Wrought  iron    . 
Malleable  cast  iron  . 
Gray  cast  iron  . 
Bessemer  steel  . 
Whitworth  mild  steel 

Annealed 

M 

Annealed 

.01378 

•03254 
.10560 
.01050 
.01080 

18251 
12408 
10783 
18196 
19840 

7248 

7479 
3928 
7860 
7080 

2.30 
8.80 

3-80 
2.96 
1.63 

*- 

13356 
34742 

!3037 
I7I37 
10289 

6 

«                « 

u 

.01446 

18736 

9840 

6-73 

- 

40120 

(  Oil-hard- 

7 

i(                                  U 

(    ened 

.01390 

18796 

11040 

11.00 

- 

65786 

8 

«<                       « 

Annealed 

•OI559 

l6l20 

10740 

8.26 

_ 

42366 

9 

«                       « 

(  Oil-hard- 
(    ened 

.01695 

l6l20 

8736 

19.38 

- 

99401 

10 

Hadfield's   manganese  ) 
steel                             J  ' 

.06554 

3IO 

- 

_ 

_ 

ii 

12 

Manganese  steel 

«                    u 

As  forged 
Annealed 

.05368 
.03928 

4623 
10578 

22O2 
5848 

23-50 
33-86 

37.13 
46.10 

34567 
"3963 

(  Oil  harH 

13 

«                 « 

\  \_/n-narci- 
(    ened 

•05556 

4769 

2158 

27.64 

40.29 

41941 

H 

«                 « 

As  forged 

.06993 

747 

_ 

_ 

_ 

_ 

15 

«                 « 

Annealed 

.06316 

1985 

540 

24.50 

50-39 

15474 

$  Oil-hard- 

16 

• 

)    ened 

.07066 

733 

— 

— 

— 

- 

17 

Silicon  steel 

As  forged 

.06163 

15148 

II073 

9.49 

1  2.6o 

45740 

18 

«<        « 

Annealed 

.06185 

14701 

8149 

7.80 

10.74 

36485 

!9 

u            « 

(  Oil-hard- 
\    ened 

.06195 

14696 

8084 

12.75 

17.14 

596i9 

20 

Chrome  steel     . 

As  forged 

.02016 

15778 

9318 

12.24 

I3-87 

6i439 

21 

«         « 

Annealed 

.01942 

14848 

7570 

8.98 

12.24 

42425 

22 

«(         « 

(  Oil-hard- 
(    ened 

.02708 

13960 

8595 

38-15 

48.45 

169455 

23 

"         "... 

As  forged 

.01791 

14680 

7568 

18.40 

22.03 

85944 

24 

"         "       .         . 

Annealed 

.01849 

!3233 

6489 

15.40 

19.79 

64842 

25 

((                   U 

(  Oil-hard- 
\    ened 

•03035 

12868 

7891 

40.80 

56.70 

167050 

26 

27 

Tungsten  steel  . 

As  forged 
Annealed 

.02249 
.02250 

i57i8 
16498 

IOI44 
IIOOS 

15.71 
I5-30 

17-75 
16.93 

es 

(  Hardened 

28 

«            « 

<    in  cold 

.02274 

- 

- 

- 

- 

- 

(    water 

(  Hardened 

29 

««            «« 

|    in  tepid 

.02249 

15610 

9482 

30.10 

34-70 

149500 

(    water 

30 

"            "     (French)    . 

(  Oil  hard- 
(    ened 

.03604 

14480 

8643 

47.07 

64.46 

216864 

31 

«                 «< 

Very  hard 

.04427 

12133 

68l8 

51.20 

70.69 

197660 

32 

Gray  cast  iron    . 

— 

.11400 

9148 

3l6l 

13-67 

I7.03 

39789 

33 

Mottled  cast  iron 

— 

.06286 

10546 

5108 

12.24 

— 

41072 

34 

White        " 

- 

.05661 

9342 

5554 

12*4 

20.40 

36383 

35 

Spiegeleisen 

.10520 

385 

77 

SMITHSONIAN  TABLES. 


368  TABLES  446-448.    MAGNETIC  PROPERTIES  OF  IRON, 

TABLE  446.  -Magnetic  Properties  of  Iron  and  Steel. 


Electro- 

Good 

Poor 

Electrical  Sheets. 

("act 

Cast 

Steel 

Cast 

lytic 
Iron. 

Steel. 

Steel. 

Iron. 

Silicon 

Ordinary. 

Steel. 

[C 

O.O24 

0.044 

0.56 

0.99 

3-" 

0.036 

0.036 

Chemical  composi-  1  j^ 
tion  in  per  cent     j  p 

O.OO4 
O.OOS 
0.008 

0.004 
0.40 
0.044 

0.18 
0.29 
0.076 

O.IO 

0.40 
0.04 

3-27 
0.56 
1.05 

0-33° 
0.200 
0.040 

3-90 
0.090 
0.009 

[s 

O.OOI 

0.027 

0-035 

0.07 

0.06 

0.068 

O.OO6 

Coercive  force    .     .     .    < 

2.83 
[0.36] 

[0-37] 

(4*3) 

16.7 
(52.4) 

11.4 
[4-6] 

[1-30] 

[0.77] 

Residual  B     .    .     .     .    | 

11400 
[10800] 

10600 
[iiooo] 

10500 
(10500) 

13000 
(75°°) 

5100 
[5350] 

[9400] 

[9850] 

Maximum  permeability  < 

1850 
[14400] 

3550 
[14800] 

700 
(170) 

375 

(1  10) 

240 
[600] 

[3270] 

[6I30] 

B  for  H=i50     .     .     .    | 

19200 

[18900] 

18800 
[19100] 

17400 
(15400) 

16700 
(11700) 

10400 
[iiooo] 

[18200] 

[17550] 

4*1  for  saturation        .    j 

21620 

[21630] 

21420 

[21420] 

20600 
(20200) 

19800 
(18000) 

16400 

[16800] 

[20500] 

[I9260] 

E.  Gumlich,  Zs.  fur  Electrochemie,  15,  p.  599;  1909. 
Brackets  indicate  annealing  at  800°  C  in  vacuum.  Parentheses  indicate  hardening  by  quenching  from  cherry-red. 

TABLE   447. -Oast  Iron  in  Intense  Fields. 


Soft  Cast  Iron. 

Hard  Cast  Iron. 

H 

B 

I 

\t- 

H 

B 

I 

V- 

114 
172 

9950 
10800 

782 
846 

87.3 
62.8 

142 

254 

7860 
9700 

6l4 

752 

55-4 
38.2 

433 

13900 

1070 

32.1 

339 

10850 

836 

30.6 

744 

'5750 

1200 

21.2 

684 

13050 

983 

19.1 

1234 

17300 

1280 

14.0 

9i5 

14050 

1044 

154 

1820 

18170 

I3OO 

IO.O 

1570 

15900 

1138 

IO.I 

12700 

31100 

1465 

2-5 

2O2O 

16800 

1176 

8-3 

13550 

32100 

'475 

2.4 

lOOXXD 

26540 

1245 

2.4 

13800 

32500 

1488 

2.4 

I32OO 

28600 

1226 

2.2 

15100 

33650 

1472 

2.2 

14800 

30200 

1226 

2.0 

B.  O.  Peirce,  Proc.  Am.  Acad.  44,  1909. 

TABLE  448.  —  Corrections  for  Ring  Specimens. 

In  the  case  of  ring  specimens,  the  average  magnetizing  force  is  not  the  value  at  the  mean  radius, 
the  ratio  of  the  two  being  given  in  the  table.  The  flux  density  consequently  is  not  uniform,  and 
the  measured  hysteresis  is  less  than  it  would  be  for  a  uniform  distribution.  This  ratio  is  also  given 
for  the  case  of  constant  permeability,  the  values  being  applicable  for  magnetizations  in  the  neigh- 
borhood of  the  maximum  permeability.  For  higher  magnetizations  the  flux  density  is  more  uni- 
form, for  lower  it  is  less,  and  the  correction  greater. 


Ratio  of 
Radial 
Width  to 

Ratio  of  Average  H  to 
H  at  Mean  Radius. 

Ratio  of  Hysteresis  for  Uniform 
Distribution  to  Actual  Hysteresis. 

Diameter 
of  Ring. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

1/2 

.0086 

1.0718 

1.  112 

1.084 

1/3 

•0397 

1.0294 

1.045 

1-033 

*/4 

.0216 

I.OI62 

I.O24 

1.018 

l/A 

•0137 

I.OI02 

I.OI5 

.on 

1/6 

.0094 

.0070 

I.OIO 

.008 

1/7 

.0069 

.0052 

1.  008 

.006 

1/8 

.0052 

.0040 

I.  OO6 

.004 

I  /IO 

•0033 

.0025 

1.003 

.002 

1/19 

.0009 

.0007 

I.OOI 

.001 

M.  G.  Lloyd,  Bull.  Bur.  Standards,  5,  p  435;  1908. 


SMITHSONIAN  TABLES. 


TABLES  449-451. 

MAGNETIC    PROPERTIES   OF    IRONS   AND    STEELS- 
TABLE  449.  —  Magnetic  Properties  of  Various  Types  of  Iron  and  Steel. 
From  tests  made  at  the  Bureau  of  Standards.    B  and  //  are  measured  in  cgs  units. 


Values  of  B. 

200O 

4000 

6000 

8000 

10,000 

12,000 

14,000 

16,000 

18,000 

20,000 

Annealed  Norway  iron 

H 

M 

.81 

2470 

1.15 

3480 

1.60 

3750 

2.18 

3670 

3.06 

3270 

4.45 

2700 

7.25 

1930 

23.6 

680 

116. 

150 



Cast  semi-steel  
Machinery  steel 

H 

M 

H 

M 

2.00 

IOOO 

5.0 

400 

2.90 

1380 

8.8 

455 

4.30 

1400 

13.1 

460 

6.46 

1240 

18.6 

430 

9.82 

IO2O 

25.8 

390 

15.1 

795 

35.8 

340 

24.9 

563 

50.5 

280 

50.5 

3i7 

76.0 

210 

135. 
133 

142. 

127 

325. 

62. 

TABLE  450.  —  Magnetic  Properties  of  a  Specimen  of  Very  Pure  Iron  (.017%  C). 
From  tests  at  the  Bureau  of  Standards.    B  and  H  are  measured  in  cgs  units. 


Values  of  B 

200O 

4000 

6000 

8000 

10,000 

12,000 

14,000 

16,000 

18,000 

20,000 

Very  pure  iron  \ 
as  received    J 

H 

M 

3.30 

606 

4.48 

893 

6.35 

945 

9.10 

880 

13.0 

770 

18.9 

635 

28.8 

486 

47.0 

340 

103. 

i75 

240. 

83 

Annealed  in  vacuo  1 
from  900°  C         / 

H 

M 

.46 

435° 

.60 

6670 

.80 

7500 

1.02 

7840 

1.38 

7250 

2.00 

6000 

3.20 

4380 

11.3 

1420 

72.0 

250 

194. 

103 

As  received:  //max       150 

-Bmax  18,900 
Br  7,650 

He         2.8 


After  annealing:  //max       150 
Bmsu.  19,500 

He       0.53 


TABLE  451.  —  Magnetic  Properties  of  Electrical  Sheets. 
From  tests  at  the  Bureau  of  Standards.    B  and  H  are  measured  in  cgs  units. 


Values  of  B 

2OOO 

4000 

6000 

8000 

10,000 

12,000 

14,000 

16,000 

18,000 

20,000 

Dynamo  steel 

H 

M 

1.00 

2OOO 

1.10 

3640 

1.43 

4200 

2.00 

4000 

3.10 

3220 

4.95 

2420 

9.20 

1520 

34.0 

470 

114. 

158 



Ordinary  trans-  1 
former  steel    / 

H 

M 

.60 

3340 

.87 

4600 

1.10 

5450 

1.48 

5400 

2.28 

4380 

3.86 

3120 

10.9 

1280 

43.0 

372 

149. 

121 



High  silicon  trans-  1 
former  steel        / 

H 
M 

.60 

4000 

.70 

5720 

.90 

6670 

1.28 

6250 

1.99 

5020 

3.60 

3340 

9.80 
143° 

47.4 
338 

166. 

109 

— 

SMITHSONIAN  TABLES. 


370 


TABLES  462-455. 

MAGNETIC    PROPERTIES   OF    IRONS    AND    STEELS- 
TABLE  452.  —  Magnetic  Properties  of  Two  Types  of  American  Magnet  Steel. 

From  tests  at  the  Bureau  of  Standards.    B  and  H  are  measured  in  cgs  units. 


Values  of  B 

2OOO 

4000 

6000 

8000 

10,000 

I2.OOO 

14,000 

16,000 

18,000 

20,000 

Tungsten  steel  . 

H 

35-0 

53-3 

63-3 

72.0 

83-4 

lOQ 

200 







M 

57 

75 

95 

in 

I2O 

110 

70 

— 

— 

— 

Chrome  steel.  .  . 

H 

34-  S 

49-0 

63.5 

88.4 

143 

270 

— 

— 

— 

— 

M 

S» 

82 

95 

91 

70 

45 

Percentage  composition:  Tungsten  steel,    €0.67     Ws.i       Cr    2.09     Si  0.25 
Chrome  steel,    C  0.81     W  0.96     Mn  0.38     Si  0.26 
Tungsten  steel:  77max  200      5max  14,000       Chrome  steel:  77max  200      Z?max  11.050 

He  62.5      BT  10,400  He  45.7      Br 


TABLE  453. -Magnetic  Properties  of  a  Ferro-Cobalt  Alloy,  Fe2Co  (35%  Cobalt). 
From  tests  at  the  Bureau  of  Standards.    B  and  H  are  measured  in  cgs  units. 


Values  of  B 

20OO 

4000 

6000 

8000 

10,000 

12,000 

14,000 

16,000 

18,000 

20,000 

As  received  

H 

M 

3.10 
645 

4-28 
935 

5-50 

IOOO 

7.17 
"IS 

9-65 
1040 

13-4 
900 

I9.I 

730 

27-3 
590 

40.0 
450 

65.0 
3io 

Annealed  at  \ 
1000°  C  / 

H 

M 

3-oo 
670 

4.11 
970 

5  -05 
1190 

6-45 
1240 

8.40 
1190 

II-  3 
1060 

15-4 
910 

21.9 
730 

3L7 

570 

50.6 
400 

Quenched     \ 
from  1000°  C  / 

H 

fJ- 

10.8 
185 

13-8 
290 

19.1 
314 

28.7 
279 

43-4 
230 

6S.8 
182 

104 
135 

163 
98 

262 
69 

— 

As  received 

Annealed  at  1000°  C      5max 

Quenched  from  1000°  C 


15,000 
15,000 
15,000 


22.9 

ZJmax  \    18.3 
1  130. 


750 

Br  \  7460 
8240 


[    3.79 
He\    3.95 
(14.  3 


TABLE  454.  —  Magnetic  Properties  of  a  Ring  Sample  of  Transformer  Steel 
in  Very  Weak  Fields. 

From  tests  made  at  the  Bureau  of  Standards.     B  and  H  are  measured  in  cgs  units. 


Values  of  H  
Values  of  B 

O.OOI 

o  45 

O.002 

0.004 
I  8<; 

0.006 

2    8? 

0.008 

O.OIO 

O.OI2 

O.OI4 

0.018 

O.02O 

462 

478 

•5* 

*66 

TABLE  455.  —  Magnetic  Properties  of  Iron  in  Very  Weak  Fields. 

The  effect  of  very  small  magnetizing  forces  has  been  studied  by  C.  Baur  and  by  Lord  Rayleigh.  The  following 
short  table  is  taken  from  Baur's  paper,  and  is  taken  by  him  to  indicate  that  the  susceptibility  is  finite  for  zero  values 
of  H  and  for  a  finite  range  increases  in  simple  proportion  to  H.  He  gives  the  formula  k  =  15  +  looF,  or  /  =  isH 
+  ioo772  The  experiments  were  made  on  an  annealed  ring  of  round  bar  1.013  cms  radius,  the  ring  having  a  radius  of 
9.432  cms.  Lord  Rayleigh's  results  for  an  iron  wire  not  annealed  give  k  =  6.4  +  S.iH,  or  /  =  6.4#  +  S-iH*.  The 
forces  were  reduced  as  low  as  0.00004  cgs,  the  relation  of  k  to  H  remaining  constant. 


First  experiment. 

Second  experiment. 

n 

k 

/ 

77 

k 

.01580 
.03081 
.07083 
.13188 

16.46 
17-65 
23.00 
28.90 

2.63 
5-47 
16-33 
38.15 

.0130 
.0847 
.0946 
.1864 

15.50 
18.38 
20.49 
25.07 

.23011 
.38422 

39-Si 
58.56 

91.56 
224.87 

.2903 
•3397 

32.40 
35-20 

SMITHSONIAN  TABLES. 


TABLES  456-458. 


37' 


PERMEABILITY  OF  SOME  OF  TKE    SPECIMENS  IN  TABLE  445. 

TABLE  456. 

This  table  gives  the  induction  and  the  permeability  for  different  values  of  the  magnetizing  force  of  some  of  the  spec* 
mens  in  Table  445-  The  specimen  numbers  refer  to  the  same  table.  The  numbers  in  this  table  have  been  taken 
from  the  curves  given  by  Dr.  Hopkinson,  and  may  therefore  be  slightly  in  error;  they  are  the  mean  values  for 
rising  and  falling  magnetizations. 


Magnetiz- 
ing force. 
H 

Specimen  i  (iron). 

Specimen  8 
(annealed  steel). 

Specimen  9  (same  as 
8  tempered). 

Specimen  3 
(cast  iron). 

B 

» 

B 

* 

B 

M 

B 

M 

I 

- 

_ 

_ 

- 

- 

_ 

265 

265 

2 

2OO 

IOO 

— 

— 

— 

— 

700 

35° 

3 

- 

- 

- 

- 

- 

- 

1625 

542 

5 
10 

10050 
12550 

2010 

1255 

1525 
9000 

300 
900 

750 
1650 

'50 
165 

3000 

600 
500 

20 
30 

15200 

727 

11500 
12650 

575 
422 

5875 
9875 

294 
329 

6500 

300 
217 

40 

15800 

395 

13300 

332 

11600 

290 

7IOO 

177 

50 

16000 

320 

13800 

276 

12000 

240 

7350 

149 

70 

16360 

14350 

205 

13400 

191 

7900 

"3 

IOO 

16800 

168 

14900 

149 

I45OO 

8500 

85 

150 

17400 

116 

15700 

105 

15800 

105 

9500 

63 

200 

17950 

90 

l6lOO 

80 

IOIOO 

80 

10190 

•5I 

T»bleg.«7-8,  463-6  give  the  results  of  some  experiments  by  Du  Bois,*  on  the  magnetic  properties  of  iron,  nickel,  and 
cobalt  under  strong  magnetizing  forces.  The  experiments  were  made  on  ovoids  of  the  metals  18  centimeters  long 
and  0.6  centimeters  diameter.  The  specimens  were  as  follows:  (i)  Soft  Swedish  iron  carefully  annealed  and 
having  a  density  7.82.  (2)  Hard  English  cast  steel  yellow  tempered  at  230°  C. ;  density  7.78.  (3)  Hard  drawn 
best  nickel  containing  99  %  Ni  with  some  SiO2  and  traces  of  Fe  and  Cu ;  density  8.82.  (4)  Cast  cobalt  giving 
the  following  composition  on  analysis:  Co  =  93.1,  Ni:=5.8,  Fe^^o.8,  Cu  =  o.2,  Si  =  o.i,  and  €  =  0.3.  The  speci- 
men was  very  brittle  and  broke  in  the  lathe,  and  hence  contained  a  surfaced  joint  held  together  by  clamps  during 
the  experiment.  Referring  to  the  columns,  //,  B,  and  n  have  the  same  meaning  as  in  the  other  tables,  S  is  the 
magnetic  moment  per  gram,  and  /  the  magnetic  moment  per  cubic  centimeter.  H  and  6"  are  taken  from  the 
curves  published  by  Du  Bois ;  the  others  have  been  calculated  using  the  densities  given. 

MAGNETIC  PROPERTIES  OF  SOFT  IRON  AT  0°  AND  1OO°  C. 

TABLE  457. 


Soft  iron  at  o°  C. 

Soft  iron  at  100°  C. 

H 

s 

/ 

B 

/* 

H 

S 

7 

B 

/* 

IOO 

iSo.O 

1408 

17790 

177.9 

IOO 

ISO.O 

1402 

17720 

177.2 

200 
400 

194-5 
208.0 

1521 

1627 

I93IO 
20830 

96.5 

52-1 

2OO 
4OO 

194.0 
2O7.O 

T1 
1613 

I9i90 
20660 

96.0 
51.6 

700 

215.5 

1685 

21870 

31.2 

700 

213.4 

1663 

21590 

29.8 

1000 

218.0 

1705 

22420 

22.4 

1000 

215.0 

1674 

22040 

21.0 

I2OO 

218.5 

1709 

22670 

18.9 

1200 

215-5 

1679 

22300 

18.6 

MAGNETIC  PROPERTIES  OF  STEEL  AT  O°  AND   1OO°  C. 

TABLE   458. 


Steel  at  o°  C. 

Steel  at  100°  C. 

H 

s 

I 

B 

M 

H 

S 

/ 

B 

^ 

IOO 

165.0 

1283 

16240 

162.4 

IOO 

165.0 

1278 

16170 

161.7 

2OO 

181.0 

1408 

17900 

89-5 

200 

180.0 

U95 

17730 

88.6 

400 

700 

193.0 
'99-5 

1500 
1552 

19250 
2O2IO 

48.1 
28.9 

400 
700 

191.0 
197.0 

1480 

1527 

19000 

47-5 
28.4 

1000 

203-5 

1583 

20900 

20.9 

IOOO 

199.0 

*543 

20380 

20.4 

1200 

205.0 

J595 

2I24O 

17.7 

1500 

203.0 

'573 

21270 

14.2 

375ot 

212.0 

1650 

24470 

6.5 

3000 
5000 

20<.5 
205.0 

1593 
1612 

23020 
25260 

7-7 
5-i 

*  "Phil.  Mag."  5  series,  vol.  xxix. 

t  The  results  in  this  and  the  other  tables  for  forces  above  1200  were  not  obtained  from  the  ovoids  above  referred 
to,  but  from  a  small  piece  of  the  metal  provided  with  a  polished  mirror  surface  and  placed,  with  its  polished  face  nor- 
mal to  the  lines  of  force,  between  the  poles  of  a  powerful  electromagnet.  The  induction  was  then  inferred  from 
the  rotation  of  the  plane  of  a  polarized  ray  of  red  light  reflected  normally  from  the  surface.  (See  Kerr's  "  Constants." 
P-  33I-) 
SMITHSONIAN  TABLES. 


372 


TABLES  45^-462. 

MAGNETISM    AND    TEMPERATURE. 
TABLE  459.  —  Magnetism  and  Temperature,  Critical  Temperature. 


The  magnetic  moment  of  a  magnet  diminishes  with  increasing  temperature.  Different  specimens  vary  widely. 
In  the  formula  Mt/Mo  =  (i  —  at)  the  value  of  a  may  range  from  .0003  to  .001  (see  Tables  457-458).  The  effect  on  the 
permeability  with  weak  fields  may  at  first  be  an  increase.  There  is  a  critical  temperature  (Curie  point)  above  which 
the  permeability  is  very  small  (paramagnetic?).  Diamagnetk  susceptibility  does  not  change  with  the  temperature. 
Paramagnetic  susceptibility  decreases  with  increase  in  temperature.  This  and  the  succeeding  two  tables  are  taken 
from  Dushman.  "  Theories  of  Magnetism,"  General  Electric  Review,  1916. 


Substance. 

Critical 
temperature, 
Curie  point. 

Refer- 
ence. 

Substance. 

Critical 
temperature, 
Curie  point. 

Refer- 
ence. 

Iron  a  form 

7*6°  C 

MnBi 

360  to  380°  C 

'  '  0  form  .'.'.'.'.'.'.'.'.'.'.'.'.' 

920 
1280 

MnSb  
MnAs  

310  "  320 
45  "     5° 

4 

Magnetite  (FejOO 

536 

MnP  

18  "     25 

589 

Heusler  alloy  

310 

^ 

ii 

555 

3 

Nickel  

340 

Cobalt-ferrite  (FeiCo) 

376 

5 

Cobalt  

1075 

6 

References:  (i)  P.  Curie;  (2)  see  Williams,  Electron  Theory  of  Magnetism,  quoted  from  Weiss;  (3)  du  Bois, 
Tr.  Far.  Soc.  8,  211,  1912;  (4)  Hilpert,  Tr.  Far.  Soc.  8,  207, 1912;  (5)  Gumaer;  (6)  Stifler,  Phys.  Rev.  33,  268,  1911. 

TABLE  460.  —  Temperature  Variation  for  Paramagnetic  Substances. 

The  relation  deduced  by  Curie  that  x  ~  C/T,  where  C  is  a  constant  and  T  the  absolute  temperature,  holds  for  some 
paramagnetic  substances  over  the  ranges  given  in  the  following  table.  Many  paramagnetic  substances  do  not  obey  the 
law  (Honda  and  Owen,  Ann.  d.  Phys.  32,  1027,  1910;  37,  657,  1912).  See  the  following  table. 


Substance. 

C  X  io« 

Range  °  C 

Refer- 
ence. 

Substance.     - 

C  X  ID" 

Range  °  C 

Refer-  | 
ence. 

Oxygen  
Air  
Palladium  
Magnetite  
Cast  iron  

33,700 
7,830 
1,520 
28,000 
38,500 

20°  to  450°  C 

20  to  1370 
850    "  1360 
850    "  1267 

Gadolinium  sulphate. 
Ferrous  sulphate.  .  .  . 
Ferric  sulphate  
Manganese  chloride. 

21,000 

11,000 

17,000 
30,000 

—  259°  to  17 
-259    "  17 
—  208    "  17 
—258    "  17 

2 
2 

3 
3 

References:  (i)  P.  Curie,  London  Electrician,  66,  500,  1912;  see  also  Du  Bois,  Rap.  du  Cong.  2,  460,  1900;  (2)  Per- 
rier,  Onnes,  Tables  annuelles,  3,  288,  1914;   (3)  Oosterhuis,  Onnes,  I.e.  2,  389,  1913. 


TABLE  461.  —  Temperature  Effect  on  Susceptibility  of  Diamagnetic  Elements. 


No  effect: 


B  Cryst.  400  to  1200° 
C  Diamond,  +170  to  200° 
C  "Sugar"  carbon 
Si  Cryst. 


P    white 
S     Cryst.;  ppt. 
Zn  —170  to  300° 
As  — 


Se        — 

Br  —170  to  18° 

Zr   Cryst.  —170  to  500° 

Cd  —170  to  300° 


Increase  with  rise  in  Temperature: 

Be 

B    Cryst.  +170  to  400° 

Decrease  with  rise  in  Temperature: 

C    Amorphous  Gd  — 1791030° 

C    Ceylon  graphite  Ge  —170  to  ooo 

Cu  Zr   500  to  1200° 

Zn  +300  to  700°  Cd  300  to  700° 


C    Diamond,  200  to  1200° 
Ag  - 


In  —170  to  150° 
Sb  +50  to  +631° 
Te  — 

I       +114  tO   +200° 


Sb  —170  to  50° 
Cs  and  Au 
Hg  —39  to  +350° 
Pb  327  to  600° 


I      —170  to  114° 
Hg  —170  to  —30* 


Tl  — 

Pb  —170  to  327° 
Bi   —170  to  268* 


TABLE  462.  —  Temperature  Effects  on  Susceptibility  of  Paramagnetic  Elements. 


No  effect: 


Li          — 

Na  —170  to  97° 

Al   657  to  1100° 


K  —i 70  to  150° 
Ca  —170  to  18° 
V  —170  to  500° 


Increase  with  rise  in  Temperature: 

Ti    —40  to  1100°  Cr     500  to  1100° 

V     500  to  1100°  Mo  —170  to  1200° 

Decrease  with  rise  in  Temperature: 

(O)  Ti  -iSoto  -40° 


As    -i 70  to  657° 
Mg  — 


Mn  250  to  1015° 
(Fe) 


Cr  —170  to  500° 
Mn  —170  to  250° 
Rb  — 


Ru  +550  to  1200° 
Rh  — 


Ni  350  to  800° 
Co  above  1150° 
Cb  —170  to  400° 


W 
Os 


Ba  —170  to  18° 
Ir  and  Th 


Pd  and  Ta 

Pt  and  U 

Rare  earth  metals 


Tables  461  and  462  are  due  to  Honda  and  Owen;  for  reference,  see  preceding  table. 
SMITHSONIAN  TABLES. 


TABLES  463-469. 
MAGNETIC    PROPERTIES    OF    METALS. 

TABLE  463.-  Cobalt  at  100°  0.  TABLE  464. -Nickel  at  100    0. 


373 


H 

S 

/ 

B 

M 

200 

1  06 

848 

10850 

54-2 

300 

116 

928 

11960 

39-9 

500 
700 

127 
'31 

1016 
1048 

13260 
13870 

26.5 
19.8 

IOOO 

'34 

1076 

14520 

M-5 

1500 

t38 

1104 

15380 

10.3 

2500 

143 

1144 

16870 

6.7 

4000 

MS 

1164 

18630 

4-7 

6000 

M7 

1176 

20780 

3-5 

9000 

149 

1192 

23980 

2.6 

At  o°  C.  this  specimen  gave  the  fol- 

lowing results  : 

7900  |  154 

I  2  "^2 

23380 

3-o 

H 

S 

/ 

B 

ft 

IOO 
2OO 
300 

35-o 
43-o 
46.0 

309 
380 
406 

3980 
4966 
5399 

39-8 
24.8 
18.0 

500 

50.0 

441 

6043 

12.  1 

700 

Si-5 

454 

6409 

9.I 

IOOO 

1500 

56.0 

468 
494 

6875 
7707 

6.9 

5-1 

2500 

S8-4 

515 

8973 

3-6 

4000 

59-° 

520 

10540 

2.6 

6000 

59-2 

522 

12561 

2.1 

9000 

59-4 

524 

I5585 

i-7 

12000 

Ato°  C 

59-6 

,.  this  si 

526 
:>ecimer 

i  gave  th 

e  fol- 

lowing  results  : 

12300    |    67.5 

595    1  I97»2 

1.6 

TABLE   465.  —  Magnetite. 

The  following  results  are  given  by  Du  Bois  *  for  a  specimen  of  magnetite. 


H 

/     [      B 

M 

500 

325 

8361 

I6.7 

IOOO 

345 

9041 

9.0 

2OOO 

35° 

10084 

5-o 

I2OOO 

35° 

20084 

i-7 

Professor  Ewing  has  investigated  the  effects  of  very  intense  fields  on  the  induction  in  iron  and  other  metals.t  The 
results  show  that  the  intensity  of  magnetization  does  not  increase  much  in  iron  after  the  field  has  reached  an  in- 
tensity of  looo  c.  g.  s.  units,  the  increase  of  induction  above  this  being  almost  the  same  as  if  the  iron  were  not 
there,  that  is  to  say,  dBl dH  is  practically  unity.  For  hard  steels,  and  particularly  manganese  steels,  much  higher 
forces  are  required  to  produce  saturation.  Hadfield's  manganese  steel  seems  to  have  nearly  constant  susceptibility 
up  to  a  magnetizing  force  of  10,000.  The  following  tables,  taken  from  living's  papers,  illustrate  the  effects  of 
strong  fields  on  iron  and  steel. 


The  results  for  nickel  and  cobalt  do  not  differ  greatly  from  those  given  above. 


TABLE   466.  — Lowmoor 
Wrought  Iron. 


H 

/ 

B 

V- 

3080 
6450 
10450 
13600 
16390 
18760 
18980 

1680 
1740 

173° 
1720 
1630 
1680 
173° 

24130 
28300 
32250 
35200 
36810 
39900 
40730 

7.83 

4-39 
3-09 
2-59 
2.25 
2.13 
2.15 

TABLE  467.  —  Vlcker's 
Tool  Steel. 


H 

/ 

B 

M 

6210 

9970 
I2I2O 
14660 

I553° 

1530 

1570 

1550 
1610 

25480 
29650 
31620 

3455° 
35820 

4-IO 
2.97 
2.60 
2.36 
2.31 

TABLE  468.  -Hadlield's 
Manganese  Steel. 


1930 
2380 
335° 
5920 
6620 
7890 
8, 

10 


in 

187 
191 


2620 

3430 
4400 

7310 

8970 

10290 

11690 

14790 


1.36 
1.44 

1.24 

1.30 

J-39 
1.51 


TABLE   469.  — Saturation  Valnes  for  Steels  of  Different  Kinds. 


i  « 

7 

B 

* 

I 

Bessemer  steel  containing  about  0.4  per  cent  carbon  .     . 
Siemens-Marten  steel  containing  about  0.5  per  cent  carbon      18000 

1770 
1660 

»88o 

38860 

2.16 

3 

Crucible  steel  for  making  chisels,  containing  about  0.6  per  , 

_onf.  ^orKr-n                                                                                             1  047° 

1480 

38010 

1.95 

4 

Finer  quality  of  3  containing  about  0.8  per  cent  carbon  .     .      18330 

1580 
1440 

38190 
37690 

2.08 
1.92 

i 

Crucible  steel  containing  I  per  cent  carbon    
Whitworth's  fluid-compressed  steel  I 

1590 

38710 

2.07 

*  "  Phil.  Mag."  5  series,  vol.  xxix,  1890. 
SMITHSONIAN   TABLES. 


t  "  Phil.  Trans.  Roy.  Soc."  1885  and  1889. 


374  TABLES  47O-471. 

DEMAGNETIZING  FACTORS   FOR   RODS. 

TABLE   470. 

ff=  true  intensity  o*  magnetizing  field,  H'  =  intensity  of  applied  field,  /=  in- 
tensity of  magnetization,  H=H' — .AY. 

Shuddemagen  says :  The  demagnetizing  factor  is  not  a  constant,  falling  for 
highest  values  of  /to  about  1/7  the  value  when  unsaturated;  for  values  of  B 
(=^H~4ir/)  less  than  10000,  N  is  approximately  constant;  using  a  solenoid 
wound  on  an  insulating  tube,  or  a  tube  of  split  brass,  the  reversal  method  gives 
values  for  TV  which  are  considerably  lower  than  those  given  by  the  step-by-step 
method  ;  if  the  solenoid  is  wound  on  a  thick  brass  tube,  the  two  methods  prac- 
tically agree. 


Values  of  NX  10*. 

Cylinder. 

Ratio 
of 

Ballistic  Step  Method. 

Length 
to 
Diameter. 

Ellipsoid. 

Uniform 
Magneti- 

Magneto- 
metric 

Dubois. 

Shuddemagen  for  Range  of 
Practical  Constancy. 

zation. 

(Mann). 

Diameter. 

0.158  cm. 

0.3  1  75  cm. 

i.i  1  1  cm. 

1.905  cm. 

5 

7015 

_ 

6800 

10 

2549 

630 

255° 

2l6o 

- 

- 

1960 

15 

1350 

280 

1400 

I2O6 

— 

— 

1075 

20 

848 

160 

898 

775 

— 

— 

67I 

3° 

432 

70 

460 

393 

388 

350 

343 

40 

266 

39 

274 

238 

234 

212 

209 

e 

181 
132 

3 

182 

n8 

116 

lol 

149 
106 

7° 

101 

13 

99 

89 

88 

80 

80 

9.8 

78 

69 

69 

66 

63 

90 

65 

7-8 

63 

55 

56 

IOO 

54 

6-3 

51.8 

45 

46 

41 

41 

150 

26 

2.8 

25.1 

20 

23 

21 

21 

200 

16 

1.57 

15.2 

ii 

12.5 

II 

II 

300 

7-5 

0.70 

7-5 

5*° 

4OO 

4-5 

2.8 

C.  R.  Mann,  Physical  Review,  3,  p.  359;  1896. 

H.  DuBois,  Wied.  Ann.  7,  p.  942 ;  1002. 

C.  L.  B.  Shuddemagen,  Proc.  Am.  Acad.  Arts  and  Sci.  43, 


p.  185,  1907  (Bibliography). 


TABLE    471. 

Shuddemagen  also  gives  the  following,  where  B  is  determined  by  the  step  method 

and/f=//'— KB. 


Ratio  of 

Values  of  KX  10*. 

to 
Diameter. 

Diameter 
0.3175  cm. 

Diameter 
i.i  to  2.0  cm. 

15 

_ 

85.2 

2O 

— 

53-3 

25 

- 

36.6 

30 

30-9 

27-3 

40 

18.6 

16.6 

50 

12.7 

1  1.6 

60 

9.25 

8-45 

80 
IOO 

3*66 

5-05 
3.26 

I50 

1.83 

1.67 

SMITHSONIAN  TABLES. 


TABLE  472. 


375 


DISSIPATION  OF  ENERGY  IN   THE   CYCLIC  MAGNETIZATION  OF  VARIOUS 

SUBSTANCES. 

C.  P.  Steinmetz  concludes  from  his  experiments*  that  the  dissipation  of  energy  due  to 
hysteresis  in  magnetic  metals  can  be  expressed  by  the  formula  e  =  aBlA,  where  e  is  the  energy 
dissipated  and  a  a  constant.  He  also  concludes  that  the  dissipation  is  the  same  for  the  same 
range  of  induction,  no  matter  what  the  absolute  value  of  the  terminal  inductions  may  be.  His 
experiments  show  this  to  be  nearly  true  when  the  induction  does  not  exceed  j-  1 5000  c.  g.  8. 
units  per  sq.  cm.  It  is  possible  that,  if  metallic  induction  only  be  taken,  this  may  be  true  up  to 
saturation  ;  but  it  is  not  likely  to  be  found  to  hold  for  total  inductions  much  above  the  satura- 
tion value  of  the  metal.  The  law  of  variation  of  dissipation  with  induction  range  in  the  cycle, 
stated  in  the  above  formula,  is  also  subject  to  verification.! 


Values  of  Constant  a. 

The  following  table  gives  the  values  of  the  constant  a  as  found  by  Steinmetz  for  a  number  of  different  specimens. 
The  data  are  taken  from  his  second  paper. 


Number  of 
specimen. 

Kind  of  material. 

Description  of  specimen. 

Value  of 

0. 

Iron 

„ 

.00^48 

3 

(( 

.00458 

4 

u 

.OO2o6 

6 

M 

Medium  thickness  tin  plate       

.00425 

Steel 

.00349 

7 

0 

(i 

.00848 

(l 

9 

{< 

ii 

u 

Same  as  8  tempered  in  cold  water    .... 

.02792 

12 

a 

Tool  steel  glass  hard  tempered  in  water 

.07476 

13 

a 

"        "      tempered  in  oil         

.02670 

14 

u 

"        "      annealed  

.01899 

15 

"                    '  ) 

(  Same  as  12,  13,  and  14,  after  having  been  subjected  ) 

(  .06130 

16 

"                    •  f 

?  to   an   alternating  m.  m.  f.  of  from  4000  to  6000  > 

]  .02700 

17 

"                    •  ) 

r  ampere  turns  for  demagnetization    .         .         .         .  ) 

(  -01445 

^      ,   . 

f~\                             of      "*-/-\T1 

.01300 

Io 
19 

"        "       "     containing  J  %  aluminium 

•01365 

20 

<(            « 

"        "       "             "          -J  %         "                  • 

.01459 

21 

Magnetite  . 

(  A  square  rod  6  sq.  cms.  section  and  6.5  cms.  long,  ) 
1  from   the  Tilly  Foster  mines,  Brewsters,   Putnam  > 
(  County,  New  York,  stated  to  be  a  very  pure  sample  ) 

.02348 
.OI22 

(  Annealed    wire,     calculated    by    Steinmetz    from  ) 

.0156 

23 
24 

|  Ewing's  experiments         ) 
Hardened,  also  from  Ewing's  experiments 

.0385 

25 

Cobalt 

$  Rod  containing  about  2  %  of  iron,  also  calculated  ) 
]  from  Ewing's  experiments  by  Steinmetz 
Consisted   of   thin   needle-like   chips  obtained  by 

.OI2O 

milling  grooves  about  8  mm.  wide  across  a  pile  of 
thin  sheets  clamped  together.     About  30  %  by  vol- 

26 

Iron  filings 

J  ume  of  the  specimen  was  iron. 
]  ist  experiment,  continuous  cyclic  variation  of  m.  m.  ) 

•0457 

2cl  experiment,  114  cycles  per  second 
[  3d          "            79~9r  cycles  per  second  . 

.0396 
•0373 

*  "  Trans.  Am.  Inst.  Elect.  Eng."  January  and  September,  1892. 
t  See  T.  Gray,  "  Proc.  Roy.  Soc."  vol.  Ivi. 


SMITHSONIAN  TABLES. 


376 


TABLE   473. 
ENERGY   LOSSES   IN   TRANSFORMER  STEELS. 


Determined  by  the  wattmeter  method. 

Loss  per  cycle  per  cc  =  AB* -\-lni B'J,  where  B  =  flux  density  in  gausses  and  n  =  frequency  in 

cycles  per  second,   x  shows  the  variation  of  hysteresis  with  B  between  5000  and  10000  gausses, 

and^y  the  same  for  eddy  currents. 


Ergs  per  Gramme  per  Cycle. 

Watts  per  Pound  at  60  Cy- 
cles and  loooo  Gausses. 

Thick- 

loooo Gausses. 

5000  Gausses. 

C    fcJQ 

Designation. 

ness. 

X 

y 

a 

5,3 

cm. 

Hyste- 

hi 

Hyste- 

S 

w* 

£  rT 

Hyste- 
resis. 

Total. 

resis.   i^'S^g 

resis. 

1^ 

ill 

Unannealed 

A 

0.0399 

!599 

186 

562 

46 

1.51 

2.  02 

0.00490 

0.41 

4-35 

4.76 

B 

.0326 

1156 

'34 

384 

36 

1.59  1.89 

•00358 

0.44 

3-14 

3-58 

C 

.0422 

1032 

242 

356 

70 

1.51    1.79 

.00319 

0.47 

2.81 

3.28 

D 

.0381 

1009 

184 

353 

48 

1.52  1  1.94 

.00312 

0.44 

2.74 

3-18 

Annealed 

•j 

E 

.0476 

735 

236 

246 

58 

1.58    !    2.02 

.00227 

0.36 

2.OO 

2.36 

F 

.0280 

666 

100 

220 

27 

i.  60       .88 

.00206       0.44 

1.81 

2.25 

G 

•0394 

563 

210 

193 

54 

i-54 

.96 

.00174  !  0.47 

r-53 

2.OO 

H* 

.0307 

412 

I46 

138-5 

39 

1.58 

.00127 

0.54 

1.  12 

1.66 

J 

.0318 

34  * 

2O2 

111.5 

55 

1.62 

.88 

.00105 

0.70 

0-93 

•63 

k* 

.0282 

394 

124 

130 

32 

1.61 

.90 

.00122 

0.54 

1.07 

.61 

L 
B 

.0346 
•0338 

38i 

354 

184 

2OO 

125 
116 

50 

57 

1.61 
1.61 

.88 
.81 

.00118 

.001  10 

0.535 

0.6  1 

1-035 
0.96 

•57 
•57 

M 

•0335 

372 

I78 

127 

46 

1.55 

•95 

.00115 

0-55 

I.OI 

.56 

N 

.0340 

3" 

210 

IO5 

56 

1.62 

.90 

.00099 

0.63 

0.87 

•5° 

P 

•0437 

334 

l84 

107 

50 

1.64 

.88 

.00103 

0-34 

0.91 

•25 

Silicon  steels 

Qt 

.0361 

3J3 

54 

98 

15 

1.63 

- 

.00094      0.14 

0.825 

0.965 

R 

•°3  '5 

288 

42  j    93 

n 

1.64 

— 

.00089 

0.15 

0.78 

0-93 

S 

.0452 

278 

72 

90 

18 

1.63 

_ 

.00086         0.12 

o-755 

0.875 

T 

•0338 

250 

60 

78 

18 

1.68 

_ 

.00077      °-r8 

0.68 

0.86 

U 

.0346 

270 

42 

86 

12 

1.66 

_ 

.00084         O-  1  2 

0-735 

0-855 

V* 

.0310 

25I-5 

47 

79 

13 

1.68 

_ 

.00078         0.17 

o.6§5 

0-855 

w* 

•0305 

197 

43 

62.3 

I2.4 

1.67 

_ 

.00061      o.i  6 

0-535     0.695 

X 

.0430 

200 

65 

64.2 

16.6     1.65 

- 

.00062 

O.I2 

0.545     0.665 

1             | 

*  German.  t   English. 

t  In  order  to  make  a  fair  comparison,  the  eddy  current  loss  has  been  computed  for  a  thickness  of  0.0357  cm.  (Gage 
No.  29),  assuming  the  loss  proportional  to  the  thickness. 

Lloyd  and  Fisher,  Bull.  Bur.  Standards,  5,  p.  453  ;  1909. 

Note.  -For  formula  and  tables  for  the  calculation  of  mutual  and  self  inductance  see  Bulletin  Bureau 
of  Standards,  vol.  8,  p.  1-237,  1912. 


SMITHSONIAN   TABLES. 


377 


TABLE   474. 
MAGNETIC    SUSCEPTIBILITY. 

If  31  is  the  intensity  of  magnetization  produced  in  a  substance  by  a  field  strength  ft   then  the 
magnetic  susceptibility  H  =  3I/*.  This  is  generally  referred  to  the  unit  mass;  italicized  figures 
refer  to  the  unit  volume.    The  susceptibility  depends  greatly  upon  the  purity  of  the  substai: 
pecially  its  freedom  from  iron.  The  mass  susceptibility  of  a  solution  containing  p  per  cent  by  weight 
of  a  water-free  substance  is,  if  H0  is  the  susceptibility  of  water,  (p/ioo)  H  +  (i  —  p/ioo)  HQ. 


Substance. 

HXio« 

!y 

Remark 

Substance. 

HXio« 

Remarks 

Ag    , 

O  IQ 

1  8° 

K.»CO« 

AgCl 

o  28 

—  O.CO 

1             O 

20° 

Sol'n 

Air,  i  Atm  .... 

-\-O.O24 

1C 

Mb    .     . 

4-0.38 

,0 

Al      

4-o.6c 

T* 

Mg 

f  0.04 

-0 

A12K2(S04)424H20 

—  i.o 

Crys. 

MgSO4.     , 

4-Q-55 

O  JO 

IB 

A,  i  Atm   .... 

—0.10 

o 

Mn    .     .     . 

4-ii 

iX 

As 

—  O  1 

rS 

MnPl 

Au    

W'J 
—  O.IC 

18 

MnSO4 

122. 

18 

,0 

Sol'n 

B  

O.7  I 

18 

BaCl2     

O.7.6 

20 

NH3 

O.OOI 

10 

Be     .... 

~'J" 
-4-O.7Q 

T  P 

Powd 

i  ]ya 

Ln  PT 

-0 

Bi      

—  i  4 

s 

!  Nad 

4-O.SI 

Id 

Br      

—  O  78 

18 

NaoCOo 

0.50 

20 

C,  arc-carbon      .     . 
C,  diamond    .     .     . 

~.j,_, 
—  2.0 
—  0.49 

18 
18 

Na2CO3.  10  H2O    . 
Nb    

O.I9 
—0.46 
4-1    7 

17 

\l 

.rOWd. 

H 

CH4,  i  Atm..     .     . 

-\-o.ooi 

16 

NiCl2    

T»'J 

-1  dO 

18 

Snl'n   1 

CO2,  i  Atm.  .     .     . 

-\-O.OO2 

16 

NiSO4 

_L-.0 

CS2  .... 

18 

I  ou- 

CaO  . 

u'/  / 

ifi 

PowH 

1    Qg 

4~O.I2O 

20 

CaCl2    
CaCO3,  marble  .     . 

V.^Y 
—0.40 
—  0.7 

X9 

P,  white 
i  P,  red    .     .     .     . 

+0.04 
—0.90 

O  CO 

20 
20 

Cd    

—  O  17 

18 

Pb 

CeBr3    

4.6.1 

18 

PbCl2 

POTO^ 

C12,  i  Atm.     .     .     . 

i  "-j 

—  O.  CQ 

16 

1  Pd 

•  °-25 
4-c8 

11 

CoCl2    

woy 

J-QO 

18 

Sol'n 

PrCl3 

i  j-° 

1        [    0 

I  S 

Snl'n    1 

CoBr2    

+47. 

18 

« 

Pt 

T/3- 

-i-  T    T 

,c 

CoI2 

1   1-" 

T« 

«< 

1  ptpi. 

1  »•• 

0  -.!'_ 

CoSO4  ..... 

1  JJ- 

4-C7. 

4( 

Rh 

4-i  i 

18 

ool  n  i 

Co(N08)2  .... 

y/' 

+  =57- 

18 

(( 

IS  

—  O  4.8 

18 

Cr     . 

-4-7  7 

18 

SO2   i  Atm 

if) 

CsCl      .     .     . 

—  o  ?8 

17 

Powd 

1  Sb 

iS 

Cu     .    .     . 

•••  •  O  OQ 

Se 

u.y4 

i  S 

CuCl2    

4-12. 

2O 

Sol'n 

Si 

O.j- 
—  O  I  " 

18 

Crv«; 

CuSO4  .     . 

4-10 

"O 

Sol'n 

SiO2  Quartz 

CuS       ... 

4-o  16 

17 

Powd 

—  Glass 

0  r\ 

FeCl3 

4-oo 

18 

Sol'n 

Sn 

uo± 

FeCl2     

4-QO 

18 

SrCl> 

i  **yj 

—  o  d" 

''O 

Sol'n  i 

FeSO4  

4-8- 

20 

«< 

Ta 

4-O  O7 

18 

Fe2(N03)6.     .     .     . 
FeCneK4    .... 
FeCneK<}   .... 

+  50. 
—0.44 

4-Q  I 

18 

Powd. 

« 

Te     .     .     .     . 
Th     
Ti 

—0.32 
4-0.18 
-L-j  i 

20 
18 
18 

He,  i  Atm. 

—  o  002 

o 

Va 

4-i  c 

18 

H2,  i  Atm. 

o  ooo 

16 

Wo 

J  o  IT 

°o 

H2,  40  Atm.   . 

o.ooo 

16 

Zn     

—  O.  I  C. 

18 

I  H2O. 

—  O  7Q 

''O 

ZnSO4 

O  -1O 

I  HC1  

—  O8o 

"O 

Zr          

—  O.4C 

18 

H2SO4 

4-0  78 

CH3OH 

-O  71 

HNO3  

—  O  7O 

''O 

C2H5OH 

O.SO 

He    . 

—O  IQ 

20 

C8H7OH 

•  -o  80 

i    .    :  :  :  : 

•-    O  A. 

"O 

C2H6OCoH5 

•-•o  60 

20 

In 

o  i4- 

18 

CHClg 

o  c;8 

Ir 

W«*3C 

+  O  I  C 

18 

C«H« 

078 

K 

20 

4-7  7 

KC1  

—  O  CO 

20 

Glycerine 

'     f 
—  o  64 

22 

KBr  

—  O  4O 

''O 

Sn^ar 

—  O.  C7 

KI     . 

—  o  38 

"O 

Paraffin 

o  <8 

KOH 

—  O  3  C 

'^'J 

Sol'n 

Petroleum 

•-••O  Ol 

K2S04  
KMnO4      .... 

V-JJ 

—0.42 

4-2.0 

20 

Toluene     .... 
\Vood    

-0.77 

—  O.2-C 

KNO3   

—  O  77 

20 

Xylene 

—  0.81 

1 

Values  are  mostly  means  taken  of  values  given  in  Landolt-Bornstein's  Physikalisch-chemischt  Tabellen. 
dally  Honda,  Annalen  der  Physik  (4),  32,  1910. 

SMITHSONIAN  TABLES. 


See  espe- 


378 


TABLE  4  75. 
MAGNETO-OPTIC  ROTATION. 


Faraday  discovered  that,  when  a  piece  of  heavy  glass  is  placed  in  magnetic  field  and  a  beam 
of  plane  polarized  light  passed  through  it  in  a  direction  parallel  to  the  lines  of  magnetic  force, 
the  plane  of  polarization  of  the  beam  is  rotated.  This  was  subsequently  found  to  be  the  case 
with  a  large  number  of  substances,  but  the  amount  of  the  rotation  was  found  to  depend  on  the 
kind  of  matter  and  its  physical  condition,  and  on  the  strength  of  the  magnetic  field  and  the 
wave-length  of  the  polarized  light.  Verdet's  experiments  agree  fairly  well  with  the  formula  — 


where  c  is  a  constant  depending  on  the  substance  used,  /  the  length  of  the  path  through  the 
substance,  //  the  intensity  of  the  component  of  the  magnetic  field  in  the  direction  of  the  path 
of  the  beam,  r  the  index  of  refraction,  and  A  the  wave-length  of  the  light  in  air.  If  H  be  dif- 
ferent, at  different  parts  of  the  path,  IH  is  to  be  taken  as  the  integral  of  the  variation  of  mag- 
netic potential  between  the  two  ends  of  the  medium.  Calling  this  difference  of  potential  z/,  we 
may  write  Q  =  Av,  where  A  is  constant  for  the  same  substance,  kept  under  the  same  physical 
conditions,  when  the  one  kind  of  light  is  used.  The  constant  A  has  been  called  "  Verdet's  con- 
stant," *  and  a  number  of  values  of  it  are  given  in  Tables  476-480.  For  variation  with  tempera- 
ture the  following  formula  is  given  by  Bichat  :  — 

R  =  A'o  (i  —  0.00104  /  —  0.000014/2), 

which  has  been  used  to  reduce  some  of  the  results  given  in  the  table  to  the  temperature  corre- 
sponding to  a  given  measured  density.  For  change  of  wave-length  the  following  approximate 
formula,  given  by  Verdet  and  Becquerel,  may  be  used  :  — 


where  p  is  index  of  refraction  and  A  wave-length  of  light. 

A  large  number  of  measurements  of  what  has  been  called  molecular  rotation  have  been  made, 
particularly  for  organic  substances.  These  numbers  are  not  given  in  the  table,  but  numbers 
proportional  to  molecular  rotation  may  be  derived  from  Verdet's  constant  by  multiplying  in  the 
ratio  of  the  molecular  weight  to  the  density.  The  densities  and  chemical  formula  are  given  in 
the  table.  In  the  case  of  solutions,  it  has  been  usual  to  assume  that  the  total  rotation  is  simply 
the  algebraic  sum  of  the  rotations  which  would  be  given  by  the  solvent  and  dissolved  substance, 
or  substances,  separately;  and  hence  that  determinations  of  the  rotary  power  of  the  solvent 
medium  and  of  the  solution  enable  the  rotary  power  of  the  dissolved  substance  to  be  calculated. 
Experiments  by  Quincke  and  others  do  not  support  this  view,  as  very  different  results  are 
obtained  from  different  degrees  of  saturation  and  from  different  solvent  media.  No  results  thus 
calculated  have  been  given  in  the  table,  but  the  qualitative  result,  as  to  the  sign  of  the  rotation 
produced  by  a  salt,  may  be  inferred  from  the  table.  For  example,  if  a  solution  of  a  salt  in  water 
gives  Verdet's  constant  less  than  0.0130  at  20°  C.,  Verdet's  constant  for  the  salt  is  negative. 

The  table  has  been  for  the  most  part  compiled  from  the  experiments  of  Verdet,t  H.  Becque- 
rcl,t  Quincke,  §  Koepsel,||  Arons,f  Kundt,**  Jahn.tt  Schonrock.fJ  Gordon,  §§  Rayleigh  and 
Sidgewick,l|||  Perkin,lT1F  Bichat.*** 

As  a  basis  for  calculation,  Verdet's  constant  for  carbon  disulphide  and  the  sodium  line  D  has 
been  taken  as  0.0420  and  for  water  as  0.0130  at  20°  C. 


*  The  constancy  of  this  quantity  has  been  verified  through  a  wide   range  of  variation  of  magnetic  field  by 
H.  E.  J.  G.  Du  Bois  (Wied.  Ann.  vol.  ^5),  p.  137,  1888. 

t    '  Ann.  de  Chim.  et  de  Phys."  [3]  vol.  52,  p.  r2g,  1858. 

$    '  Ann.  de  Chim.  et  de  Phys."  [5]  vol.  12;  "  C.  R."  vols.  90,  p.  1407,  1880,  and  100,  p.   1374,  1885. 
§    '  Wied.  Ann."  vol.  24,  p.  606,  1885. 
'  Wied.  Ann."  vol.  26,  p.  456,  1885. 

•  Wied.  Ann."  vol.  24,  p.  161,  1885. 

«*    '  Wied.  Ann."  vols.  23,  p.  228,  1884,  and  27,  p.  191,  1886. 

'  Wied.  Ann."  vol.  43,  p.  280,  1891. 
$J    'Zeits.  fur  Phys.  Chem."  vol.  n,  p.  753,  1893. 
&§    '  Proc.  Rov.  Soc."  36,  p.  4,  1883. 

'  Phil.  Trans.  R.  S."  176,  p.  343,  1885. 
*  '     •  Jour.  Chem.  Soc." 
***    '  Jour,  de  Phys."  vols.  8,  p.  204,  1879,  and  9,  p.  204  and  p.  275,  1880. 

SMITHSONIAN  TABLES. 


TABLE  476. 
MAGNETO-OPTIC   ROTATION. 

Solids. 


379 


Substance. 

Formula. 

Wave- 
length. 

Verdet's 
Constant. 
Minutes. 

Temp.  C 

Authority. 

ZnS 
C 
PbB2O4 
Se 
Na2B4O7 
Cu2O 

A* 

0.589 

« 
« 

0.687 
0.589 
0.687 

0.0095 
0.2234 
O.OI27 
O.O6OO 
0.4625 
O.OI7O 
0.5908 

18-20° 
'5 
15 
'5 
15 
15 

IS 

Quincke. 
Becquerel. 

M 

<; 

«( 

Blende     

Diamond     .... 

Lead  borate     .... 
Selenium     .          . 

Sodium  borate     .    .     . 
Ziqueline  (Cuprite)  .     . 

CaFl2 

0-2534 

0.05989 

20 

Meyer,  Ann.  der 

•3655 

•435» 

.02526 
.01717 

u 

Physik,  30,  1909. 

.4916 

.01329 

« 

.589 

.00897 

« 

1.  00 

.00300 

« 

2.50 

.00049 

« 

3.00 

.00030 

« 

Glass,  Jena:  Medium  phosphate  crn. 

0.589 

0.0161 

18 

DuBois,  Wied.  Ann. 

Heavy  crown,  01143    . 
Light  flint,        0451 
Heavy  flint       0500 

•  < 
« 

O.022O 
0.0317 
O.o6o8 

• 

51,  1894. 

"     '     "         8161.     . 

« 

0.0888 

« 

Zeiss,  Ultraviolet 

o-3i3 

0.0674 

16 

Landau,    Phys.    ZS. 

• 

0.405 

.0369 

M 

9,  1908. 



0.436 

.O3II 

« 

Quartz,  along  axis,  i.e., 

Si02 

0.2194 

0.1587 

20 

Borel,  Arch.  sc.  phys. 

plate  cut  1  to  axis 

•2573 

.1079 

" 

1  6,  1903. 

.3609 

.04617 

" 

.4800 

•02574 

" 

.5892 

.01664 

« 

•6439 

.01368 

« 

Rock  salt    .         .     . 

NaCl 

0.2599 

0.2708 

20 

Meyer,  as  above. 

.3100 

.1561 

(4 

.4046 

•0775 

" 

.4916 

.0483 

(t 

.6708 

.0245 

(( 

1.  00 

.01050 

" 

2.00 

.00262 

« 

4.00 

.00069 

" 

Sugar,  cane  :  along 

Ci2H22Oii 

0.451 

.0122 

2O 

Voigt,   Phys.  ZS.  9, 

axis  HA 

.'626 

.0076 
.0066 

« 

1908. 

axis  HA1      .     . 

- 

0.451 

O.OI29 

" 

•540 

.0084 

" 

.626 

.0075 

" 

Sylvite     

KC1 

0.4358 

0.0534 

2O 

Meyer,  as  above. 

.5461 
.6708 

.0316 
.O2OI2 

M 

.00 

.OIO5I 

" 

1.  2O 

.00608 

" 

2.OO 

.OO2O7 

" 

4-00 

.00054 

SMITHSONIAN   TABLES. 


3  So 


TABLE  477. 
MAGNETO-OPTIC  ROTATION. 

Liquids  :  Verdet's  Constant  for  A.  —  0.589/i. 


Substance. 

Chemical  formula. 

Density  in 
grams  per 
c.  c. 

Verdet's 
constant 

in  minutes. 

Temp.  C 

Authority. 

Acetone 

C8H60 

0-7947 

O.OII3 

20° 

Jahn. 

Acids  :  Acetic 
Butyric 

C2H402 
C4H802 

1.0561 
0.9663 

.OIO5 
.0116 

21 

y 

Perkin. 

"       Formic 

CH202 

1.2273 

.0105 

" 

"       Hydrochloric 

HCI 

1.2072 

.O224 

" 

M 

"       Hydrobromic 

HBr 

1.7859 

•0343 

" 

" 

"       Hydroiodic 

HI 

1-9473 

•OS'S 

« 

" 

"       Nitric 

HNOi 

1.5190 

.0070 

13 

<« 

"       Sulphuric 

H2SO4 

.0121 

15 

Becquerel. 

Alcohols  :  Amvl 

C6HnOH 

0.8107 

.0128 

20 

Jahn. 

Butyl 

C4H9OH 

0.8021 

.0124 

ii 

Ethyl 

C2H6OH 

0.7900 

.0112 

« 

"           Methyl 

CH8OH 

0.7920 

.0093 

« 

"           Propyl 

C8H7OH 

0.8042 

.0120 

u 

Benzene 

C6H6 

0.8786 

.0297 

•* 

Bromides  :  Bromoform 

CHBr8 

2.902  r 

.0317 

y 

Perkin. 

Ethyl 

C2H5Br 

1.4486 

.0183 

u 

Ethylene 

C2H4Br2 

2.1871 

.0268 

« 

" 

Methyl 

CHgBr 

I-733I 

.0205 

0 

" 

Methylene 

CH2Br2 

2.4971 

.0276 

15 

" 

Carbon  bisulphide 

CS2 

•0433 

0 

Gordon. 

«                                    X 

" 

— 

.0420 

18 

Rayleigh. 

Chlorides  :  Amyl 

CHC1 

0.8740 

.0140 

20 

Jahn. 

"           Arsenic 

AsCl3 

— 

.0422 

y 

Becquerel. 

"           Carbon 

CC14 

— 

.0321 

« 

"           Chloroform 

CHC13 

1.4823 

.0164 

20 

Jahn. 

Ethyl 

C2H5C1 

0.9169 

0.0138 

6 

Perkin. 

"           Ethylene 

C2H4C12 

1.2589 

.0166 

y 

" 

1            Methyl 

CHgCl 

.0170 

Fecquerel. 

Methylene 

CH2C12 

i-3361 

.0162 

« 

Perkin. 

'           Sulphur  bi- 

S2C12 

•°393 

« 

Becquerel. 

Tin  tetra 

SnCl4 

— 

.0151 

• 

H 

'           Zinc  bi- 

ZnCl2 

— 

•°437 

f 

M 

lodides  :  Ethyl 

C2H6I 

1.9417 

+ 

.0296 

t 

Perkin. 

Methyl 

CH3I 

2.2832 

•0336 

• 

M 

Propvl 

C3H7I 

1.7658 

.0271 

1 

i 

Nitrates  :  Ethyl 
"          Methyl 

C2H6O.NOa 
CH8O.NO2 

1.1149 

1.2157 

.0091 
.0078 

u 

< 

Propyl 

C3H7O.NO2 

1.0622 

.0100 

«( 

< 

Paraffins:  Heptane 

C7H16 

0.6880 

.0125 

« 

< 

"           Hexane 

C«HM 

0.6743 

/  -r+j 

.0125 

<« 

• 

"           Pentane 

C6H12 

0.6332 

.0118 

«< 

< 

Phosphorus,  melted 
Sulphur,  melted 

P 

S 

.1316 

.0803 

33 
114 

Becquerel. 

Toluene 

C7H8 

0.8581 

.0269 

28 

Schonrock. 

Water,  A  =  0.2496  yu 

H20 

.1042 

See  Meyer, 

0.275 

.0776 

Ann.  der 

0.3609 

.0384 

Physik,  30, 

0.4046 

.0293 

1909.  Meas- 

0.500 

.0184 

ures  by 

0.589 

.0131 

Landau, 

0.700 

.0091 

Siertsema, 

I.OOO 

.00410 

Ingersbll. 

1.300 

.00264 

Xylene 

CgHio 

0.8746 

.0263 

27 

Schonrock. 

SMITHSONIAN  TABLES. 


TABLE  478. 

MAGNETO-OPTIC  ROTATION. 

Solutions  of  acids  and  salts  In  water.    Verdet's  constant  lor  A  =  0.589/i. 


381 


Chemical 
formula. 

Density, 
grams 
per  c.  c. 

Verdet's 
constant 
in  minutes. 

Temp. 

* 

Chemical 
formula. 

Density, 
grams 
per  c.  c. 

Verdet's 
constant 
in  minutes. 

Temp. 

* 

C8H60 
HBr 

u 

0.9715 

'•3775 
1.1163 

0.0129 
0.0244 
0.0168 

20° 

P 

LiCl 
MnCl2 

1.0619 
1.0316 
1.1966 

0.0145 
0.0143 
0.0167 

20° 

B 

HC1 

I-I573 

O.O2O4 

" 

If 

M 

1.0876 

o.oi  50 

«r 

" 

1.0762 

0.0168 

" 

" 

HgCl2 

1.0381 

0.0137 

16 

s 

HI 

1.0158 
I-9°57 

0.0140 
0.0499 

" 

P 

NiCl2 

1.0349 
1.4685 

0.0137 
0.0270 

15 

B 

1-4495 

0-0323 

" 

1.2432 

0.0196 

M 

1.1760 

O.O2O5 

" 

M 

" 

J-I233 

O.OI62 

M 

M 

HNOi 

1.3560 

O.OIO5 

" 

II 

KC1 

i.  6000 

0.0163 

M 

ft 

NH3 
NH4Br 

0.8918 
1.2805 

0.0153 
O.O226 

y 

;; 

NaCl 

1.0732 
1.2051 

O.OI45 
O.OlSo 

2O 
15 

B 

M 

1.1576 

0.0186 

" 

" 

" 

1.0546 

0.0144 

n 

BaBr2 

l-S399 

1.2855 

O.O2I5 
0.0176 

20 

j 

SrC]2 

1.0418 
1.1921 

0.0144 
O.OI62 

" 

J 

CdBr2 

1.3291 

0.0192 

" 

" 

" 

1.0877 

0.0146 

M 

it 

" 

1.  1608 

O.OI62 

* 

" 

SnCl2 

1.3280 

O.O266 

15 

V 

CaBr2 

1.2491 

0.0189 

" 

" 

" 

I.TII2 

0.0175 

" 

I-I337 

0.0164 

M 

«< 

ZnC]2 

1.2851 

0.0196 

U 

it 

KBr 

1.1424 

0.0163 

" 

« 

" 

I-I595 

0.0161 

It 

<« 

" 

1.0876 

0.0151 

" 

" 

K2CrO4 

1.3598 

0.0098 

u 

«< 

NaBr 

1.1351 

0.0165 

" 

" 

K2Cr2O7 

1.0786 

0.0126 

» 

« 

SrBr2 

1.0824 
1.2901 

0.0152 
0.0186 

l< 

« 

Hg(CN)2 

1.0638 
1.0605 

0.0136 
0-0135 

16 

M 

S 

.. 

" 

1.1416 

0.0159 

" 

If 

NH4I 

1.5948 

0.0396 

15 

P 

K2C08 
Na2CO8 

1.1906 
1.  1006 

O.OI4O 
O.OI4O 

2O 

M 

M 

1.5109 
1.2341 

0-0358 
0.0235 

" 

NH4C1 

1.0564 
1.0718 

0.0137 
0.0178 

15 

V 

Cdl 

1.5156 
1.1521 

0.0291 
0.0177 

2O 
M 

M 

BaCl2 

1.2897 

0.0168 

2O 

J 

KI 

1.6743 

0.0338 

15 

B 

" 

1.1338 

O.OI49 

" 

" 

" 

I-3398 

0-0237 

'* 

CdCl2 

1.3179 

0.0185 

" 

" 

" 

1.1705 

0.0152 

« 

" 

u 

J-2755 

0.0179 

U 

a 

Nal 

I-I939 

O.O2OO 

" 

J 

H 

1.1732 

0.0160 

" 

" 

1.1191 

0.0175 

M 

II 

0.0157 

* 

NH4N08 

1.2803 

O.OI2I 

15 

P 

CaCI2 

1.1504 

0.0165 

M 

KN08 

1.0634 

O.OI3O 

20 

J 

u 

1.0832 

0.0152 

" 

NaN08 

I.III2 

O.OI3I 

" 

" 

CuCl2 

1.5158 

O.O22I 

5 

B 

U2O3N2O6 

2.0267 

0.0053 

M 

B 

" 

0.0156 

" 

?> 

1.1963 

O.OII5 

" 

M 

FeCl2 

M331 

0.0025 

5 

" 

(NH4)2S04 

1.2286 

O.OI4O 

15 

P 

" 

1.2141 

0.0099 

M 

NH4.HSO4 

I.44I7 

0.0085 

u 

" 

« 

1.1093 

O.OIlS 

" 

BaSO4 

I.I788 

O.OI34 

20 

J 

Fe2Cl6 

I-6933 

—  O.2O26 

" 

M 

1.0938 

0.0133 

« 

M 

" 

I-53I5 

—  O.IT4O 

u 

CdSO4 

1.1762 

0.0139 

w 

" 

" 

—  0.0348 

" 

M 

1.0890 

0.0136 

" 

" 

u 

i.'  1  68? 

—  O.OOI5 

" 

14804 

I.I762 

0.0137 

H 

" 

" 

1.0864 

O.O08  I 

" 

MnS04 

I.244I 

0.0138 

" 

" 

" 

1.0445 

O.OII3 

" 

K2SO4 

1-0475 

0.0133 

" 

u 

1.0232 

O.OI22 

Na2SO4 

I.  O66  1 

0.0135 

*  J,  Jahn,  P,  Perkin,  V,  Verdet,  B,  Becquerel,  S,  Schonrock;  see  p.  378  for  references. 
SMITHSONIAN  TABLES. 


TABLES  479,  48O. 

TABLE  479.  -Magneto-Optic  Rotation. 

Gases. 


Verdet's 

Substance. 

Pressure. 

Temp. 

constant  in 

Authority. 

minutes. 

Atmospheric  air                        . 
Carbon  dioxide 

Atmospheric 

Ordinary 
u 

6.83  X  io-6 

13.00       " 

Becquerel. 

Carbon  disulphide  , 
Ethylene          .                          - 
Nitrogen          .                          , 

74  cms. 

Atmospheric 
u 

70°  C. 

Ordinary 
« 

23.49      " 
3448       " 
6.92       " 

Bichat. 
Becquerel. 

Nitrous  oxide  .                         .        . 

u 

(i 

16.90       " 

«« 

Oxygen    ...                 .. 

u 

u 

6.28       « 

ii 

Sulphur  dioxide 

II 

ii 

31-39      " 

u               .. 

246  cms. 

20°  C. 

38.40      » 

Bichat. 

See  also  Siertsema,  Ziting.  Kon.  Akad.  Watt.,  Amsterdam,  7,  1899;  8,  1900. 

Du  Bois  shows  that  in  the  case  of  substances  like  iron,  nickel,  and  cobalt  which  have  a  variable 
magnetic  susceptibility  the  expression  in  Verdet's  equation,  which  is  constant  for  substances  of  con- 
stant susceptibility,  requires  to  be  divided  by  the  susceptibility  to  obtain  a  constant.  For  this 
expression  he  proposes  the  name  "  Kundt's  constant."  These  experiments  of  Kundt  and  Du 
Bois  show  that  it  is  not  the  difference  of  magnetic  potential  between  the  two  ends  of  the  medium, 
but  the  product  of  the  length  of  the  medium  and  the  induction  per  unit  area,  which  controls  the 
amount  of  rotation  of  the  beam. 


TABLE  480.  — Verdet's  and  Kundt's  Constants. 

The  following  short  table  is  quoted  from  Du  Bois'  paper.     The  quantities  are  stated  in  c.  g.  s.  measure,  circular 
measure  (radians)  being  used  in  the  expression  of  "  Verdet's  constant  "  and  "  Kundt's  constant." 


Verdet's  constant. 

Name  of  substance. 

Magnetic 
susceptibility. 

Wave-length 
of  light 

Kundt's 
constant. 

Number. 

Authority. 

Cobalt      . 

_ 

6.44  X  i  o~5 

3-99 

Nickel      . 

_ 

_ 

_ 

i 

3-!5 

Iron 

- 

_ 

- 

6.56 

2.63 

Oxygen  :   I  atmo.     . 
Sulphur  dioxide 

+  0.01  26  X  io~5 

—  0.0751    " 

0.000179  X  io~6 
0.302 

Becquerel. 

5.89 

0.014 
—  4.00 

Water 

—  0.0694 

o-377 

Arons 

—5-4 

Nitric  acid 

—0.0633    " 

°-356 

Becquerel. 

-5.6 

Alcohol    . 

—  0.0566    " 

0-330 

De  la  Rive. 

-5.8 

Kther.      . 

—0.0541     " 

°-3r5 

" 

-5-8 

Arsenic  chloride 
Carbon  disulphide  . 

—  0.0876     " 
—  0.0716     " 

1.222 
1.222 

Becquerel. 
Rayleigh. 

—14.9 

—17.1 

Faraday's  glass 

—0.0982     " 

1.738 

Becquerel. 

—17.7 

SMITHSONIAN   TABLES. 


TABLES  481  -483. 
TABLE  481.  -  Values  of  Eerr's  Constant.* 


383 


Du  Bois  has  shown  that  the  rotation  of  the  major  axis  of  vibration  of  radiations  normally  reflected  from  a  magnet  is 
algebraically  equal  to  the  normal  component  of  magnetization  multiplied  into  a  constant  K.  He  calls  this  con- 
stant K,  Kerr's  constant  for  the  magnetized  substance  forming  the  magnet. 


Color  of  light. 

Spectrum 
line. 

Wave- 
length 
in  cms. 
X  io« 

Kerr's  constant  in  minutes  per  c.  g.  s.  unit  of  magnetization. 

Cobalt. 

Nickel. 

Iron. 

Magnetite. 

Red    

Li  a 

D 
b 
F 
G 

67.7 
62.0 

58.9 
51-7 
48.6 

43-1 

—  O.O2O8 
—0.0198 
—0.0193 
—  0.0179 
—  O.OlSo 
—  O.Ol82 

—0.0173 

—  0.0160 
—0.0154 
—  0.0159 
—  0.0163 
—0.0175 

—0.0154 
—  0.0138 
—0.0130 
—  O.OIII 
—  O.OIOI 

—  0.0089 

+0.0096 
+O.OI2O 
+0.0133 
+0.0072 
+0.0026 

Red  

Yellow        .    .    . 

Blue  

Violet    . 

*H.  E.  J.  G.  Du  Bois,  "  Phil.  Mag."  vol.  29. 


TABLE  482.— Dispersion  of  Eerr  Effect. 


Wave-length. 

o-SM 

I.OfJL 

i-SV- 

2.0fi. 

2-SK 

Steel      .     .     . 

—II7. 

—  l&. 

-14'. 

—  II'. 

-c/.o 

Cobalt  .    .    . 

—  9-5 

—  "-S 

—  9-5 

II. 

-6.5 

Nickel   .     .     . 

—  5-5 

—  4.0 

o 

+  1-75 

+3-o 

Field  Intensity—  10,000  C.  G.  S.  units.     (Intensity  of  Magnetization  =r  about  800  in  steel,  700  to   800  in  cobalt, 
about  400  in  nickel).     Ingersoll,  Phil.  Mag.  u,  p.  41,  1906. 


TABLE  483.  -  Dispersion  of  Eerr  Effect. 


Mirror. 

Field 
(C.  G.  S.) 

•  4ifx 

•  44M 

.481* 

•  52M 

.56* 

.60^ 

.64ft 

.66* 

Iron      .     . 

21,500 

—.25 

—.26 

—.28 

—•31 

-36 

—.42 

—•44 

—45 

Cobalt  .     . 

20,000 

-36 

—•35 

—•34 

—•35 

—•35 

—•35 

—•35 

-.36 

Nickel  .     . 

I9,OOO 

—.16 

—•'5 

—•13 

—•13 

—.14 

—.14 

—.14 

—.14 

Steel     .     . 

I9,2OO 

—.27 

—.28 

—•31 

—•35 

-.38 

—.40 

—•44 

—•45 

Invar    .     . 

19,800 

—  .22 

—•23 

—.24 

—•23 

—•23 

—.22 

—•23 

—•23 

Magnetite 

l6,400 

—.07 

—  .02 

+.04 

+.06 

+.08 

+.06 

+•04 

+•03 

Foote,  Phys.  Rev.  34,  p.  96,  1912. 

See  also  Ingersoll,  Phys.  Rev.  35,  p.  312,   1912,  for  "The  Kerr  Rotation  for  Transverse  Magnetic  Fields,"  and 
Snow,  1.  c.  2,  p.  29,  1913,  "  Magneto-optical  Parameters  of  Iron  and  Nickel." 

SMITHSONIAN  TABLES. 


TABLES  484-486. 
RESISTANCE  OF   METALS.     MAGNETIC  EFFECTS. 

TABLE  484.— Variation  of  Resistance  of  Bismuth,  with  Temperature,  in  a  Transverse 

Magnetic  Field. 


Proportional  Values  of  Resistance. 

H 

-192° 

-135° 

—  100° 

-37° 

0° 

+  18° 

+60° 

+  100° 

+  183° 

o 

0.40 

0.60 

0.70 

0.88 

1.  00 

1.  08 

•25 

.42 

1.79 

2000 

1.16 

0.87 

0.86 

0.06 

.08 

.11 

.26 

•43 

1.  80 

4000 

2.32 

1.20 

1.  10 

.18 

.21 

.31 

.46 

1.82 

6OOO 

4.00 

2  O6 

1.  60 

1.29 

.30 

•32 

•39 

1.85 

8000 

5-90 

2.88 

2.OO 

1.50 

•43 

•42 

.46 

.57 

1.87 

1  0000 

8.60 

3.80 

2-43 

1.72 

•57 

•54 

•54 

.62 

1.89 

I2OOO 

10.8 

4.76 

2.93 

•71 

•67 

.62 

.  1.67 

1.92 

14000 

12.9 

5-82 

3-50 

2.16 

•87 

.80 

.70 

1.73 

1.94 

I6OOO 
18000 

15-2 
17-5 

6.95 
8.  15 

4.11 
4.76 

2.38 
2.60 

2.02 
2.18 

1-93 
2.06 

.79 
.88 

1.80 
1.87 

1.96 
1.99 

20000 

19.8 

9-50 

5-40 

2.81 

2.33 

2.20 

•97 

1.95 

2.03 

25OOO 
30000 

25-S 
30.7 

13-3 
18.2 

7-30 
9-8 

3.50 

4.20 

2.73 

3.17 

2.52 
2.86 

2.22 
2.46 

2.10 
2.28 

2.09 

2.17 

35000 

35-5 

20.35 

12.2 

4.95 

3.62 

3-25 

2.69 

2-45 

2.25 

TABLE  485,  —  Increase  of  Resistance  of  Nickel  due  to  a  Transverse  Magnetic 
Field,  expressed  as  %  of  Resistance  at  0°  and  H  =  0. 


H 

-190° 

-75° 

0° 

+18° 

+  100° 

+  182° 

o 

+0 

o 

0 

0 

0 

0 

1000 

+0.20 

+0.23 

+0.07 

+0.07 

+0.96 

+0.04 

2000 

+0.17 

+0.16 

+0.03 

+0.03 

+0.72 

—0.07 

30OO 

o.oo 

—  O.O5 

-0.34 

—0.36 

-0.14 

—0.60 

4000 

-0.17 

-0.15 

—0.60 

—0.72 

—0.70 

-I.  IS  . 

6000 

—0.19 

—  0.20 

—  0.70 

—0.83 

—  1.02 

-1-53 

8000 

—0.19 

—0.23 

—0.76 

—0.90 

-   -IS 

-1.66 

1  0000 

—  0.18 

—  0.27 

—0.82 

—  0.95 

-    .23 

-1.76  • 

I2OOO 

-0.18 

—  0.30 

—0.87 

—  I.OO 

—  .30 

—  1.85 

I40OO 

—  0.18 

—  0.32 

—0.91 

-   .04 

-    .37 

-1.95 

16000 

-0.17 

-0.35 

-0.94 

-   .09 

-   .44 

-2.05 

18000 

-0.17 

-0.38 

—  0.98 

-    .13 

-   -51 

-2.15 

200OO 

—  0.16 

-0.41 

-1.03 

-    -17 

-1.59 

-2.25 

25000 

-0.14 

-0.49 

—  1.  12 

-    .29 

-1.76 

-2.50 

30000 

—  0.12 

-0.56 

—  1.22 

-1.40 

-1.95 

—  2.73 

35000 

—  O.IO 

—0.63 

-1.32 

-i.SO 

-2.13 

-2.98 

F.  C.  Blake,  Ann.  der  Physik,  28,  p.  449;  1909. 


TABLE  486.  —  Change  of  Resistance  of  Various  Metals  in  a  Transverse  Magnetic  Field. 

Room  Temperature. 


Metal. 

Field  Strength 
in  Gausses. 

Per  cent 
Increase. 

Authority. 

Nickel 

1  0000 

—  1.2 

Williams,  Phil.  Mag.  9,  1905. 

** 

" 

—  1.4 

Barlow,  Pr.  Roy.  Soc.  71,  1903. 

44 

6000 

—  i.o 

Dagostino,  Atti  Ac.  Line.  17,  1908. 

" 

IOOOO 

—  1.4 

Grummach,  Ann.  der  Phys.  22,  1906. 

Cobalt 

41 

—0.53 

Cadmium 

• 

+0.03 

Zinc 

* 

+0.01 

Copper 

• 

+0.004 

Silver 

• 

+0.004 

Gold 

' 

+0.003 

Tin 

+O.002 

Palladium 

+O.OOI 

Platinum 

' 

+O.OO05 

Lead 

" 

+O.O004. 

Tantalum 

«• 

+O.OOO3 

Magnesium 
Manganin 

6000 

+O.OI 
+O.OI 

Dagostino,  /.  c. 

Tellurium 

? 

+0.02  tO  0.34 

Goldhammer,  Wied  Ann.  31.  1887. 

Antimony 

? 

+0.02  tn  o.T<S 

•' 

Different  specimens  show  very 

Grummach,  I.  c. 

diverse  results,  usually  an    in- 

Barlow, I.  c. 

crease  in  weak  fields,  a  decrease 

Williams,  I.  c. 

in  strong. 

Nickel  steel 

Alloys  behave  similarly  to  iron. 

Williams,  I.  c. 

TABLES  487,  488.  385 

TABLE  487.  —Transverse  Oalvanomagnetlc  and  Thermomagnetlc  Effects. 

Effects  are  considered  positive  when,  the  magnetic  field  being  directed  away  from  the  observer, 
and  the  primary  current  of  heat  or  electricity  directed  from  left  to  right,  the  upper  edge  of  the 
specimen  has  the  higher  potential  or  higher  temperature. 

h '  =  difference  of  potential  produced;   T=  difference  of  temperature  produced;  /=  primary 

current;    ^  =  primary  temperature  gradient;    B=  breadth,  and  D=  thickness,  of  specimen 
//=  intensity  of  field.     C.  G.  S.  units. 

Hall  effect  (Galvanomagnetic  difference  of  Potential),  E  =  A' 


D 


Ettingshausen  effect  (  "  " 

Nernst  effect  (Thermomagnetic       " 
Leduc  effect  (  "  " 


"  Temperature),  T=  T  D 

j* 
"  Potential),  E- 


"  Temperature),  T=Sf/B^c 


Substance. 

Values  of  R. 

P  X  io«. 

Q  X  io«. 

^XlO*. 

-{-400  to  800 

-T-^OO 

_L  ">6oooo 

Antimony     ...          ... 

+  O.Q  ''  O  22 

4-2 

1  4°° 

Steel    

-I-  OI  2  "  O  O^"? 

"O  07 

1  f^. 

H"eusler  alloy    .          . 

-j-  OIO  "  O  0^6 

-1-09 

-{-•007  "  o  on 

—  o  06 

—  IOOO    "    I  COO 

I  7O 

Cobalt      

-j-.ooi6  "  o  0046 

-4-o  01 

—  r-l8oO    "    2°4O 

-f39 

4-  r  i 

Zinc      

1   3 

Cadmium      

+  OQOC  e 

T~!3 

.WUVJJJ5 

-j-  00040 

up  to  —  c  o 

_l_  - 

Lead    

—  j-  OOOOQ 

rO   (?\ 

^  5 

Tin  

—  OOOO3 

-     J.  O  C*\ 

Platinum  ...          ... 

—  OOO0 

—  .00052 

—no  to  270 

18 

German  silver  

—  OOO^4. 

Gold    

—  000^7  to  00071 

Constantine  .... 

—  OOOQ 

Manganese                  . 

—  OOOO1 

—  OOO7  to    OOI2 

_}_  CO  tO   I  7O 

1 

Silver             

—  0008  "   ooi  5 

—  ^4.6   "    4.7O 

J 

—  .OO2^ 

Magnesium  ....          . 

—  .00094  to   0035 

Aluminum                   . 

—  00076  "    00^7 

Nickel 

—  OOJ.^    "     O^d. 

-f-O  O4  to  O  IQ 

-{-''OOO   "    QOOO 

»  r 

Carbon     

—  .017 

4-c 

-l-IOO 

4J? 

Bismuth        

' 
—  Up  to  ID. 

1     '  3' 
•+-  1  to  4.O 

.          1 
"P  up  to  132000 

-^''OO 

TABLE  488.  —  Variation  of  Hall  Constant  with  the  Temperature. 


Bismuth.1 

Antimony.8 

H 

—182° 

-90° 

-23° 

4-11.5° 

4-100° 

H 

—  186° 

—79 

o 

4-21.5° 

4-58° 

IOOO 
2OOO 
3OOO 
4000 
5000 
0000 

62.2 

49-7 
45-8 
42.6 
40.1 

28.0 
25.0 
22.9 
21.5 

20.2 
18.9 

ll'° 

16.0 
12.9 

12.7 
12.  1 

"•5 

II.O 

10.6 

7.28 

7-17 
7.06 

6.95 
6.84 
6.72 

0.263 

0.252 
0.245 

0.249 
0.243 
02.35 

0.217 
0.21  1 
O.2O9 

0.203 

Bismuth.8 

H 

4-14.5°        4-104° 

125° 

i 
I 

89° 

a39° 

259° 

269° 

270° 

890 

5.28          2.57 

2.12 

42           1.24 

I.  II 

0.97 

0.83 

0.77* 

1  Barlow,  Ann.  der  Phys.  12,  1903.  s  Everdingen,  Comm.  Phys.  Lab.  Leiden,  58. 

*  Traubenberg,  Ann.  der  Phys.  17,  1005.  *  Melting-point. 

Both  tables  taken   from  Jahn,  Jahrbuch  der  RadioactivitSt  und  Electronik,  5,  p.  166;  1908,  who  has  collected  data  of 
all  observers  and  gives  extensive  bibliography. 

SMITHSONIAN  TABLES. 


386 


TABLES  489-491. 

RONTGEN   (X-RAYS)   RAYS. 

TABLE  489.  — Cathode  and  Canal  Rays. 


Cathode  (negative)  rays  consist  of  negatively  charged  particles  (charge  4.77  x  io~10  esu, 
1.591  x  lo"90  emu,  mass,  9  x  lo"28  g  or  1/1800  H  atom,  diam.  4  X  10  13  cm)  emitted  at  low 
pressures  in  an  electric  discharge  tube  perpendicularly  to  the  cathode  (.*.  can  be  focused)  with 
velocities  (io9  to  io10  cm/sec.)  depending  on  the  acting  potential  difference.  When  stopped  by 
suitable  body  they  produce  heat,  ionization  (inversely  proportional  to  velocity  squared),  photo- 
graphic action,  X-rays,  phosphorescence,  pressure.  The  bulk  of  energy Js  transformed  into 
heat  (Pt,  Ta,  W  may  be  fused).  In  an  ordinary  X-ray  tube  carrying  io  3  ampere  the  energy 
given  up  may  be  of  the  order  of  100  cal/m.  Maximum  thickness  of  glass  or  Al  for  appreciable 
transmission  of  high  speed  particles  is  .0015  cm.  Maximum  velocity  Vd  with  which  a  cathode 
ray  of  velocity  F0  may  pass  through  a  material  of  thickness  d  is  given  by  F04  -  F<*4  =  ad  x  io40; 
a  =  2  for  air,  732  for  Al  and  2540  for  Au,  cm-sec,  units  (Whiddington,  1912).  Cathode  rays 
have  a  range  of  only  a  few  millimeters  in  air. 

Canal  (positive)  rays  move  from  the  anode  with  velocities  about  io8  cm/sec,  in  opposite 
direction  to  the  cathode  rays,  carry  a  positive  charge,  a  mass  of  the  order  of  magnitude  of  the 
H  molecule,  cause  strong  ionization,  fluorescence  (LiCl  fluoresces  blue  under  cathode,  red  under 
canal  ray  bombardment),  photographic  action,  strong  pulverizing  or  disintegrating  power  and 
by  bombardment  of  the  cathode  liberate  the  cathode  rays. 


TABLE  490.  —  Speed  of  Cathode  Rays. 

The  speed  of  the  cathode  particles  in  cm/sec,  as  dependent  upon  the  drop  of  potential  to 
which  they  owe  the  speed,  is  given  by  the  formula  v  =  5.95  VE-io7.  The  following  table  gives 
values  of  5.95  VE. 


Voltage 

IO 

20 

30 

40 

CO 

60 

7° 

80 

oo 

IOO 

Velocity  X  io~7.  .  . 

18.8 

26.6 

32.6 

37-6 

42.1 

46.  1 

49.8 

53-3 

56.5 

59-5 

Voltage    . 

IOO 

200 

•*oo 

400 

<COO 

600 

700 

800 

QOO 

IOOO 

Velocity  x  io~7  .  .  . 

59-5 

84.2 

103.1 

119.  i 

133-1 

145.8 

IS7-S 

168.3 

178.6 

188. 

For  voltages  1000  to  16,000  multiply  2d  line  by  10,  etc. 


TABLE  491.  —  Cathodic  Sputtering. 

The  disintegration  of  the  cathode  in  an  electric  discharge  tube  is  not  a  simple  phenomenon. 
The  particles  taking  part  in  the  sputtering  must  be  either  large  or  of  high  speed  or  both  (2000+ 
gauss  field  required  for  their  deviation).  It  depends  upon  the  nature  of  the  residual  gas.  H,  N, 
CO2  are  not  generally  favorable;  Ar  is  especially  favorable,  also  He,  Ne,  Kr  and  Xe.  Raised 
temperature  favors  it.  The  relative  sputtering  from  various  metals  is  shown  in  the  following 
table  (Crookes,  Pr.  R.  S.  1891);  the  residual  gas  was  air,  pressure  about  .05  mm  Hg. 


Metal 

Pd 

An 

Ar 

Pb 

Sn 

Pt 

Cu 

Cd 

Ni 

Ir 

Fe 

Al 

Ms 

Brass 

Sputtering  

IOO 

92 

76 

69 

52 

40 

37 

3i 

IO 

10 

5 

0 

0 

47 

For  further  data  on  cathode,  canal  and  X-rays,  see  X-rays  by  G.  W.  C.  Kaye,  Longmans, 
1917,  upon  which  much  of  the  above  and  the  following  data  for  X-rays  is  based.  See  also  J.  J. 
Thomson,  Positive  Rays,  Longmans,  1913. 


SMITHSONIAN  TABLES. 


TABLES  492-493. 

RONTGEN   (X-RAYS)   RAYS. 

TABLE  492.  —  X-rays,  General  Properties. 

X-rays  are  produced  whenever  and  wherever  a  cathode  ray  hits  matter.  They  are  invisible, 
of  the  same  nature  as,  and  travel  with  the  velocity  of  light,  affect  photographic  plates,  excite 
phosphorescence,  ionize  gases  and  suffer  deviation  neither  by  magnetic  nor  electric  fields  as  do 
cathode  rays.  In  an  ordinary  X-ray  tube  (vacuum  order  o.ooi  to  o.oi  mm  Hg)  the  cathode 
(concave  for  focusing,  generally  of  aluminum)  rays  are  focused  on  an  anticathode  of  high  atomic 
weight  (W,  Pt,  high  atomic  weight,  high  melting  point,  low  vapor  pressure,  to  avoid  sputtering, 
high  thermal  conductivity  to  avoid  heating).  Depth  to  which  cathode  rays  penetrate,  order 
of  0.2  x  io~5  cm  in  Pb,  90,000  volts  (Ham,  1910),  24  x  io~5  cm  in  Al,  22,000  volts  (Warburg, 
1915).  Note:  High  speed  H  and  He  molecules  (2  x  io8  cm/sec.)  can  penetrate  o.ooi  to  0.006 
mm  mica;  He  a  particles  (2  x  io9  cm/sec.),  0.04  mm  glass. 

The  X-rays  from  an  ordinary  bulb  consist  of  two  main  classes: 

Heterogeneous  ("general,"  "independent")  radiation,  which  depends  solely  on  the  speed  of 
the  parent  cathode  rays.  It  is  always  present  and  its  range  of  hardness  (wave-lengths)  depends 
on  the  range  of  speeds  of  the  cathode  rays.  Its  energy  is  proportional  to  the  4th  power  of  these 
speeds. 

Homogeneous  ("characteristic,"  "monochromatic")  radiation  (K,  L,  M,  etc.  radiations, 
see  Table  498  for  wave-lengths),  characteristic  of  the  metal  of  the  anticathode.  Generated  only 
when  cathode  rays  are  sufficiently  fast.  There  is  a  critical  velocity  for  each  characteristic 
radiation  from  each  material,  proportional  to  the  atomic  weight  of  the  anticathode.  The  critical 
velocity  for  the  K  radiation  is  VK  =  A  x  io8,  when  A  is  the  atomic  weight  of  the  radiator  (e.g. 
anticathode);  VL  =  i/2(A  -48)io8. 

The  following  relation  has  been  found  to  hold  experimentally  between  the  voltage  V  through 
which  the  cathode  particles  fall  and  the  maximum  frequency  v  of  the  X-rays  produced:  eV 
=  hv,  where  e  is  the  electronic  charge  and  h,  Planck's  constant.  Blake  and  Duane  (Phys.  Rev. 
io,  624,  1917)  found  for  h,  6.555  X  lo"27  erg  second. 

As  the  speed  of  the  cathode  rays  is  increased,  shorter  and  shorter  wave-lengthed  "independent" 
X-rays  are  produced  until  the  critical  speed  is  reached  for  the  "characteristic"  rays;  with  faster 
speeds,  the  cathode  rays  become  at  first  increasingly  effective  for  the  characteristic  radiation, 
then  less  so  as  the  independent  radiation  again  predominates. 

When  cathode  rays  hit  the  anticathode  some  75  per  cent  are  reflected,  the  more  the  heavier 
its  atomic  weight.  The  chances  of  the  remainder  hitting  an  atom  so  as  to  generate  an  X-ray 
are  slight;  only  i/iooo  or  1/2000  of  the  original  energy  goes  into  X-rays.  If  £z  and  Ee  are  the 
energies  of  the  X  and  the  parent  cathode  rays,  A  the  atomic  weight  of  the  anticathode,  /3  the 
velocity  of  the  cathode  rays  as  fraction  of  the  light  value  (3  x  io10  cm/sec.),  Beatty  showed 
(Pr.  R.  S.  1913)  that  Ex  =  Ec  (.51  X  ioM/32);  this  refers  only  to  the  independent  radiations; 
when  characteristic  radiations  are  excited  their  energy  must  be  added  and  the  tube  becomes 
considerably  more  efficient.  No  quantitative  expression  for  the  latter  has  been  developed. 

When  an  X-ray  strikes  a  substance  three  types  of  radiation  result:  scattered  (sometimes  called 
secondary)  X-rays,  characteristic  X-rays  and  corpuscular  rays  (negatively  charged  particles). 
The  proportions  of  the  rays  depend  on  the  substance  and  the  quality  of  the  primary  rays.  When 
the  substance  is  of  low  atomic  weight,  by  far  the  greater  portion  of  the  X-rays,  if  of  a  penetrating 
type,  are  scattered.  With  elements  of  the  Cr-Zn  group  most  of  the  resulting  radiation  is  "charac- 
teristic." With  the  Cu  group  the  scattered  radiation  (1/200)  is  negligible.  Heavier  elements, 
both  scattered  and  characteristic  X-rays.  Corpuscular  radiation  greater,  mass  for  mass,  for 
elements  of  high  atomic  weight  and  may  mask  and  swamp  the  characteristic  radiation.  Hence 
an  X-ray  tube  beam,  heterogeneous  in  quality,  allowed  to  fall  on  different  metals,  —  Cu,  Ag,  Fe, 
Pt,  etc.,  —  excites  characteristic  X-rays  of  wide  range  of  qualities.  Exciting  ray  must  be  harder 
than  the  characteristic  radiation  wished.  The  higher  the  atomic  weight  of  the  material  struck 
(radiator),  the  more  penetrating  the  quality  of  the  resulting  radiation  as  shown  by  the  following 
table,  which  gives  A,  the  reciprocal  of  the  distance  in  cm  in  Al,  through  which  the  rays  must  pass 
in  order  that  their  intensity  will  be  reduced  to  1/2.7  of  their  original  intensity. 
TABLE  493.  —  Rontgen  Secondary  Rays. 


Radiator. 

Cr 

Fe 

Co 

Ni 

Cu 

Zn 

As 

Se 

Sr 

Al 

Sn 

Atomic  weight.  .  .. 

52. 
367 

55-8 
239 

59-0 
J93 

58.7 
1  60 

63.6 
129 

^ 

75-o 
61 

79-2 
51  . 

87.6 

35-  2 

108. 
6.75 

119. 
4-33 

With  the  radiator  at  45  °  to  the  primary  X-rays  at  most  only  about  50  per  cent  of  the  energy 
goes  to  characteristic  rays  and  only  about  i/io  of  the  latter  escape  the  surface  of  the  radiator. 
The  /3  radiations  of  radioactive  elements  may  possibly  be  regarded  (Rutherford)  as  a  characteristic 
radiation  produced  by  the  expulsion  of  the  a  particles.  The  hardness  of  some  corresponds  to  the 
K  and  L  radiations. 

For  more  complete  data  on  X-rays,  see  X-rays,  G.  W.  C.  Kaye,  Longmans,  1917,  upon  which 
these  X-ray  tables  are  greatly  based. 
SMITHSONIAN  TABLES. 


TABLES  494-495. 

RONTGEN   (X-RAYS)    RAYS- 

TABLE  494.  —  Corpuscular  Rays. 

Corpuscular  rays  are  given  off  in  greatest  abundance  when  radiator  emits  its  characteristic  radiation.  Intensity 
increases  with  atomic  weight  Uth  power,  Moore,  Pr.  Phys.  Soc.).  Greater  number  emitted  at  right  angles  to  incident 
\  olocity  runj,'e  (6  to  8.5)10*  cm/sec,  ro  =  velocity  when  leaving  radiator  =  icfl(A  =  Atomic  weight)  =  critical 
velocity  necessary  to  excite  characteristic  radiation,  therefore  corpuscular  rays  have  practically  the  same  velocity  as 
the  original  generating  cathode  rays.  Are  of  uniform  quality  when  excited  by  characteristic  rays  and  follow  exponen- 
tial law  of  absorption  in  gases.  If  A  is  the  absorption  coefficient  and  A  the  atomic  weight,  \A*  =  Xro4  =  constant 
(Whiddington,  Beatty).  X  is  defined  by  7  =  7o  *""*  where  7  and  7o  are  the  intensities  after  and  before  absorption  and 
d  the  thickness  of  the  absorptive  layer  in  cm.  The  following  values  for  X  in  air  for  characteristic  radiations  from  various 
substances  are  due  to  Sadler.  (At  o°  C  and  76  cm  Hg.) 


Metal  emitting 
corpuscles. 

Exciting  characteristic  radiation  from 

Ni 

Cu 

Zn 

As 

Se 

Sr 

Mo 

Rh 

Ag 

Sn 

Al    . 

38.9 

37-0 

3F8 
36.2 

29.6 
30.2 
30.4 

26.4 

20.0 
21.  S 
20.8 

15.2 

iS-S 
15-2 

IO.Q 

10.8 

8.90 
8.84 
8.81 

6.54 
6.41 
6.67 

Fe.. 

Cu  

TABLE  495.  —  Intensity  of  X-Rays.    lonization. 

The  intensity  of  the  radiation  from  an  X-ray  bulb  is  proportional  to  the  current.    Except  at  low  voltages  it  equals 

he  break-down  voltage  and  K  a  constant  for  the  tube  (Kronke). 


—  co*)  where  i  is  the  current,  v  the  applied  voltage,  vo  t  . 

The  intensity  of  X-rays  is  most  accurately  measured  by  the  ionization  they  produce.  This  may  be  referred  to  the 
International  Radium  Standard  (see  Table  508).  It  is  proportional  to  the  4th  power  of  the  speed  of  the  parent  cathode 
rays  (Thomson),  (true  only  of  independent  rays,  Beatty,  1913).  The  saturation  current  due  to  X-ray  ionization  is 
usually  of  the  order  of  lo'10  to  io~15  ampere.  When  X-rays  pass  through  a  substance,  only  once  in  a  while  is  an  atom 
struck,  only  perhaps  i  in  a  billion,  and  ionized.  The  ionization  is  probably  an  indirect  process  through  the  mediation 
of  corpuscular  rays.  In  the  absence  of  secondary  radiations  the  ionization  is  proportional  to  the  mass  of  the  gas 
(that  is,  its  pressure  at  constant  temperature).  It  depends  on  the  nature  of  the  gas,  but  is  little  affected  by  the  quality 
of  the  rays.  The  following  results  are  due  to  Crowther,  1908. 


Gas  or  vapor. 

lonization  relative  to  air  =  i. 

Density, 

air  =  i. 

Soft  X-rays 
6  mm  spark. 

Hard  X-rays 
27  mm  spark. 

Hydrogen  Hz 

0.07 
i  -S3 
2.24 
5-  35 
3-78 
4.96 
7-93 

O.OI 

1-57 
18.0 
67. 
72. 
I4S. 
425- 

0.18 
1.49 
17-3 

,3: 

125. 

Carbon  dioxide  COz.  .  . 

Ethyl  chloride  CzHsCl.  . 

Carbon  tetrachloride  CCh   .  . 

Ethyl  bromide  CaHiiBr  
Methyl  iodide  CHsI  
Mercury  methyl  Hg(CHs)2  

SMITHSONIAN  TABLES. 


TABLES  496-497. 

RONTGEN   (X-RAYS)    RAYS. 

TABLE  496.  —  Mass  Absorption  Coefficients,  \/d. 

The  quality  by  which  X-rays  have  been  generally  classified  is  their  "hardness"  or  penetrating  power.  It  is  greater 
the  greater  the  exhaustion  of  the  tube,  but  for  a  given  tube  depends  solely  upon  the  potential  difference  of  the  elec- 
trodes. With  extreme  exhaustion  the  X-rays  have  an  appreciable  effect  after  passing  through  several  millimeters  of 
brass  or  Al.  The  penetrability  of  the  characteristic  radiation  is  in  general  proportional  to  the  sth  power  of  the  atomic 
weight  of  the  radiator.  The  absorption  of  any  substance  is  equal  to  the  sum  of  the  absorptions  of  the  individual  atoms 
and  is  independent  of  the  chemical  combination,  its  physical  state  and  probably  of  the  temperature.  Most  of  the 
following  table  is  from  the  work  of  Barkla  and  Sadler,  Phil.  Mag.  17,  739,  1909.  For  starred  radiators,  L  radiations 
used;  for  others  the  K. 

If  7o  be  the  intensity  of  a  parallel  beam  of  homogeneous  radiation  incident  normally  on  a  plate  of  absorbing  material 
of  thickness  /,  then  I  =  I0  e~^x  gives  the  intensity  /  at  the  depth  x.  Because  of  the  greater  homogeneity  of  the  secondary 
X-rays  they  were  used  in  the  determination  of  the  following  coefficients.  The  coefficients  X  have  been  divided  by  the 
density  d. 


Radiator. 

Absorber. 

C 

Mg 

Al 

Fe 

Ni 

Cu 

Zn 

Ag 

Sn 

Pt 

Au 

Cr... 

iS-3 

10.  I 

8.0 
6.6 

5-2 

4-3 
2-5 

2.0 

.46 

•  35 
•  31 
.29 
.26 

126. 
80. 
64- 
52. 
41. 
35- 
J9- 
16. 

2.2 

136. 
88. 
72. 
59- 
48. 
39- 

22. 
19. 

ii 

1.2 

30. 

22. 

11: 

8. 
7- 

104. 
66. 
67- 
314- 
268. 

221. 

134- 
116. 
17- 

129. 
84. 
67. 
56. 
63- 
265. 
166. 
141. 
23- 

143- 
95- 
75- 
62. 
53- 
56. 
176. 
ISO. 
24. 

127. 
177. 
139- 
127. 
77- 
70. 

170. 

112. 
92- 

74- 
01. 

50. 
204. 
175- 
27. 

S8o. 
381. 
314- 
262. 
214. 
175- 

X3: 

11: 
56. 
46. 

35- 
140. 
106. 
78. 
73- 
42. 
40. 

714- 
472. 
392. 
328. 
272. 
225. 
132. 

112. 

16. 

(Si7.) 
340. 
281. 
236. 
194- 
162. 
106. 
93- 
56. 
47- 

133- 
"3- 
128. 
125 
134- 
132     . 

(507.) 
367- 
306. 
253- 

210. 
I78. 

106. 

ICO. 

61. 

52. 

Fe 

Co  
Ni.. 

Cu  
Zn... 

As 

Se  

Ag 

Sn  
Sb... 

I  

Ba  
W* 

Pt*.  . 

Pb* 

Bi*.  .. 

Th  *  

U* 

TABLE  497.  —  Absorption  Coefficients  of  Characteristic  Radiations  in  Gases. 

The  penetrating  power  of  X-rays  ranges  in  normal  air  from  i  to  10,000  cm  or  more.  The  absorptive  power  of  i 
cm  air  =  1/820  that  of  water.  X  (see  preceding  table  for  definition)  for  air  for  soft  bulb  (1.5  to  5  cm  spark  gap,  4  to 
10  m  air)  ranges  from  .0010  to  .0018;  for  hard  bulb  (30  cm  spark  gap,  4  to  10  m  air),  .00029.  (Eve  and  Day,  Phil. 
Mag.  1912.)  The  absorption  coefficient  for  gases  for  characteristic  or  monochromatic  radiations  varies  directly  with 
the  pressure.  For  different  characteristic  radiations  it  is  proportional  to  the  coefficients  in  air.  It  varies  with  the  sth 
power  of  the  atomic  weight  of  the  radiator.  The  following  table  is  taken  from  Kaye's  X-rays  and  is  based  on  the  work 
-of  Barkla  and  Collier  (Phil.  Mag.  1912)  and  Owen.  All  are  for  the  gas  at  o°  C  and  76  cm  Hg. 


Air 

CO2 

SOz 

CjH&Br 

CH,I 

X 

\/d 

X 

\/d 

X 

\/d 

X 

\/d 

X 

\/d 

Fe. 

.0202 
.0165 
.0136 
.0109 
.0090 
•  0053 
.0044 
-0039 
.0023 
.00127 
.00077 

iS-6 
12.7 

10.5 
8.43 
6.96 
4.10 
3-40 

3-02 

1.78 

0.98 
0.59 

.0456 

.0319 
.0227 
.0184 
.00988 
.00782 

.00420 
.00281 

23.1 

16.1 
it-  5 
9-31 
5.00 
3.96 

2.12 
1.42 

•  24 

.20 
.166 
•134 
.112 
.066 
.0546 
.OSO 
.0281 
.Ol6o 
.0079 

83.3 
69.4 

57.6 
46.5 
38.9 
22.9 
19.1 
17.4 
9.76 
5.56 
2-75 

.512 
.407 
.325 
.260 
•  215 
.128 

.110 

.096 
•  325 
.210 
.108 

105. 
83.2 
66.3 
53-1 
43-9 
26.1 
22.4 
19.6 
66.3 
42.9 

22.0 

2.16 

i.  80 
1-54 
1.27 
•743 
.619 
•552 
.338 
.197 
•  113 

339- 

282. 
241. 

& 

8:, 

53-0 

30.9 
17.7 

Co 

Ni... 

Cu.  .. 

Zn.... 

As  
Se. 

Br... 

Sr... 

Mo. 

AK 

SMITHSONIAN  TABLES. 


390 


TABLE  498. 
X-RAY  SPECTRA  AND  ATOMIC   NUMBERS- 


Kaye  has  shown  that  an  element  excited  by  sufficiently  rapid  cathode  rays  emits  Rontgen  rays  characteristic  of 
that  substance.  These  were  analyzed  and  the  wave-lengths  determined  by  Moseley  (Phil.  Mag.  27,  703,  1914),  using 
a  crystal  of  potassium  ferrocyanide  as  a  grating.  He  noted  the  K  series,  showing  two  lines,  and  the  L  series  with  several. 
He  found  that  every  element  from  Al  to  Au  was  characterized  by  integer  N,  which  determines  its  X-ray  spectrum; 
N  is  identified  with  the  number  of  positive  units  associated  with  its  atomic  nucleus.  The  order  of  these  atomic  num- 
bers (AT)  is  that  of  the  atomic  weights,  except  where  the  latter  disagrees  with  the  order  of  the  chemical  properties. 
Known  elements  now  correspond  with  all  the  numbers  between  i  and  92  except  6.  There  are  here  six  possible  elements 
still  to  be  discovered  (atomic  nos.  43,  61,  72,  75,  85). 

The  frequency  of  any  line  in  an  X-ray  spectrum  is  approximately  proportional  to  A  (N  —  ft)2,  where  A  and  ft  are 
constants.  All  X-ray  spectra  of  each  series  are  similar  in  structure,  differing  only  in  wave-lengths.  QK  =  fr/fw); 
Q^  =  (r/,ftt»o)  where  r  is  the  frequency  of  the  a  line  and  vo  the  fundamental  Rydberg  frequency.  The  atomic  number 
for  the  K  series  =  QK+ i  and  for  the  L  series,  QL  +  7-4  approximately,  vo  =  3.29  X  lo1* 

Moseley's  work  has  been  extended,  and  the  following  tables  indicate  the  present  (1919)  knowledge  of  the  X-ray 
spectra. 

(a)  K  SERIES  (WAVE-LENGTHS,  X  X  io8  CM). 


Element, 

0304 

OlOZ 

atomic 

0» 

0i 

Bl 

(not 

03 

Ctl 

(not 

0.2 

number. 

separable) 

separable) 

ii      Na 

_ 

_ 

11.951 

_                    . 

12        Mg 

— 

9-477 

9-845 

— 

9.856 

— 

9-915 



13      Al 

— 

7.986 

8.300 

— 

8.310 

— 

8.360 



14     Si 

—  . 

6-759 

7.080 

__ 

7.088 

^_ 

7  .  1  SI 

— 

IS      P 

16      S 

_ 

5.8o8 
5.018 

6.122 
5-314 

— 

6.  129 
5-317 

— 

6!i68 
5-360 



17      Cl 

— 

4-394 

4.692 

— 

4-712 

—  . 

18      Ar 

_ 

^_ 



__ 

__ 

19      K 

— 

3-449 



3-724 

— 

3-735 

— 

3.738 

20      Ca 

3-074 

3.086 



3-328 

— 

3-355 

— 

3-359 

21      Sc 

2.778 



3.011 

— 

3.028 

— 

3-032 

22        Ti 

2.492 

2-509 



2.729 

— 

2-742 

— 

2.746 

23      Va 

~ 

2.281 

~ 

~ 

2.498 

~ 

2.502 

Element, 

Element, 

atomic 

02 

01 

Cli 

02 

atomic 

02 

0i 

Oi 

0.1 

number. 

number. 

24      Cr 

.069 

2.079 

.284 

.288 

43 

_ 

25      Mn 
26      Fe 
27      Co 
28      Ni 
29      Cu 

.892 

Uss 

•  379 

.902 
.748 
.613 
•497 
•391 

•093 
.928 
.781 
.653 
•539 

.097 
•932 
-785 
.657 

•  543 

44     Ru 
45      Rh 
46     Pd 
47     Ag 
48     Cd 

0-537 
.491 

0.574 
•  547 
.501 
.501 
•479 

0.645 
.615 
.562 
.562 
•  538 

0.619 
.567 
.567 
•  543 

30      Zn 
31      Ga 

.281 

.294 
.206 

•433 
•338 

•437 
•342 

49     In 

50     Sn 

•440 

•453 
•  432 

•  510 

•  487 

-515 
.490 

32      Ge 

.121 

•131 

•257 

•251 

Si     Sb 

.^08 

.416 

.468 

•472 

33      As 

.038 

-052 

.170 

.174 

52     Te 

•404 

-456 

34      Se 

— 

•993 

.104 

.109 

53     I 

— 

•  388 

•437 

_ 

35      Br 
36      Kr 

0.914 

•929 

•035 

.040 

54     X 
55      Cs 

~ 

•352 

•  398 

.402 

37      Rb 
38      Sr 

^767 

.825 
-779 

0.922 
.871 

0.926 
.876 

56     Ba 
57     La 

~ 

•343 
•  329 

-388 
•372 

•  393 
.376 

39      Y 

•733 

.746 

•  835 

.840 

58     Ce 

—  • 

•  314 

•  355 

.360 

40      Zr 
41      Nb 

.657 

•  70S 
.669 

.788 
•  749 

•793 

•  754 

59     Pr 
60     Nd 

•"" 

.301 
.292 

•  342 
•  330 

•347 
•335 

42      Mo 

.633 

.710 

.714 

74     W 

.177 

•  203 

•  335 

SMITHSONIAN  TABLES. 


TABLE   498  (continued). 

X-RAY  SPECTRA  AND  ATOMIC   NUMBERS- 
(6)  L  SERIES  (WAVE-LENGTHS,  X  X  10*  CM). 


391 


Element, 

Element, 

atomic 

I 

at 

tti 

0.3 

atomic 

I 

at 

Oi 

1) 

number. 

number. 

30      Zn 

_ 

_ 

12.346 

_ 

60       Nd 

_ 

•379 

.369 

33      As 

— 

— 

9.701 



62       Sa 

— 

.  210 

.200 



35      Br 

— 

— 

8.391 

8.360 

63       Eu 

— 

.131 

.121 



37      Rb 
38      Sr 
39      Y 

= 

- 

7-335 
6.879 
6.464 

7.305 
6.440 

64       Gd 
65       Tb 
66       Dy 

= 

•054 
-083 
.916 

•043 

973 

.907 

i  -935 

40      Zr 

— 

— 

6.083 

6.057 

67       Ho 

— 

-854 

•843 



41      Nb 

— 

5-731 

5.724 

5.709 

68       Er 

— 

•794 

.783 

1-725 

42      Mo 

— 

5-410 

5.403 

5.381 

70       Ad 

1.892 

.681 

.670 

1.618 

44      Ru 

— 

4-853 

4-845 

4.823 

7i       Cp 

1.834 

.629 

.619 

— 

11   w 

— 

4-374 

4-596 

4-577 
4-352 

73       Ta 
74       W 

1.672 

.528 
.481 

.518 
•471 

1-435 

$    cl 

— 

4-155 
3-959 

4.146 
3-949 

4-133 

76       Os 

77       Ir 

1.840 

•398 
.360 

.388 
-350 



49      In 

— 

3-774 

3-766 

— 

78       Pt 

1.499 

•  323 

-313 

1.242 

50      Sn 

— 

3.604 

3-594 

— 

79       Au 

1-457 

-283 

.271 

1.197 

51      Sb 

— 

3-443 

3-434 

— 

-251 

.240 

— 

52      Te 

— 

3-299 

3-290 

__ 

81       Tl 

1-385 

•215 

.205 

1.124 

53      I 

— 

3-155 

3.146 

— 

82       Pb 

1-348 

.186 

•  175 

1.091 

55      Cs 

— 

.899 

.891 

— 

83       Bi 

I-3I7 

•153 

.144 

1-059 

56      Ba 

— 

.786 

-776 

— 

84       Po 

.109 

57      La 

— 

.674 

.665 



88       Ra 

__ 

— 

.010 

— 

58      Ce 

— 

•573 

.563 

— 

90       Th 

1.  117 

0.969 

•957 

— 

59      Pr 

•472 

.462 

92       U 

i.  066 

0.922 

0.911 

~ 

Element, 

atomic 

ft 

ft 

fr 

ft 

/3a 

7i 

72              7s 

74 

number. 

33      As 

_ 

9-449 

_ 

_ 

_ 

_ 

__ 



35      Br 

— 

8.141 

— 

— 

— 

—  . 

—                — 

— 

37      Rb 

— 

7.091 

— 

—  . 

— 

— 

—                — 

— 

38     Sr 

— 

6.639 

— 

— 

— 

— 

—             — 

— 

39      Y 

— 

6.227 

— 

—  . 

— 

— 

—                     —  — 

— 

40      Zr 

— 

5-851 

— 

— 

— 

5-386 

—             — 

— 

41      Nb 

— 

5-493 

5-317 

— 

—  • 

—              — 

— 

42      Mo 

— 

5-175 

—  . 

—. 



—                     — 

—  • 

44      Ru 

— 

4.630 

— 

— 

— 



—              — 

— 

45      Rh 

— 

4-372 

^— 

—  - 

— 

— 

—  ~                     — 

—  —  ' 

46      Pd 

4.071 

4.144 

3-904 

4-030 

—  . 

3-720 

3-597 

— 

47      Ag 

3-861 

3.928 

3-698 

3-823 

— 

3-515 

—              — 

— 

48      Cd 

3-676 

3-733 

3-514 

3.639 

— 

3-331 

—              — 

— 

49      In 
50      Sn 

3-337 

3-550 
3-381 

3-354 
3-172 

3-300 

3.160 
-999 

2  .  903            2  .  889 

2.831 

51      Sb 

3-184 

3-222 

3-021 

3.149 

— 

.849 

2.782 

— 

52      Te 

3-044 

3-074 

.881 

3.007 

—  • 

.712 



— 

53      I 

2.911 

•934 

.750 

.873 

— 

-583 



— 

55      Cs 

2.668 

.684 

.514 

.629 

—  . 

-350 

2-234 

— 

56      Ba 

2.558 

.569 

.407 

.520 

— 

-245 

—              — 

— 

57      La 

2-453 

.461 

.307 

.414 

— 

.146 

—              — 

— 

58      Ce 

2-357 

-359 

.212 

•  307 

— 

.052 

2.003 

— 

59      Pr 

— 

-259 

.210 

.217 

— 

.958 

1-937         1-933 

— 

60      Nd 

2.  167 

.167 

.036 

.128 

— 

.875 

1.803         1-775 

— 

62      Sa 



.000 

.884 

.965 

— 

•  725 

1.659 

— 

63      Eu 
64     Gd 

1.923 
I.8SI 

.918 

.844 

.810 

•744 

.888 
.811 

— 

.662 
•  597 

I  .  599          I  .  590 
(1.562)       (1.558) 



65      Tb 

1.784 

-775 

.682 

•  745 

1.659 

•  531 

1.477          1.470 

1-437 

SMITHSONIAN  TABLES. 


392 


TABLE  498  (continued). 
X-RAY  SPECTRA  AND  ATOMIC   NUMBERS. 


(6)  L  SERIES  (WAVE-LENGTHS,  X  X  io«  CM). 

Element, 

71 

atomic 

0« 

ft 

ft 

ft 

fr 

72               7s 

74 

number. 

66         Dy 
67         Ho 
68         Er 

.721 
-657 
-599 

.709 
.646 
.586 

.622 
.568 
-514 

.683 
.620 
.560 

- 

1.470 
1.415 
1-367 

1.422         .418 
I  .  369         •  365 

1.323      .316 

— 

70         Ad 

•490 

•474 

.414 

•  451 

1.422 

i. 

20? 

1.228         .223 

— 

7i         Cp 
73         Ta 
74         W 
76         Os 
77          Ir 
78          Pt 

-437 
-343 
.296 
.214 
.176 
.142 

-421 
-323 
.278 
.194 
•154 
.  1  20 

.368 
.280  . 

•*£ 

.167 
-133 
.  ior 

-399 
-303 
-258 
.176 
.138 
.098 

I.  101 

1.072 

1.224 
1.  135 
1.105 

I.  02  1 
0.989 
0.958 

1.188           .183 
i.ioi           .097 
1.064           -058 

0.962           .956 
0.933           -929 

0.917    1 

0.900   1 

79          Au 

.  102 

.080 

.065 

-059 

1-035 

O. 

Q22 

0.898           .894 

0.869 

80         Hg 
81         Tl 

.036 

-049 
.012 

•°4J 
.006 

.998 

0.977 

0. 

o. 

89b 

864 

0.844           .840 

0.808 

82         Pb 

.        .008 

-083 

-983 

.968 

0.842 

0.820           .816 

0.792 

83         Bi 

•977 

•950 

•954 

•937 

0.923 

o. 

810 

0-794           .790 

0.762 

84         Po 

.920 

— 

— 

—              — 

— 

88         Ra 









«M 

—              



oo         Th 



.766 

•  797 

•  758 



0.654 

0.635 

— 

92         U 

~ 

.720 

.756 

.710 

~~ 

o. 

615 

0.596 

: 

(c)  M  SERIES  (WAVE-LENGTHS,  X  X  zo8  CM). 

Element, 

atomic                       a 

0 

Ti 

72 

dl                              52                           6 

number. 

79              Au               5  •  838 

5-623 

5.348 

5.284 

5.146           5.102 

81              Tl                5.479 

5-256 

4.826              4-73S 

82              Pb               5-303 

5-095 

4.910 



4-695 

83              Bi               5-"7 

4-903 

4.726 



4.561              4-532              4-456 

90              Th               4-139 

3-941 

3.812 

3.678 

.                                         —                                        —. 

92               U                 3-905 

3-715 

3.480 

3-363              3-324 

Reference:   Jahrbuch  der  Radioaktivitat  und  Elektronik,  13,  296,  1916. 


(d)  TUNGSTEN  X-RAY  SPECTRUM  (WAVE-LENGTHS,  X  X  lo8  CM). 

The  wave-lengths  of  the  tungsten  X-ray  spectrum  have  been  measured  more  frequently  than  those  of  any  other 
element.  The  following  values  are  perhaps  the  most  accurate  that  have  hitherto  been  published.  Compton,  Physical 
Review,  7,  646,  1916  (errata,  8,  753,  1916). 


Line. 

X 

Line. 

X 

Line. 

X 

a 

•  0249 

e 

1.2185 

3 

1-3363 

b 

0399 

f 

I.  2420 

k 

1-4735 

c' 

c" 

.0582 
.0652 

i 

I.  2601 

1.2787 

/ 

i  .  4844 

d 

•  0959 

i 

1.2985 

Other  references  on  the  X-ray  spectrum  of  tungsten:    Gorton,  Physical  Review,  7,  203,  1916;   Hull,  Proc.  Nat. 
Acad.  Sci.  2,  265,  1916;  Dershem,  Physical  Review,  n,  461, 1918;  Overn,  Physical  Review,  14, 137,  1919. 
The  following  values  for  tungsten  are  from  Duane  and  Patterson,  Phys.  Rev.  16,  p.  526,  1920 : 


Critical  Absorption  wave-lengths  X  10"  cm. 

Ka       .17806  l,al     1.2136  La.,  1.0726 

Emission  wave-length  X  io»  cm. 

Ko,      .21341  Kaj      .20860  K/3       .18420 

L«4     1-4^39  Lat  1.47306 

L^4     1.2985  L/3t     1.27892  L/3S  1.260! 

LY,     1.09608  Ly2     1.0655  Ly3  1.0596 


Las       1.024 


KA        .17901 

LTJ  1.4176 

L0.,  1.24193 

Ly4  1.0261 


L/36     1.2040 


SMITHSONIAN  TABLES. 


TABLE    499. 
X-RAY   ABSORPTION   SPECTRA  AND  ATOMIC   NUMBERS- 


393 


A  marked  increase  in  the  absorption  of  X-rays  by  a  chemical  element  occurs  at  frequencies 
close  to  those  of  the  X-rays  characteristic  of  that  element.  The  absorption  coefficient  is  much 
greater  on  the  short  wave-length  side.  In  the  K  series  the  a  lines  are  much  stronger  than  the 
corresponding  /3  and  7  lines,  but  the  wave-lengths  of  the  a  lines  are  greater.  There  is  a  marked 
increase  in  the  absorption  at  wave-lengths  considerably  shorter  than  the  a  lines  and  near  the 
/3  lines.  Bragg  came  to  the  conclusion  that  the  critical  absorption  frequency  lay  at  or  above 
the  7  of  the  K  series.  The  7  line  has  a  frequency  about  i  per  cent  higher  than  the  corresponding 
/3  line.  For  the  L  series  there  are  3  characteristic  marked  absorption  changes  (de  Broglie). 

The  critical  absorption  wave-lengths  of  the  following  table  are  due  to  Blake  and  Duane, 
Phys.  Rev.  10,  697,  1917.  The  equation  v  =  i>0(N  -  3.5)2  where  v  is  Rydberg's  fundamental 
frequency  (109,675  X  the  velocity  of  light)  and  N  the  atomic  number,  represents  the  data  with 
considerable  accuracy.  The  nuclear  charge  is  obtained  by  Q  =  2e(N  -  3.5). 


Element. 

Atomic 
number. 

AU 

Element. 

Atomic 
number. 

AU 

Element. 

Atomic 
number. 

Au 

Bromine  
Krypton  
Rubidium  .... 
Strontium.  .  .  . 
Yttrium  .  .  . 

35 
36 
37 
38 
39 
40 

4i 

42 

.9179 

.8143 
.7696 

.7255 
.6872 

•6503 
.6180 

Ruthenium 
Rhodium  .  . 
Palladium. 
Silver 

44 
45 
46 

47 
48 

49 
50 
Si 

.5584 
•5324 
•5075 
.4850 
.4632 

•  4434 
.4242 
.4065 

Tellurium.  . 
Iodine  

52 
53 
54 
55 
56 
57 
58 

.3896 
•3727 

•3444 
•3307 
.3188 

•3073 

Xenon  
Caesium  .  .  . 
Barium.  .  .  . 
Lanthanum 
Cerium.  .  .  . 

Cadmium.  . 
Indium  .... 
Tin 

Zirconium.  .  .  . 
!  Columbium  .  . 
Molybdenum. 

Antimony  . 

SMITHSONIAN  TABLES. 


394  TABLES  600-502.  -  RADIOACTIVITY. 

Radioactivity  is  a  property  of  certain  elements  of  high  atomic  weight.  It  is  an  additive 
property  of  the  atom,  dependent  only  on  it  and  not  on  the  chemical  compound  formed  nor 
affected  by  physical  conditions  controlling  ordinary  reactions,  viz :  temperature,  whether  solid  or 
liquid  or  gaseous,  etc. 

With  the  exception  of  actinium,  radioactive  bodies  emit  o,  0,  or  y  rays,  a  rays  are  easily  ab- 
sorbed by  thin  metal  foil  or  a  few  cms.  of  air  and  are  positively  charged  atoms  of  helium  emitted 
with  about  1/15  the  velocity  of  light.  They  are  deflected  but  very  slightly  by  intense  electric  or 
magnetic  fields.  The  $  rays  are  on  the  average  more  penetrating,  are  negatively  charged  particles 
projected  with  nearly  the  velocity  of  light,  easily  deflected  by  electric  or  magnetic  fields  and 
identical  in  type  with  the  cathode  rays  of  a  vacuum  tube.  The  y  rays  are  extremely  penetrating 
and  non-deviable,  analogous  in  many  respects  to  the  very  penetrating  Rontgen  rays.  These  rays 
produce  ionization  of  gases,  act  on  the  photographic  plate,  excite  phosphorescence,  produce  certain 
chemical  reactions  such  as  the  formation  of  ozone  or  the  decomposition  of  water.  All  radio- 
active compounds  are  luminous  evert  at  the  temperature  of  liquid  air. 

Table  506  is  based  very  greatly  on  Rutherford's  Radioactive  Substances  and  their  radiations 
(Oct.  1912).  To  this  and  to  Landolt-Bornstein  Physikalisch-chemische  Tabellen  the  reader  is  re- 
ferred for  references.  In  the  three  radioactive  series  each  successive  product  (except  Ur.  Y,  and 
Ra.  C2)  results  from  the  transformation  of  the  preceding  product  and  in  turn  produces  the  follow- 
ing. When  the  change  is  accompanied  by  the  ejection  of  an  a  particle  (helium,  atomic  weight  =  4.0) 
the  atomic  weight  decreases  by  4.  The  italicized  atomic  weights  are  thus  computed.  Each  pro- 
duct with  its  radiation  decays  by  an  exponential  law  ;  the  product  and  its  radiation  consequently 
depend  on  the  same  law.  I  =  Ioe~At  where  Io  =  radioactivity  when  t  =  O,  I  that  at  the  time  t, 
and  A.  the  transformation  constant.  Radioactive  equilibrium  of  a  body  with  its  products  exists 
when  that  body  is  of  such  long  period  that  its  radiation  may  be  considered  constant  and  the 
decay  and  growth  of  its  products  are  balanced. 

International  radium  standard :  As  many  radioactivity  measures  depend  upon  the  purity  of  the 
radium  used,  in  1912  a  committee  appointed  by  the  Congress  of  Radioactivity  and  Electricity, 
Brussels,  1910,  compared  a  standard  of  21.99  mS-  °^  Pure  Ra-  chloride  sealed  in  a  thin  glass  tube 
and  prepared  by  Mme.  Curie  with  similar  standards  by  Honigschmid  and  belonging  to  The 
Academy  of  Sciences  of  Vienna.  The  comparison  showed  an  agreement  of  i  in  300.  Mme. 
Curie's  standard  was  accepted  and  is  preserved  in  the  Bureau  international  des  poids  et  mesures 
at  Sevres,  near  Paris.  Arrangements  have  been  made  for  the  preparation  of  duplicate  standards 
for  governments  requiring  them. 

TABLE  500.  —Relative  Phosphorescence  Excited  by  Radium. 
(Becquerel,  C.  R.  129,  p.  912,  1899.) 


Without  screen, 

Hexagonal  zinc  blende   .... 

13-36 

With  screen    . 

.04 

« 

« 

Diamond         ...... 

1.14 

« 

ii 

.01 

it 

•« 

Double  sulphate  Ur  and  K   . 
Calcium  fluoride     

1.  00 

•3° 

" 

«    :    : 

•  31 

.02 

The  screen  of  black  paper  absorbed  most  of  the  a  rays  to  which  the  phosphorescence  was  greatly  due.     For  the  last 
column  the  intensity  without  screen  was  taken  as  unity.     The  y  rays  have  very  little  effect. 

TABLE  501.  — The  Production  of  a  Particles  (Helium). 

(Geiger  and  Rutherford,  Philosophical  Magazine,  20,  p.  691,  1910.) 


Radioactive  substance  (i  gram.) 

a  particles 
per  sec. 

Helium  per  year. 

Uranium    
Uranium  in  equilibrium  with  products     . 
Thorium  "           "                                         . 
Radium     ........ 
Radium  hi  equilibrium  with  products 

2.37  X  10* 
9.7    X  io* 
2.7    X  io4 
3-4    X  io«> 
13.6    X  ioio 

2.75  X  io—5  cu.  mm. 
n.o    X  io—  5  "       " 
3.1     X  io-6  "       " 

39             "       " 
158             "       " 

TABLE  502. —Heating  Effect  of  Radium  and  Its  Emanation. 

(Rutherford  and  Robinson,  Philosophical  Magazine,  25,  p.  312,  1913.) 


Heating  effect  in  gram-calories  per  hour  per  gram  radium. 

a  rays. 

0  rays. 

y  rays. 

To*]. 

Radium    .... 
Emanation 
Radium  A        ... 
Radium  B  -f  C 

25.1 
28.6 
30-5 
39-4 

4-7 

6.4 

25-1 
28.6 
30.5 
50.5 

Totals      .... 

123.6 

4-7 

6-4 

134-7 

Other  determinations :  Hess,  Wien.  Ber.   121,  p.  i,  1912,  Radium  (alone)  25.2  cal.  per  hour  per  gram.     Meyer  and 
Hess,  Wien.  Ber.  121,  p.  603,  1912,  Radium  in  equilibrium,  132.3  gram.  cal.  perohour  per  gram.     See  also,  Callendar, 
Phys.  Soc.  Proceed.  23,  p.  i,  1910;  Schweidler  and  Hess,  Ion.  i,  p.  161,  1909;  Angstrom,  Phys.  ZS.  6,  685,  1905,  etc. 
SMITHSONIAN  TABLES. 


395 


TABLES  603-505. 
RADIOACTIVITY. 

TABLE  503.  — Stopping  Powers  of  Various  Substances  for  a  Rays. 

s,  the  stopping  power  of  a  substance  for  the  a  rays  is  approximately  proportional  to  the  square 

root  of  the  atomic  weight,  w. 


Substance 

H2 

Air 

02 

C2H2 

C2H4 

Al 

N20 

CO, 

CH8Br 

CS2 

Fe 

s      ... 

.24 

1.0 

1.05 

i.  ii 

'•35 

1-45 

1.46 

1.47 

2.09 

2.18 

2.26 

Vw.     .     . 

.20 

1.0 

1.05 

I.i; 

1.44 

1-37 

1.52 

1.51 

2.03 

1.95 

1.97 

Substance 

Cu 

Ni 

Ag 

Sn 

C.H. 

CH 

C2H5I 

CC14 

Pt 

Au 

Pb 

s       ... 

2.43 

2.10 

2.46 

2.2O 

3-'7 

2.74 

& 

3-37 
3-53 

^ 

3-'3 

4.02 
3-59 

4.16 
3-68 

4-45 
3-70 

4.27 
3-78 

Bragg,  Philosophical  Magazine,  n,  p.  617,  1906. 

TABLE  504,-  Absorption  of  0  Rays  by  Various  Substances. 

/*,  the  coefficient  of  absorption  for  ft  rays  is  approximately  proportional  to  the  density,  D. 

Table  506  for  n  for  Al. 


See 


Substance    .     . 

B 

C 

Na 

Mg 

Al 

Si 

P 

S 

K 

Ca 

fJL/D       .        .       .       . 

4-65 

4.4 

4-95 

S-i 

5.26 

5'5 

6.1 

6.6 

6-53 

6.47 

Atomic  Wt.     . 

ii 

12 

23 

24.4 

27 

28 

3i 

32 

39 

40 

Substance    .     . 

Ti 

Cr 

Fe 

Co 

Cu 

Zn 

Ar 

Se 

Sr 

Zr 

fJL/D       .... 

6.2 

6.25 

6.4 

6.48 

6.8 

6.95 

8.2 

8.65 

8-s 

8-3 

Atomic  Wt.     . 

48 

52 

56 

59 

63-3 

65.5 

75 

79 

87.5 

90.7 

Substance   .     . 

Pd 

Ag 

Sn 

Sb 

I 

Ba 

Pt 

Au 

Pb 

U 

Ai/D    .     .     .     . 

8.0 

8.3 

9.46 

9.8 

10.8 

8.8 

9.4 

9-5 

10.8 

IO.I 

Atomic  Wt.     . 

106 

108 

118 

120 

126 

137 

195 

197 

207 

240 

For  the  above  data  the  £  rays  from  Uranium  were  used. 
Crowther,  Philosophical  Magazine,  12,  p.  379,  1906. 

TABLE   506^- Absorption  of  7  Rays  by  Various  Substances. 


Substance. 

Density. 

Radium  rays. 

Uranium  rays. 

Th.  D. 
Mcm)-i 

Meso.  Tha 
M(cm)-1 

Range  of 
thickness 
cm. 

/u  (cm)-1 

IOOJA/D 

Mem)-1 

IOOM/D 

Hg    .    . 
Pb     .    . 

T3-59 

11.40 

.642 

•495 

4.72 

4-34 

.832 

•725 

6.12 
6.36 

.462 

.620 

•3  to    3-5 
.0  "    7.9 

Cu    .      . 
Brass      . 
Fe 
Sn 
Zn 

8.8  1 

& 

7.24 
7.07 

•351 
•325 

•3°4 
.281 
.228 

3-93 

.416 
•392 
.360 
•341 
•329 

4.72 
4.70 
4.72 
4.70 
4-65 

.294 
.271 
.250 
.236 

•233 

•373 

•355 
.316 

•3°5 
.300 

.0  "    7.6 
.0  "    5.86 
.0  "    7-6 
•o  "    5-5 
.0  "    6.0 

Slate      . 
Al 

2.85 
2.77 

.118 
.in 

4.14 
4.06 

•134 
.130 

4.69 
4.69 

.096 
.092 

.119 

.0  "    9.4 

.0   "    II.  2 

Glass      . 

S   .     .     . 

2.52 
1.79 

.105 
.078 

4.16 
4-38 

.122 
.092 

4.84 
5.l6 

.089 
.066 

•«3 

.083 

.0  "  11.3 
.0  "  1  1.  6 

Paraffin  . 

.86 

.042 

4.64 

•043 

5.02 

.031 

.050 

.0  "  11.4 

In  determining  the  above  values  the  rays  were  first  passed  through  one  cm.  of 
Russell  and  Soddy,  Philosophical  Magazine,  21,  p.  130,  1911. 

SMITHSONIAN  TABLES. 


396 


TABLE  606. 
RADIOACTIVITY. 


P  =  1/2  period  =  time  when  body  is  one  half  transformed.  A  =  transformation  constant  (see  previous  page). 
The  initial  velocity  of  the  a  particle  is  deduced  from  the  formula  of  Geiger  V3  =  aR,  where  R  =  range  and  assuming 
the  velocity  for  RaC  of  range  7.06  cm.  at  20°  is  2.06  X  io»  cm  per  sec.,  i.e.,  v  =  1.077^. 


1  ,  , 

URANIUM-RADIUM  GROUP. 

a   rays. 

Atomic 
weights. 

1/2  period, 
P 

Transforma- 
tion 
constants. 

x  _  -6931 

Rays. 

Range. 
760""", 
15°  C 

Initial 
velocity. 

Kinetic 
energy. 

Whole  no. 
of  ions 
produced. 

cm 

cm  per  s 

Ergs. 

By  an  a 
particle. 

Uranium  i  .  .  .  . 
Uranium  Xi..  . 
Uranium  X2.  .  . 

238.2 
234.2 
234-2 

5  X  io»  y. 
24.6  d. 
1.15  m. 

1.4  X  io~10y. 
.0282  d. 
.01  sec. 

flj-r 

2.50 

1-45  Xio» 

.65    X  10-5 

i  .  26  X  10" 

Uranium  2  .... 
Uranium  Y.  .  .  . 

234-2 

23O  .  2? 

io6  yr. 
1.5  d. 

7  X  io-7  y. 
.46d. 

a 
0 

2.90 

1.53  Xio» 

.  72   X  10-5 

1.37  X  108 

Ionium  

230.2 

io5  yr. 

7  .  o  X  io6  y. 

3.11 

i  .  56  X  io8 

•75   XlO-6 

1.40X10* 

Radium  
Ra  Emanation  . 

226 
222 

1730  y. 
3-8sd. 

.  00040  y. 
.  180  d. 

a+0 
a 

3-30 
4.16 

1.61 

i-73         " 

•79 
•92 

1.50 
1.74 

Radium  A  

218 

3.0  m. 

.231  m. 

a 

4-75 

1.82         " 

I.OI 

1.88        " 

Radium  B  

214 

26.8  m. 

.0258  m. 

0  +  7 

Radium  Ci.  .  .  . 

214 

19-5  m. 

.0355  m. 

a  +  /3 

— 

— 

— 

— 

RaCz  

210? 

1.4  m. 

.495  m. 

Q 

^_ 

, 

__ 



Radium  C'  

700000  s. 

a 

6  94 

2.o6Xio9 

I.3I   X  I0~8 

2.37X108 

Ra  D,  radio- 

lead  

210 

IS-  8y. 

.  044  y. 

slow/3 

— 

— 



— 

Ra  E. 

2IO 

4  8*  d. 

14'?  d 

S  +  T 

___. 

Ra  F.  Polonium 

210 

136  d. 

.00510  d. 

a 

3-84 

1.68  X  io« 

.87  X  io-« 

1.63    X  TO* 

ACTINIUM  GROUP. 

Actinium  
Radio-  Act.  .  .  . 
Actinium  X  ... 

A,  230? 
A 
A  -4 

19-5  d. 

10.  2  d. 

•0355  d. 
.o68d. 

a? 
a 

3-56 
4.  26 

i.64X  io« 
1.7 

1.76 

.  82  X  10-5 

•9 

•94 

•55X10* 

.8 
•  79 

Act.  Emanation 

A  -8 

3.95. 

.1783. 

a 

5-57 

1.91        " 

I.  12 

•04 

Actinium  A.  ... 

A   -  12 

.002  s. 

•  350  s. 

a 

6.27 

1.98 

I.  21 

.  20 

Actinium  B..  .  . 

A  -  16 

36  m. 

.0193  m. 

slow  0 

Actinium  Ci.  .  . 
Actinium  D  .  .  . 

A  -  16 

A    —  20 

2.1  m. 
4.7  m. 

•  33m. 
.147 

a 

0  +  7 

5-iS 

1.85  Xio» 

I  .  05    X  10-5 

1.94  X  io5 

Actinium  C'.  .  . 

A    —  20 

a 

6-45 

2.00            " 

1.23 

— 

THORIUM  GROUP. 

Thorium  
Mesothorium  i 

232 
228 

1.3  X  io10y. 

5-3  X  io-" 
.126  yr. 

a 

none 

2.72 

r  .  50  X  io» 

.  69  X   10-5 

1.32    X  105 

Mesothorium  2 

228 

6.2  hr. 

.112  h. 

0  +  7 





__. 



Radiothorium.  . 
Thorium  X.... 

228 
224 

2  yr. 
3-65d. 

•347y- 
.  190  d. 

a 

3-87 
4-3° 

r  .  70  X  io» 

i-75 

.89     XlO-5 

•94 

I.66X  108 
1.8          " 

Th.  Emanation. 

22O 

54  sec. 

.0128  s. 

a 

5-oo 

1.85        " 

1.04 

1.9           " 

Thorium  A.  ... 
Thorium  B  

216 

212 

o.  14  sec. 
10.6  h. 

4-95  s. 
.0654  h. 

a 

0  +  7 

5-70 

1.94 

I.  IS 

2.2 

Thorium  Ci  .  .  . 

212 

60  m. 

.0118  m. 

a  +0 

4.80 

i  .  76  X  io» 

.95    X  10-6 

i  8     X  io5 

Thorium  D.... 

208 

3.1  m. 

.  224  m. 

. 

Thorium  C'  .  .  . 

212 

iQ-u  sec. 

7  X  101°  sec. 

a 

8.6 

2.22    X  IO9 

i  •  53  X  io-5 

2.9       X   105 

Potassium  

39-1 

? 

P 

P 

Rubidium  

85-5 

? 

? 

* 

I 

I 

See  The  Constants  of  Radioactivity,  Wendt,  Phys.  Rev.  7,  p.  389,  1916. 
SMITHSONIAN  TABLES. 


TABLE  606  (continued). 
RADIOACTIVITY. 


397 


fj.  =  coefficient  of  absorption  for  ft  rays  in  terms  of  cms.  of  aluminum;  Mlf  of  the  y  rays  in  cms  of  Al   so  that  if 
/o  is  the  incident  intensity,  J  that  after  passage  through  d  cms,  /  =  Joe  dp. 


URANIUM  -RADIUM  GROUP. 

/3  rays. 

7  rays. 

Remarks. 

Absorption 
coefficient  =  n 

Velocity 
light  =  i 

Absorption 
coefficient  =  /xi 

Ur  i  

5io 
14.4 
300 

200 

13,  80,  890 
13,  S3 

130 
43 

Wide  range 
•52,  .65 

.  36  to  .  74 
.80  to  .98 

Wide  range 

24,  .70,  .140 
354,  16,  .27 

230.40,  .51 
•  IIS 

45,  -99 

Like  Ra  D 
585 

i  gram  U  emits  2.37  X  io«  a  particles  per 
sec. 
/9  rays  show  no  groups  of  definite  veloci- 
ties.    Chemically  allied  to  Th. 

Not  separable  from  Ur  i. 
Probably  branch  product.    Exists  in  small 
quantity. 
Chemical  properties  of  and  non-separable 
from  Thorium. 
Chemical  properties  of  Ba.    i  gr  emits 
per  sec.  in  equilib.  13.6  X  to10  a  par- 
ticles. 
Inert  gas,  density  in  H,  boils  -65°  C, 
density  solid  5-6,  condenses  low  pres- 
sure —  150°  C. 
Like  solid,  has  +  charge,  volatile  in  H. 
400°,  in  O  about  550°. 
Volatile  about  400°  C  in  H.      Separated 
pure  by  recoil  from  Ra  A. 
Volatile  in  H  about  430°,  in  O  about  1000°. 
Probably  branch  product.    Separated  by 
recoil  from  Ra  C. 
Separated  with  Pb,  not  yet  separable  from 
it.    Volatile  below  1000°. 

Separated  with  Bi.    Probably  changes  to 
Pb.    Volatile  about  1000°. 

UrXi  
UrXi... 

Ur  2... 

Ur  Y 

Io  

Ra  

Ra  Em  

RaA  
RaB  

RaCi  
Ra  C2 

RaD 

RaE... 
Ra  F  

ACTINIUM  GROUP. 

Act      .     .  . 

170 

Very  soft 
28~S 

— 

25,  .  190 

120,31,  -45 
.798 

Probably     branch     product     Ur  series. 
Chemically  allied  to  Lanthanum. 

Chemical  properties  analogous  to  Ra. 
Inert  gas,  condenses  between  —120°  and 
—150°. 
Analogous  to  Ra  A.    Volatile  above  400°. 
<?        "  Ra  B.         "           "      700°. 
"        "  Ra  C. 
(Obtained  by  recoil.) 

Rad.  Act.  .  .  . 
Act  X  
Act  Em  

Act  A 

ActB  
ActCi  
ActD  

THORIUM  GROUP. 

Th  
Mes.Th.  i.. 

Mes.  Th.  2  .  . 
Rad.  Th  

Th.  X  .  . 
Th.  Em  

Th  A 

20  tO  38.5 

About  330 

no 
15.6 

24.8 

.37  to  .66 

•47       -Si 
.63       .72 

•  3,  -4,  -93-5 

26,  .116 

160,  32,  .36 
Weak 

.006 

Volatile  in  electric  arc.    Colorless  salts  not 
spontaneously  phosphorescent. 
Chemical  properties  analogous  to  Ra  from 
which  non-separable. 

Chemically   allied   to  Th,  non-separable 
from  it. 
Chemically  analogous  to  Ra. 
Inert  gas,  condenses  at  low  pressure  be- 
tween  —  120°  and   —150". 
+  charged,  collected  on  —  electrode. 
Chemically  analogous  to  Ra  B.    Volatile 
above  630°  C. 
Chemically  analogous  to  Ra  C.    Volatile 
above  730°. 
Th.  Cland  Th.D  are  probably  respect  i 
/3  and  <i  rav  products  from  Th.  Ci. 
Got    by    recoil    from  Th.  C.      Probably 
transforms  to   Hi 

Th.  B  
Th.  Ci  
Th.  C'  
Th.  D  

K.., 
Rb  

38,  102 
380,  1020 

- 

— 

Activity  =  i/iooo  of  Ur. 
=  1/500  of  Ur. 

SMITHSONIAN  TABLES. 


398 


TABLES  507-510. 
RADIOACTIVITY. 

TABLE  507.  —Total  Number  oi  Ions  produced  by  the  a,  0.  and  7  Rays. 


The  total  number  of  ions  per  second  due  to  the  complete  absorption  in  air  of  the  /8  rays  due  to  I 
gram  of  radium  is  9  Xio14,  to  the  y  rays,  i3Xio14. 

The  total  number  of  ions  due  to  the  a  rays  from  i  gram  of  radium  in  equilibrium  is  2-56XIO16. 
If  it  be  assumed  that  the  ionization  is  proportional  to  the  energy  of  the  radiation,  then  the  total 
energy  emitted  by  radium  in  equilibrium  is  divided  as  follows :  92.1  parts  to  the  a,  3.2  to  the  )8,  47 
to  the  7  rays.  (Rutherford,  Moseley,  Robinson.) 

TABLE   508.— Amount  of  Radium  Emanation.    Curie. 

At  the  Radiology  Congress  in  Brussels  in  1910,  it  was  decided  to  call  the  amount  of  emanation 
in  equilibrium  with  i  gram  of  pure  radium  one  Curie.  [More  convenient  units  are  the  millicurie 
(io~3Curie)  and  the  microcurie  (io~6Curie)].  The  rate  of  production  of  this  emanation  is  1.24X10— 9 
cu.  cm.  per  second.  The  volume  in  equilibrium  is  0.59  cu.  mm.  (760  cm.,  O°C.)  assuming  the  emana- 
tion mon-atomic. 

The  Mache  unit  is  the  quantity  of  Radium  emanation  without  disintegration  products  which 
produces  a  saturation  current  of  io~ 3  unit  in  a  chamber  of  large  dimensions,  i  curie  =  2.5 Xio9 
Mache  units. 

The  amount  of  the  radium  emanation  in  the  air  varies  from  place  to  place  ;  the  amount  per  cubic 
centimeter  of  air  expressed  in  terms  of  the  number  of  grams  of  radium  with  which  it  would  be  in 
equilibrium  varies  from  24Xio~12  to  35oXio-12. 

TABLE  509.— Vapor  Pressure  of  the  Radium  Emanation  In  cms.  of  Mercury. 

(Rutherford  and  Ramsay,  Phil.  Mag.  17,  p.  723,  1909,  Gray  and  Ramsay,  Trans. 
Chem.  Soc.  95,  p.  1073,  I9°9-) 

Temperature  C°.    —127°  — 101°  —65°  —56°  — 10°   +17°  +49°   +73°   +100°   +104°    (crit) 
Vapor  Pressure.          0.9  5         76       100       500     1000     2000     3000      4500      4745 

TABLE  510.  -  References  to  Spectra  of  Radioactive  Substances. 

Radium  spectrum:  Dema^ay,  C.  R.  131,  p.  258,  1900. 

Radium  emanation  spectrum  :     Rutherford  and  Royds,  Phil.  Mag.  16,  p.  313,  1908  ;  Watson,  Proc. 

Roy.  Soc.  A  83,  p.  50,  1909. 
Polonium  spectrum:  Curie  and  Debierne,  Rad.  7,  p.  38,  1910,  C.  R.  150,  p.  386,  1910* 

SMITHSONIAN  TABLES. 


TABLES  511-512. 
TABLE  511.  -    Molecular  Velocities. 


399 


The  probability  of  a  molecular  velocity  *  is  (4/  VTT)^*,  the  most  probable  velocity  being  taken  as  unity.    The 
number  of  molecules  at  any  instant  of  speed  greater  than  c  is  tlT(fa»/*)i /jfrto* &+«*•*»*  }  (see  table), 
where  .V  is  the  total  number  of  molecules.    The  mean  velocity  G  (sq.  it.  of  mean'sq.)  is  proportional  to  the  mean 
kinetic  energy  and  the  pressure  which  the  molecules  exert  on  the  walls  of  the  vessel  and  Is  equal  to  i  s  800  VfTm  cm/* 
where  T  is  the  absolute  temperature  and  m  the  molecular  weight.    The  most  probable  velocity  U  denoted  b 
average  arithmetical  velocity  by  ft. 

G  =  w  V77^  =  i .  225^;       a  =  w  V4/r 


by  W,  the 


1.I2&W; 


C  - 


-  I.086Q. 


The  number  of  molecules  striking  unit  area  of  inclosing  wall  is  (i/4)tfQ  (Meyer's  equation),  where  N  is  the  number 
of  molecules  per  unit  volume;  the  mass  of  gas  striking  is  (i/4)pfi  where  p  is  the  density  of  the  gas.  For  air  at  normal 
pressure  and  room  temperature  (20°  C)  this  is  about  14  g/cmVsec.  See  Langmuir,  Phys.  Rev.  2.  1913  (vapor  pres- 
sure of  W)  and  J .  Arner.  Ch.  Soc.  37,  iQiS  (Chemical  Reactions  at  Low  Pressures),  for  fertile  applications  of  these  latter 
equations.  The  following  table  is  based  on  Kinetic  Theory  of  Gases,  Dushman,  Gen.  Elec.  Rev  18  xois  and  Jeans 
Dynamical  Theory  of  Gases,  igi6. 


Gas 

Molec- 

Sq.  rt.  mean  sq. 
G  X  io-«  cm/sec. 

Arithmetical  average  velocity, 
12  X  ID-'  cm/sec. 

weight. 

273° 

293° 

373° 

223° 

273° 

293° 

373° 

1000° 

I5OO8 

2000° 

6ooo» 

Air  

28.96 
17.02 
39-88 
28.00 
44.00 

485 
633 
413 
493 
393 

502 

655 
428 

5" 

408 

S67 
740 
483 
576 
459 

404 
527 
344 
410 
327 

447 
583 
38l 
454 
362 

463 
604 
395 

471 
376 

522 
68  1 
445 
531 
434 

855 
l"5 
729 
870 
094 

1047 
1367 
892 
1065 
850 

1209 
1577 
IO30 
1230 

081 

2094 
2734 
1784 
2130 
1700 

Ammonia. 

Argon  
Carbon  monoxide  .  . 
Carbon  dioxide.  .  .  . 

Helium  

4.00 

1311 

1358 

1533 

1092 

1208 

1252 

1412 

2300 

2840 

3270 

5680 

Hydrogen  
Krypton  

2.01 
82.  Q2 

1838 
286 

1904 
296 

2149 
335 

1534 
238 

1696 
263 

1755 
272 

1980 
308 

3241 
502 

3970 
618 

4583 
712 

7040 
I23O 

Mercury  

200.6 

184 

191 

215 

154 

170 

176 

199 

325 

308 

459 

796 

Molybdenum  

96.0 

— 

469 

57S 

664 

II5O 

Neon  

20.2 

S84 

6os 

68* 

486 

S^8 

557 

629 

1030 

1260 

1460 

2520 

Nitrogen  

28.02 

493 

5" 

577 

410 

454 

471 

531 

869 

1064 

1229 

2128 

Oxygen. 

\2    OO 

461 

478 

539 

384 

425 

8n 

006 

Tungsten  

184.0 

339 

416 

480 

Kl 

Water  vapor  

18.02 

I3O    2 

6iS 
228 

637 
236 

720 
267 

512 
I  QO 

566 

2IO 

587 
218 

662 
246 

1084 

1317 

1533 

57O 

Itt 

Free  electron,  molecular  weight  =  1/1835  when  H  =  i;  G=  1.  114  X  io7  at  o8  C  and  ft  =  1.026  X  io7 

at  o°  C. 

TABLE  512.  —  Molecular  Free  Paths,  Collision  Frequencies  and  Diameters. 

The  following  table  gives  the  average  free  path  L  derived  from  Boltzmann's  formula  n  ( .  35O2pl2),  n  being  the  vis- 
cosity, p  the  density,  and  from  Meyer's  formula  At (.3097pQ).  Experimental  values  (Verb.  d.  Phys.  Ges.  14,  596, 1912: 
15,  373.  I9J3)  agree  better  with  Meyer's  values,  although  many  prefer  Boltzmann's  formula.  As  the  pressure  decreases, 
the  free  path  increases,  at  one  bar  (ordinary  incandescent  lamp)  becoming  5  to  io  cm.  The  diameters  may  be  deter- 
mined from  L  by  Sutherland's  equation  {i.402/"\/27r./VL(i  +  C/T)}$,  N  being  the  number  of  molecules  per  unit 
vol.  and  C  Sutherland's  constant;  from  van  der  Waal's  b.  {zb/2NVir}$'>  from  the  heat  conductivity  k,  the  specific 
heat  at  constant  volume  cv,  {.itfpGcv/Nk}}  (Laby  and  Kaye);  a  superior  limit  from  the  maximum  density  in  solid 
and  liquid  states  (Jeans,  Sutherland,  1916)  and  an  inferior  limit  from  the  dielectric  constant  D,  [(D  —  i)j/r.V}l» 
or  the  index  of  refraction  n,  {(n2  —  i)2/7r/vH.  The  table  is  derived  principally  from  Dushman,  I.e. 


1  
Gas. 

L  X  TO*  (cm) 
Average  free  path.* 

Collision 
frequency. 
Q/L 
Xio-« 

20°  C* 

lo'  X  Molecular  diameters  (cm): 

From  L 
(vis- 
cosity) 
M 

From 
van  der 

Waal's 

B 

From 
heat 
conduc- 
tivity 

Limiting 

Boltzmann. 

Meyer. 

Max 

density 
P 

Min. 
D  or  H 

o°C 

20°  C 

20°  C 

5-92 
8.98 
8.46 
5.56 
25-25 
16.00 
9-5 

8~So 
9-05 
5-6 

6.60 
9.88 
9-23 
6.15 
27-45 
17-44 

(14-7°) 
9.29 
9-93 

5-83 
8-73 
8.16 
5-44 
33-10 
15.40 

(I3.o) 

8.21 

8.78 

9150 

4000 
5100 
6120 
4540 
10060 

5070 
4430 

2  97 
2.88 
3   19 

1.90 
2.40 

2jj 

3-08 

2-94 
3   12 
3-23 
2.6S 

2-34 
(3-69) 
3  oi 
3  15 
2.92 
4-02 

2.86 

3  40 
2-30 
2.32 
3   M 

3-53 

3-42 

217 

3-27 

J:3 

2.40 
3  35 

3  23 
2.99 
3-5S 

2.66 
•74 
90 
92 

(   '.70) 
95 
(I'll) 

Argon  
Carbon  monoxide 
dioxide.. 
Helium  
Hydrogen  

Mercury  
Nitrogen  
Oxygen  
Xenon  

*  Pressure  =  io8  bars  =  io«  dynes  -i-  cm1  =  75  cm  Hg. 


SMITHSONIAN  TABLES. 


400 


TABLES  513-514. 
TABLE  513.  —  Cross  Sections  and  Lengths  of  Some  Organic  Molecules. 


According  to  Langmuir  (J.  Am.  Ch.  Soc.  38,  2221,  1916)  in  solids  and  liquids  every  atom  is  chemically  combined 
to  adjacent  atoms.  In  most  inorganic  substances  the  identity  oi  the  molecule  is  generally  lost,  but  in  organic  com- 
pounds a  more  permanent  existence  of  the  molecule  probably  occurs.  When  oil  spreads  over  water  evidence  points 
to  a  layer  a  molecule  thick  and  that  the  molecules  are  not  spheres.  Were  they  spheres  and  an  attraction  existed  be- 
tween them  and  the  water,  they  would  be  dissolved  instead  of  spreading  over  the  surface.  The  presence  of  the  —  COOH, 
—  CO  or  —OH  groups  generally  renders  an  organic  substance  soluble  in  water,  whereas  the  hydrocarbon  chain  decreases 
the  solubility.  When  an  oil  is  placed  on  water  the  —COOH  groups  are  attracted  to  the  water  and  the  hydrocarbon 
chains  repelled  but  attracted  to  each  other.  The  process  leads  the  oil  over  the  surface  antil  all  the  —COOH  groups 
are  in  contact  if  possible.  Pure  hydrocarbon  oils  will  not  spread  over  water.  Benzene  will  not  mix  with  water.  When 
a  limited  amount  of  oil  is  present  the  spreading  ceases  when  all  the  water-attracted  groups  are  in  contact  with  water. 
If  weight  w  of  oil  spreads  over  water  surface  A ,  the  area  covered  by  each  molecule  is  AM/wN  where  M  is  the  molec- 
ular weight  of  the  oil  (O  =  16),  N,  Avogadro's  constant.  The  vertical  length  of  a  molecule  /  =  M/apN  =  W/pA 
where  p  is  the  oil  density  and  a  the  horizontal  area  of  the  molecule. 


Substance. 

Cross 
section 
in 
cm* 
X  lo" 

/  in  cm 
(length) 
X  108 

Substance. 

Cross 
section 
in 
cm2 
Xio" 

/  in  cm 
(length) 
Xio" 

Palmitic  acid  CisHsiCOOH  .  . 

24 

19  6 

Cetyl  alcohol  CieHssOH 

21 

21  .9 

Stearic  acid  CnHssCOOH  

24 

21.8 

Myricyl  alcohol  CsoHeiOH  

29 

35-  2 

Cerotic  acid  C26H5iCOOH  
Oleic  acid  Ci-HssCOOH  . 

18 

29.0 
10  8 

Cetyl  palmitate  CuHsiCOOCieHss  . 
Tristearin  (CigHssOzjsCsHs 

21 
69 

44-0 
23  7 

Linoleic  acid  CnHsiCOOH.  .  . 

47 

10.  7 

Trielaidin  (CisHssOz^CsHs  

137 

ii  .9 

Linolenic  acid  CnHwCOOH  
Ricinoleic  acid  CnH32(OH)COOH..  .  . 

66 
90 

7.6 
5-8 

Triolein  (CisHssO'^CsHs  
Castor  oil  (CnH32(OH)COO)3C3H5. 
Linseed  oil  (CnH3iCOO)3C3H5  

145 
280 
143 

II.  2 
5-7 
II.  0 

TABLE  514.  —  Size  of  Diffracting  Units  in  Crystals.^ 

The  use  of  crystals  for  the  analysis  of  X-rays  leads  to  estimates  of  the  relative  sizes  of  molecular  magnitudes.  The 
diffraction  phenomenon  is  here  not  a  surface  one,  as  with  gratings,  but  one  of  interference  of  radiations  reflected  from 
the  regularly  spaced  atomic  units  in  the  crystals,  the  units  fitting  into  the  lattice  framework  of  the  crystal.  In  cubical 
crystals  {100}  this  framework  is  built  of  three  mutually  perpendicular  equidistant  planes  whose  distance  apart  in 
crystallographic  parlance  is  dioo.  This  method  of  analysis  from  the  nature  of  the  diffraction  pattern  leads  also  to  a 
knowledge  of  the  structure  of  the  various  atoms  of  the  crystal.  See  Bragg  and  Bragg,  X-rays  and  Crystal  Structure. 
1918. 


Crystal. 

Elementary 
diffracting  element. 

Side  of  cube. 

Molecules  or 
atoms  in  unit 
cube. 

KC1  
NaCl  
ZnS... 

Face-centered  cube  * 

cm 
6.30  X  io-8 
5.56  X  io-8 
5  46  X  io~ 

4    molecules 

CaF2.  .  . 

"           "           "     t 

a 

FeS2  
Fe 

.,          ,,           „     | 

5.26  X  io- 
2  86  X  io~ 

Al.. 

Face-centered  cube 

4  05  X  10" 

Na 

Ni  

Face-centered  cube 

2.76  X  iQ- 
3.52  X  IQ- 

2 
4 

*  Each  atom  is  so  nearly  equal  in  diffracting  power  (atomic  weight)  in  KC1  that  the  apparent  unit  diffracting  element 
is  a  cube  (simple)  of  J  this  size.  Elementary  body -centered  cube,  —  atom  at  each  corner,  one  in  center;  e.g.,  Fe,  Ni  (in 
part),  Na,  Li?  Elementary  face-centered  cube,  —  atom  at  each  corner,  one  in  center  of  each  face;  e.g.,  Cu,  Ag,  Au, 
Pb,  Al,  Ni  (in  part) ,  etc.  Simple  cubic  lattice,  —  atom  in  each  corner.  Double  face-centered  cubic  or  diamond  lattice 
—  C  (diamond);  Si,  Sb,  Bi,  As?,  Te?. 

t  Diamond  lattice.  J  Cubic-holohedral.  §  Cubic-pyritohedral. 

Metals  taken  from  Hull,  Phys.  Rev.  10,  p.  661,  1917 

t  See  Table  528  for  best  values  of  calcite  and  rock-salt  grating  spaces. 

Note  :  —  (Hull,  Science  52,  227,  1920).  Ca,  face-centered  cube,  side  5.56  A,  each  atom  12  neighbors  3.93  A  distant. 
Ti,  centered  cube,  cf.  Fe,  side  3.14  A,  8  neighbors  2.72  A.  Zn,  6  nearest  neighbors  in  own  plane.  2.67  A,  3  above,  3 
below,  2.92  A.  Cd,  cf.  Zn,  2.98  A,  3.30  A.  In,  face-centered  tetragonal,  4  nearest  3.24  A,  4  above,  4  below,  3.33  A. 
Ru,  cf.  Zn,  2.69  A,  2.64  A.  Pd,  face-centered  cube,  side  3.92  A,  12  neighbors.  2.77  A.  Ta,  centered  cube,  side 
3.27  A,  8  neighbors  2.83  A.  Ir,  face-centered  cube,  side  3.80  A,  12  neighbors,  2.69  A  (A  =io~8  cm). 

Note  :  —  (Bragg,  Phil.  Mag.  40,  169,  1920).  Crystals  empirically  considered  as  tangent  spheres  of  diameter  in  table, 
atom  at  center  of  sphere.  When  lattice  known  allows  estimation  of  dimensions  of  crystal  unit.  Table  foot  of  next  page 
(atomic  numbers,  elements,  diameter  in  Angstroms,  io-8cm). 

SMITHSONIAN  TABLES. 


TABLE  515. 

4OI 

ELECTRONS.   RUTHERFORD   ATOM.    BOHR   ATOM.    MAGNETIC  FIELD   OF  ATOM- 

References:  Millikan,  The  Electron,  1917;  Science,  45,  421,  1917;  Humphreys.  Science.  46,  273,  1917;  Lodge 
Nature,  104,  15  and  82.  1919;  Thomson,  Conduction  of  Electricity  through  Gases;  Campbell.  Modern  Electrical 
Theory;  Lorentz,  The  Theory  of  Electrons;  Richardson,  The  Electron  Theory  of  Matter,  1914. 

Electron:  an  elementary  +  or  —  unit  of  electricity. 

Free  negative  electron:  (corpuscle,  J.  J.  Thomson);  mass  =  9.01  X  io-»g  -  1/1845  H  atom,  probably  all  of 
electrical  origin  due  to  inertia  of  self-induction. 

Theory  shows  that  when  speed  of  electron  =  i/io  velocity  of  light  its  mass  should  be  appreciably  dependent  upon 
that  speed.  If  mo  be  mass  for  small  velocity  v,  m  be  the  transverse  mass  for  v,  v/( velocity  of  light)  =  /8,  then  m  - 
mo(i  —  /S2)^,  Lorentz,  Einstein; 

for/3  =0.01  o.io          0.2          0.3  0.4  0.5  0.6  0.7  0.8  0.9 

ml  mo  =  1.00005         1.005         1-02         1.048         1.091         1.155         1.250        1.400        1.667         2.2Q4 

(Confirmed  by  Bucherer,  Ann.  d.  Phys.  1909,  Wolz,  Ann.  d.  Phys.  Radium  ejects  electrons  with  3/10  to  98/100  velocity 
of  light.)  m,  due  to  charge  =  2E2/^a,  E  =  charge,  a  =  radius,  whence  radius  of  electron  =  2  X  io~13  cm  =  1/50,000 
atomic  radius.  Cf.  (radius  of  earth)/ (radius  of  Neptune's  orbit)  =  1/360,000. 

Positive  electron:  heavy,  extraordinarily  small,  never  found  associated  with  mass  less  than  that  of  H  atom.  If 
mass  all  electrical  (?)  radius  must  be  1/2000  that  of  the  —  electron.  No  experimental  evidence  as  with  —  electron, 
since  high  enough  speeds  not  available.  Penetrability  of  atom  by  /3  particle  (may  penetrate  10,000  atomic  systems 
before  it  happens  to  detach  an  electron)  and  a  particles  (8000  times  more  massive  than  —  electron,  pass  through  500,000 
atoms  without  apparent  deflection  by  nucleus  more  than  2  or  3  times)  shows  extreme  minuteness.  Upper  limit  •  not 
larger  than  icr"  cm  for  Au  (heavy  atom)  or  10'",  H  (light  atom)  (Rutherford).  Cf.  (radius  sun)/(radms  Neptune's 
orbit)  =  1/3000,  but  sun  is  larger  than  planets.  (Hg  atoms  by  billions  may  pass  through  thin-walled  highly-evacuated 
glass  tubes  without  impairing  vacuum,  therefore  massive  parts  of  atoms  must  be  extremely  small  compared  to  volume 
of  atom.) 

Rutherford  atom:  number  of  free  +  charges  on  atomic  nuclei  of  different  elements  =  approximately  \  atomic 
weight  (Rutherford,  Phil.  Mag.  21,  1911,  deflection  of  a  particles);  Barkla  concluded  free  —  electrons  outside 
nucleus  same  in  number  (Phil.  Mag.  21,  191 1,  X-ray  scattering).  If  mass  is  electromagnetic,  then  lack  of  exact  equiva- 
lence may  be  due  to  overlapping  fields  in  heavy  crowded  atoms,  a  sort  of  packing  effect;  the  charge  on  U  =  92,  at.  wt. 
=  238.5.  Moseley  (Phil.  Mag.  26,  1912;  27,  1914)  photographed  and  analyzed  X-ray  spectra,  showing  their  exact 
similarity  in  structure  from  element  to  element,  differing  only  in  frequencies,  the  square  roots  of  these  frequencies 
forming  an  arithmetical  progression  from  element  to  element.  Moseley's  series  of  increasing  X-ray  frequencies  is  with 
one  or  two  exceptions  that  of  increasing  atomic  weights,  and  these  exceptions  are  less  anomalous  for  the  X-ray  series 
than  for  the  atomic -weight  series.  It  seems  plausible  then  that  there  are  92  elements  (from  H  to  U)  built  up  by  the 
addition  of  some  electrical  element.  Moseley  assigned  successive  integers  to  this  series  (see  Table  531)  known  now  as 
atomic  numbers. 

Moseley's  discovery  may  be  expressed  in  the  form 

«i  _  Ei         A2       £i« 
n2  "  £,  °r   Xi  ~  Et* 

where  E  is  the  nuclear  charge  and  A  the  wave-length.  Substituting  for  the  highest  frequency  line  of  W,  \t  =  0.167 
X  io~8  cm  (Hull),  £2  =  74  =  Nw,  and  Ei  =  i,  then  Xi  =  highest  possible  frequency  by  element  which  has  one 
+  electron;  Ai  =  91.4  wtju.  Now  the  H  ultra-violet  series  highest  frequency  line  =  91.2  my.  (Lyman);  i.e..  this  ultra- 
violet line  of  H  is  nothing  but  its  K  X-ray  line.  Similarly,  it  seems  equally  certain  that  the  ordinary  Balmer  series  of 
H  (head  at  365  mfj.)  is  its  L  X-ray  series  and  Paschen's  infra-red  series  its  M  X-ray  series. 

There  may  be  other  —  electrons  on  the  nucleus  (with  corresponding  -f-  charges)  since  they  seem  to  be  shot  out 
by  radioactive  processes.  They  may  serve  to  hold  the  +  charges  together.  He,  atomic  no.  =  2,  has  2  free  -f-  charges, 
at.  wt.  =  4;  may  imagine  nucleus  has  4  +  electrons  held  together  by  2  —  electrons,  with  2  —  electrons  outside  nucleus. 
H  has  one  +  and  one  —  electron. 

The  application  of  Newton's  law  to  Moseley's  law  leads  to  Ei/Ez  =  ai/a\-,  where  the  a's  are  the  radii  of  the  inmost 
—  electronic  orbits,  i.e.,  the  radii  of  these  orbits  are  inversely  proportional  to  the  central  charges  or  atomic  numbers. 

(Note:  When  an  a  particle  (-f-  charge  =  2e)  is  emitted  by  a  radioactive  element,  its  atomic  number  decreases  by 
2,  the  emission  of  a  —  charged  particle  increases  its  atomic  number  by  i.) 

Bohr  atom:  (Phil.  Mag.  26,  i,  476,  857,  1913;  29,  332,  1915;  30,  394,  1915).  The  experimental  facts  and  the  law 
of  circular  electronic  orbits  limit  the  electrons  to  orbits  of  particular  radii.  \Vhen  an  electron  is  disturbed  from  its 
orbit,  e.g.,  struck  out  by  a  cathode  ray,  or  returns  from  space  to  a  particular  orbit,  energy  must  be  radiated.  Ii 
gestive  that  the  emission  of  a  /3  ray  requires  a  series  of  y  ray  radiations.  H  does  not  radiate  unless  ionized  and  then 
gives  out  a  spectrum  represented  by  Balmer's  formula  v  =  N(i/m"  —  i/n2)  where  v  is  the  frequency,  N,  a  constant, 
and  «i  for  all  the  lines  in  the  visible  spectrum  has  the  value  2,  «,  the  successive  integers,  3,  4.  5,  .  .  .;  if  m  =  i  and  «, 

2,3,4,.  •   ..Lyman's  ultra-violet  series  results;  if  m  =3,n.  4,5,6 Paschen's  infra-red  series.    These  con 

tions  led  Bohr  to  his  atom  and  he  assumed:    (a)  a  series  of  circular  non-radiating  orbits  governed  as  above;  (b 

tion  taking  place  only  when  an  electron  jumps  from  one  to  another  of  these  orbits,  the  amount  radiated  and  its  frequency 

SMITHSONIAN  TABLES. 

(This  Table  supplements  Table  514). 

3  Li       3.00  13  Al       2.70  25  Mn     a.95t  3&  Kr      2.35*  54  Xe     2.70* 

Gl       3.o  .4  Si          .35  26  Fe      2.80  37  Rb      4-5°  55  4-75 


4  Gl       2.30  14  Si 

6  C        1.54  16  S 

7  N       1.30  .7  Cl 


. 

8  O         .30  18  A 

9  F          .35  19 

' 


20    r  e        2.00  J/     rww       ^O"  f/J 

27  Co      2.75  38  Sr      3.90  56  Ba      4.20 

28  Ni      2.70  47  Ag      3-55  »'  Tl       4.50 


.10  28  INI  2.70  47  "K  -*-55 

.05*  29  Cu  2.75  48  Cd  3.20                82  Pb      3-80 

9r          ,.35                  .v-          .15  30  Zn  2.65 

10  Ne     1.30*           '  20  Ca      3.40  33  As  2.52 

11  Na     3.55                 22  Ti       2.80  34  Se  2.3$  52  «  2.65 

12  Mg     2.85                 24  Cr      2.8ot  35  Br  2.38  53  I  2.80 


*  Outer  electron  shell.  t  Cr,  "electronegative,"  2.35;  Mn,  ditto,  2.35. 

Broughall  (Phil.  Mag.  41,  p.  872,  t92i)  computes  in  the  same  units  from  Van  der  Waal's  constant  "  b  "  the  diame- 
ters  of  He,  N    A,  Kr,  and^C  as  273,  2.6,  2.9,  3.1,  and  3.4-     These  inert  elements  correspond  to  JW«^««g2 
filled  successive  electron  shells.     The  corresponding  atomic  numbers  are  2,  10,  18,  36  and  54.     for  Langmu 


filled  successive  electron  shells.     The  corresponding  at 
see  J.  Am.  Ch.  Soc.,  p.  868,  1919,  Science  54,  p.  59,  i921 


4O2  TABLE  515  (continued). 

BOHR  ATOM.  MAGNETIC  FIELD  OF  ATOM- 

being  determined  by  kv  =  Ai  —  At,  h  being  Planck's  constant  and  A\  and  At.  the  energies  in  the  two  orbits;  (c)  the 
various  possible  circular  orbits,  for  the  case  of  a  single  electron  rotating  around  a  single  positive  nucleus,  to  be  deter- 
mined by  T  =  (i/2)rhn,  in  which  r  is  a  whole  number,  n  is  the  orbital  frequency,  and  T  is  the  kinetic  energy  of  rotation. 

The  remarkable  test  of  this  theory  is  not  its  agreement  with  the  H  series,  which  it  was  constructed  to  fit,  but  in  the 
value  found  for  N.  From  (a),  (b),  and  (c)  it  follows  that  N  =  (2T^etE2m)/h3  =  3-294  X  lo15,  within  i/io  per  cent  of 
the  observed  value  (Science,  45,  p.  327). 

The  radii  of  the  stable  orbits  =  TW/4ir*me*,  or  the  radii  bear  the  ratios  i,  4,  9, 16,  25.  If  normal  H  be  assumed  to  be 
with  its  electron  in  the  inmost  orbit,  then  20.  =  i.i  X  io~8;  best  determination  gives  2.2  X  io~8.  The  fact  that  H 
emits  its  characteristic  radiations  only  when  ionized  favors  the  theory  that  the  emission  process  is  a  settling  down  to 
normal  condition  through  a  series  of  possible  intermediate  states,  i.e.,  a  change  of  orbit  is  necessary  for  radiation.  That 
in  the  stars  there  are  33  lines  in  the  Balmer  series,  while  in  the  laboratory  we  never  get  more  than  12,  is  easily  explica- 
ble from  the  Bohr  theory. 

Bohr's  theory  leads  to  the  relationship  v%    —  v%     =VL     (see  x'ray  tables) ,  Rydberg-Schuster  law. 

/8  a  a 

For  further  development,  see  Sommerfeld,  Ann.  d.  Phys.  51,  i,  1916,  Paschen,  Ann.  d.  Phys.,  October,  1916; 
Harkins,  Recent  work  on  the  structure  of  the  atom,  J.  Am.  Ch.  Soc.  37,  p.  1396,  1915;  39,  p.  856,  1916. 

Magnetic  field  of  atom :  From  the  Zeeman  effect  due  to  the  action  of  a  magnetic  field  on  the  radiating  electron  the 
strength  of  the  atomic  magnetic  field  comes  out  about  ip8  gauss,  2000  times  the  most  intense  field  yet  obtained  by  an 
electromagnet.  A  similar  result  is  given  by  the  rotation  of  a  number  of  electrons,  Aio3,  where  A  is  the  atomic 
weight;  for  Fe  this  gives  io8  gauss.  For  other  determinations,  see  Weiss  (J.  de  Phys.  6,  p.  661,  1907;  7,  p.  249,  1908), 
Ritz  (Ann.  d.  phys.  25,  p.  660,  1908),  Oxley  (change  of  magnetic  susceptibility  on  crystallization,  Phil.  Tr.  Roy.  Soc. 
215,  p.  95,  1915)  and  Merritt  (fluorescence,  1915);  Humphreys,  "The  Magnetic  Field  of  an  Atom,"  Science,  46,  p.  276, 
1917- 

SMITHSONIAN  TABLES. 


TABLES  516-518.  4°3 

Note:  The  phenomena  of  Electron  Emission,  Photo-electric  Effect  and  Contact  (Volta)  Potential  treated  in  the 
subsequent  tables  are  extremely  sensitive  to  surface  conditions  of  the  metal.  The  most  consistent  observations  have 
been  made  in  high  vacua  with  freshly  cut  metal  surfaces. 

TABLE  516.    Electron  Emission  from  Hot  Metals. 

Among  the  free  electrons  within  a  metal  some  may  have  velocities  great  enough  to  escape  the  surface  attraction. 

The  number  n  reaching  the  surface  with  velocities  above  this  critical  velocity  =  N(RT/2irM)le~KT  where  N  ** 
number  of  electrons  in  each  cm3  of  metal,  R  the  gas  constant  (83.15  X  io»  erg-dyne),  T  the  absolute  temperature,  M 
the  atomic  weight  of  electron  (.000546,  O  =  16),  v>  the  work  done  when  a  "gram-molecule"  of  electrons  (6.06  X  io» 
electrons  or  96,500  coulombs)  escape.  It  seems  very  probable  that  this  work  is  done  against  the  attraction  of  the 
electron's  own  induced  image  in  the  surface  of  the  conductor.  When  a  sufficiently  high  +  field  is  applied  to  escaping 
electrons  so  that  none  return  to  the  conductor,  then  the  saturation  current  has  been  found  to  follow  the  equation 


assuming  N  and  w  constant  with  the  temperature;  this  is  equivalent  to  the  equation  for  n  just  given  and  is  known  as 
Richardson's  equation.  In  the  following  table  due  to  Langmuir  (Tr.  Am.  Electroch.  Soc.  29,  125,  1916)  12000  =  satura- 
tion current  per  cm2  for  T  =  2000  K°;  <£  =  w/F  -  Rb/F  =  work  done  when  electrons  escape  from  metal  in  terms  of 
equivalent  potential  difference  in  volts;  F  =  Faraday  constant  =  96,500  coulombs. 


Metal. 

a 
amp/cm2 

b 

J?000 

amp/cm1 

</» 

(volts). 

Tungsten  * 

2  36  X  io7 

52500 

0.0042 

4   52 

Thorium  
Tantalum                 

2.0    X  108 

I.  12    X  IO7 

39000 
50000 

30.0 
0.007 

3.36 

4.31 

21      X  IO7 

50000 

.013 

4.31 

Carbon  (untreated)  
Titanium  

1300? 
2400? 

48000 
28000? 
37000? 

.048? 
.0010? 

4.14 

2.4? 
3.2? 

Platinum  f  
BaO-SrO,  Pt-6  %  Ir  core.  .   .  . 

1.25  X  io7 
1.6     Xio« 

51060 

•  0035 
3-aS 

4-4 
'•7 

*  Best  determined  value  of  table,  pressure  less  than  io~7  mm  Hg. 
TABLE  517.    Photo-electric  Effect. 


t  Schlichter,  1915. 


A  negatively  charged  body  loses  its  charge  under  the  influence  of  ultra-violet  light  because  of  the  escape  of  nega- 
tive electrons  freed  by  the  absorption  of  the  energy  of  the  light.  The  light  must  have  a  wave-length  shorter  than  some 
limiting  value  Xo  characteristic  of  the  metal.  The  emission  of  these  electrons,  unlike  that  from  hot  bodies,  is  independ- 
ent of  the  temperature.  The  relation  between  the  maximum  velocity  v  of  the  expelled  electron  and  the  frequency  v 
of  the  light  is  (i/2)mv2  =  hv  —  P  (Einstein's  equation)  where  h  is  Planck's  constant  (6.58  X  lo"27  erg.  sec.);  hv  some- 
times taken  as  the  energy  of  a  "quanta,"  P,  the  work  which  must  be  done  by  the  electron  in  overcoming  surface  forces. 
(i/2)mvz  is  the  maximum  kinetic  energy  the  electron  may  have  after  escape.  Richardson  identifies  the  P  of  Einstein's 
formula  with  the  w  of  electron  emission  of  the  preceding  table.  The  minimum  frequency  v&  (corresponding  to  maxi- 
mum wave-length  Xo)  at  which  the  photo-electric  effect  can  be  observed  is  determined  by  hv  =  P.  P  applies  to  a 
single  electron,  whereas  w  applies  to  one  coulomb  (6.062  X  io23  electrons);  therefore  w  =  NP  =  .oo399J'o  ergs.  <£  = 
(12.4  X  io-5)Xo  volts.  See  Millikan,  Pr.  Nat.  Acad.  2,  78,  1916;  Phys.  Rev.  7,  355,  1916;  4,  73,  1914;  Hennings, 
Phys.  Rev.  4,  228,  1914. 

TABLE  518.    Ionizing  Potentials  and  Single-line  Spectra. 

When  electrons  are  accelerated  through  gases  or  vapors,  especially  those  with  small  electron  affinity  (inert  gases, 
metallic  vapors)  at  well-defined  potentials  a  large  transfer  of  energy  takes  place  between  the  moving  electrons  and 
the  gas  atoms.  There  appear  to  be  two  types  of  inelastic  encounters  under  such  circumstances:  the  first  accompanied 
by  the  emission  of  a  radiation  of  a  single  line  at  a  potential  called  the  resonance  potential  and  satisfying  the  relation 
hv  =  eV  where  V  is  the  potential  fall,  v  the  frequency  and  h  Planck's  constant;  the  second  ionizes  the  gas  (ionization 
potential),  exciting  the  radiation  of  a  composite  spectrum.  The  latter  potential  satisfies  a  relation  hv  =  eV  except 
that  v  is  now  the  limiting  frequency  of  a  series  of  lines.  The  following  table  was  communicated  by  Tate  and  Foote 
(see  Phil.  Mag.  36,  64,  1918). 


Ionization 

X 

Resonance 

Metal 

x 

potential.* 

M 

potential.* 

At  „_ 

Observers. 

Obs. 

Comp. 

Obs. 

Comp. 

Na  .  .  .  . 

241  2.  63  t 

5-13 

S-ii 

6-57 

5889.97 

' 

.12 

2.09 

6.63 

Tate  and  Foote 

E  
Rb.  . 

2856.651: 
2968.40! 

4.1 
4.1 

4-32 
4-iS 

6.22 

6.46 

7664.94 
7800.29 

;0S 

1.61 
1.58 

6.31 
6.62 

Foote,  Rognley,  Mohler 

Cs..    .. 
Mg.    .- 
Zn.  .    .  . 

3184.28* 
1621.  7§ 
1319  95§ 

3-9 
7-75 
9-5 

3-87 
7.6t 
9-34 

6.59 
6.67 
6.66 

8521.12 

4571.38' 

3075.99' 

; 

.65 

1-45 
2.70 
4.01 

6.69 
6.43 
6.  70 

Foote  and  Mohler 
Tate  and  Foote 

Cd..   .. 
Hg.    .. 

u87-96§ 

8.92 
10.35 

8.95 
10.38 

6.53 
6.53 

3260.17' 
2536.72' 

; 

3-88 
4-9 

3.78 
4.86 

6.71 
6.60 

Tate,  Davis,  Goucher, 

others 

TL.    .. 
Ca..   .. 

2027.56! 

7-3 
6.04 

6.08 

— 

11513.22 

6717.69' 

j 

1.07 
1-93 

1.07 
1.84 

6.54 

Tate  and  Mohler 
Mohler  and  Foote 

Ca..    .. 
As 

— 

II    e 

— 

— 

4226.73 

3-0 

4-7 

2.92 

~ 

Foote,  Rognley,  Mohler 

Pb  

— 

8.0 

— 

— 

— 

1.26 

— 

— 

Mohler  and  Foote 

MEAN  OF  COMPUTED  h  = 

6.55  X  IO"*7  ERG.   SEC. 

*  Computed  from  relation  Ve  =  hv  or  V  =  I2334/X  volts;    X  in  Angstrom  units, 
t  Computed  from  h  =  o.53o8X7io-M  t  Limit  of  principal  series. 

§  Limit  of  principal  series  of  single  lines,  i.sS.  I  Short  wave-length  line  of  first  doublet  of  principal 

1  Combination  series  line  i.s5  -  2p*  **  First  line  principal  senes  single  lines  1.55  -  zP. 

SMITHSONIAN  TABLES. 


404 


TABLE    519. 
CONTACT  ^VOLTA)  POTENTIALS- 


There  has  been  considerable  controversy  over  the  reality  and  nature  of  the  contact  differences  of  potential  between 
two  metals.  At  present,  due  to  the  studies  of  Lan^muir,  there  is  a  decided  tendency  to  believe  that  this  Volta  differ- 
ence of  potential  is  an  intrinsic  property  of  metals  closely  allied  to  the  phenomena  just  given  in  Tables  516  to  518  and 
that  the  discrepancies  among  different  observers  have  been  caused  by  the  same  disturbing  surface  conditions.  The 
following  values  of  the  contact  potentials  with  silver  and  the  relative  photo-sensitiveness  of  a  few  of  the  metals  are 
from  Henning,  Phys.  Rev.  4,  228,  1914.  The  values  are  for  freshly  cut  surfaces  in  vacuo.  Freshly  cut  surfaces  are 
more  electro-positive  and  grow  more  electro-negative  with  age.  That  the  observed  initial  velocities  of  emission  of 
electrons  from  freshly  cut  surfaces  are  nearly  the  same  for  all  metals  suggests  that  the  more  electro-positive  a  metal  is 
the  greater  the  actual  velocity  of  emission  of  electrons  from  its  surface. 


Contact  potential  with  Ag 

Ag 
o 

Cu 

•  05 

Fe 

•  IQ 

Brass 

.21 

Sn 

•  27 

Zn 
•  SO 

Al 
•99 

Mg 

i  .42 

Relative  photo-sensitiveness 

5° 

60 

*5 

45 

70 

80 

500 

IOOO 

From  the  equation  w  =  RT  logCY^/Ng),  where  w  is  the  work  necessary  per  gram-molecule  when  electrons  pass 
through  a  surface  barrier  separating  concentrations  NA  and  Ng  of  electrons,  it  can  be  shown  (Langmuir,  Tr.  Am. 
Eletroch.  Soc.  29,  142,  1916,  el  seq.)  that  the  Volta  potential  difference  between  two  metals  should  be 

n  -  f2=  j;  {W2  -  in  +  RT  \og(NA/NB)}  =  w*~Wl  =  </>2  -  </>! 

(see  Table  517  for  significance  of  symbols),  since  the  number  of  free  electrons  in  different  metals  per  unit  volume  is  so 
nearly  the  same  that  RT  log  (NA/N g)  may  be  neglected.  The  contact  potentials  may  thus  be  calculated  from  photo- 
electric phenomena  (see  Table  517  for  references).  They  are  independent  of  the  temperature.  The  following  table 
gives  a  summary  of  values  of  <j>  in  volts  obtained  from  the  various  phenomena  where  an  electron  is  torn  from  the  attrac- 
tion of  some  surface.  In  the  case  of  ionization  potentials  the  work  necessary  to  take  an  electron  from  an  atom  of  metal 
vapor  is  only  approximately  equal  to  that  needed  to  separate  it  from  a  solid  metal  surface. 


(a)  THE  ELECTRON  AFFINITY  OF  THE  ELEMENTS,  IN  VOLTS. 


Photo- 

Metal. 

Contact. 
(Henning.] 

Therinionic 
(Langmuir.] 

electric 
and 
contact. 

Photo- 
electric. 
(Richardson) 

Miscel- 
laneous. 

Single- 
line 
spectra. 

Adjusted 
mean. 

(Mifflkan.) 

Tungsten  

4-52 

4-52 

Platinum  

— 



4-3 

4-45 



4.4? 

Tantalum  



4  31 





4-  3 

Molybdenum  



4.31 









4-  3 

Carbon. 

Silver  

4-05 









Copper. 

(4  o) 

Bismuth 

Tin  

3  78 





3-5 





3-8 

Iron 

~  Rfi 

3   2? 

Zinc  
Thorium  

3.46 

3.36 

— 

3-4 

— 

4.04 

3-4 

3-4 

Aluminum  

3-o6 



2.8 





Magnesium  
Titanium 

2.63 

— 

3-2 

— 

4-35 

2.7 

Lithium  

_ 

2-35 

— 



1.85 

2-35 

Sodium  

1.82 

2.1 

2.  II 

1.82 

(b)  It  should  not  be  assumed  that  all  the  emf  of  an  electrolytic  cell  is  contact  emf.  Its  emf  varies  with  the  elec- 
trolyte, whereas  the  contact  emf  is  an  intrinsic  property  of  a  metal.  There  must  be  an  emf  between  the  two  electrodes 
of  such  a  cell  dependent  upon  the  concentration  of  the  electrolyte  used.  The  following  table  gives  in  its  first  line  the 
electrode  potential  e^  of  the  corresponding  metals  (in  solutions  of  their  salts  containing  normal  ion  concentration)  on 
assumption  of  no  contact  emf  at  the  junction  of  the  metals.  The  second  line,  $  —  eh  —  3.7  volts,  gives  an  idea  of  the 
electrode  potentials  (arbitrary  zero)  exclusive  of  contact  emf. 


Metal 

Ag 

Cu 

Bi 

Sn 

Fe 

Zn 

Mg 

Li 

Na 

eh  

+0.80 

+0.34 

4-o.  20 

—  O.IO 

-0-43 

—0.76 

-i  55 

-3-03 

-2.73 

4>-«A-3.7  

-0.40 

+0.04 

4-O.20 

—  0.  20 

-0-43 

—0.46 

-0-55 

-1.65 

—0.85 

SMITHSONIAN  TABLES. 


TABLES  620-631. 
IONIC   MOBILITIES  AND   DIFFUSIONS. 


405 


The  process  of  ionization  is  the  removal  of  an  electron  from  a  neutral  molecule,  the  molecule  thus  acquiring  a  result- 
ant -f  charge  and  becoming  a  +  ion.  The  negative  carriers  in  all  gases  at  high  pressures,  except  inert  gases,  consist 
for  the  most  part  of  carriers  with  approximately  the  same  mobilities  as  the  -f-  ions.  The  negative  electrons  must, 
therefore,  change  initially  to  ions  by  union  with  neutral  molecules. 

The  mobility,  U,  of  an  ion  is  its  velocity  in  cm/sec,  for  an  electrical  field  of  one  volt  per  cm.  The  rates  of  diffusion, 
D,  are  given  in  cm3/sec.  U  =  DP/Ne,  where  P  is  the  pressure,  N,  the  number  of  molecules  per  unit  volume  of  a  gas 
and  e  the  electronic  charge. 

Nature  of  the  gas  and  the  mobilities:  (i)  The  mobilities  are  approximately  proportional  to  the  inverse  sq.  rts.  of 
the  molecular  weights  of  the  permanent  gases;  better  yet  when  the  proportionality  is  divided  by  the  4th  root  of  the 
dielectric  constant  minus  unity;  (2)  The  ratio  U  +  /U  —  seems  to  be  greater  than  unity  in  all  the  more  electro- 
negative gases. 

Mobilities  of  Gaseous  Mixtures:  Three  types:  (i)  Inert  gases  have  high  mobilities;  small  traces  of  electro- 
negative gases  make  values  normal.  (2)  Mixed  gases:  lowering  of  mobilities  is  greater  than  would  be  expected  from 
simple  law  of  mixture.  (3)  Abnormal  changes  produced  by  addition  of  small  quantities  of  electro-negative  gases: 


e.g.:  normal  mobility 
6  mm  CzHsBr  gave 
6  mm  CzHsI 
10  mm  CjHsOH   " 
9  mm  CsHsO      " 


U+  =  1.37 
1-37 
1-37 
0.91 
i  IS 


U  - 


Wellisch,  Pr. 
Roy.  Soc.  8zA, 
p.  500,  1009. 


Temperature  Coefficient  of  Mobility:  There  is  no  decided  change  with  the  temperature. 

Pressure  Coefficient  of  Mobility:  Mobility  varies  inversely  with  the  pressure  in  air  from  100  to  i/io  atmosphere 
for  —  ion,  to  i/iooo,  for  +  ion;  below  i/io  atmosphere  all  observers  agree  that  the  negative  ion  in  air  increases 
abnormally  rapidly. 

Free  Electrons:  In  pure  He,  Ar,  and  N,  the  negative  carriers  have  a  high  mobility  and  are,  in  part  at  any  rate, 
free  electrons;  electrons  become  appreciable  in  air  at  10  cm  pressure. 

TABLE  520.  —  Ionic  Mobilities. 


Dry  gas. 

Mobilities. 

K       i 

Observer. 

Dry  gas. 

Mobilities. 

K       i 

Observer. 

+ 

- 

+ 

- 

H  
He  
Ar  

N 

6.70 
5-09 
1-37 
1.27 
1.36 
0.81 
0.74 
1.40 

7-95 
6.31 

i.  80 
0.85 
0.80 
1.78 

.000273 
.000074 

.000100 

.000590 
.000540 
.000960 
.00770 
.000590 

Zeleny 
Franck 

Zeleny 
Wellisch 

Mean 

Nitrous  oxide  
Ethyl  alcohol  

ecu  

Ethyl  chloride 

0.82 
0.34 
0.30 
0.33 
0.29 
o.  29 
0.30 
0.17 

0.90 
0.27 
0.31 
0.31 
0.31 
0.28 
0.31 

O.  IO 

.00107 
.00940 
.00426 
.01550 
.00742 
.01460 
.00870 

Wellisch 

0  
CO,  
NHa  

Air  

Ethyl  ether  
Methyl  bromide  .... 
Ethyl  formate  
Ethyl  iodide  

Franck,  Jahr.  d.  Rad.  u.  Elek.  9,  p.  2.  1912;   Wellisch,  Pr.  Roy.  Soc.  SaA,  p.  500,  1009.    The  following  values  are 
from  Yen,  Pr.  Nat.  Acad.  4,  19  8. 

H2 

N2 

Air. 

S02 

CoHi2 

CiH60 

C:H«0 

CjHiCl 

CHjI 

C-HJ 

u  +  

5-54 

1-30 

i-37 

.412 

.385 

-363 

.  .507 

.W 

.216 

1.81 

U  -  

8-45 

i.  80 

1.81 

.414 

•  451 

-373 

•  331 

•  -U7 

.220 

1.81 

U-/U+. 

i.  S3 

1.38 

1.34 

I.  00 

1.17 

i  •  o;> 

1.07 

1.04 

1.05 

I.  00 

TABLE  521.  —  Diffusion  Coefficients. 

The  following  table  gives  the  observed  and  computed  (D  =  sooUP/Ne  =  very  nearly  0.023610  value*  of  the 
diffusion  coefficients.  The  diffusion  coefficients  are  given  for  some  neutral  molecules  as  actually  determined  for  some 
gases  into  gases  of  nearly  equal  molecular  weight.  Table  taken  from  Loeb,  "  The  Nature  of  the  Gaseous  Ion,  J.  Franklin 
Inst.  184,  p.  775,  1917. 


Gas  diffused 

D 

II  -4- 

D  +  lc 

r  ions. 

into 

moK-t 

Computed. 

ved. 

Ar... 
Hz 

He 

No 

o.  706 
•  73Q 

5.09 

6.  02 

I.  20 

o.  14; 

o  i.\; 

Air 

Oi 

.178 

1-35 

0.0319 

0.028 

&:::::::::::::  :: 

CO? 

N2 

NzO 
CO 

.171 
1.5-1.0 

i    >i 

1.27 
.82 
.81 

.0299 
-0193 
.019^ 

.oaj 
.oaj* 

CzHsOH 

COj 

o.  069? 

v} 

.00805 



Air  
HzO 

Ethyl  acetate 
Air 

093 
.246 

:5i 

I-3S 

.0071 
•  0319 

- 

NHj 

NHa 

.190* 

0.74 

•  0174 

— 

*  COs  into  COs.        t  Ethyl  formate.         J  Estimated. 


SMITHSONIAN  TABLES 


4o6 


TABLES  522-524. 

COLLOIDS. 
TABLE  522.  —  General  Properties  of  Colloids. 


For  methods  of  preparing  colloids,  see  The  Physical  Properties  of  Colloidal  Solutions,  Burton,  1916;  for  general 
properties,  see  Outlines  of  Colloidal  Chemistry,  J.  Franklin  Inst.  185,  p.  i,  1918  (contains  bibliography). 

The  colloidal  phase  is  conditioned  by  sufficiently  fine  division  (i  X  icr4  to  io~7  cm).  Colloids  are  suspensions  (in 
gas,  liquid,  solid)  of  masses  of  small  size  capable  of  indefinite  suspension;  suspensions  in  water,  alcohol,  benzole,  glyc- 
erine, are  called  hydrosols,  alcosols,  benzosols,  glycerosols,  respectively.  The  suspended  mass  is  called  the  disperse 
phase,  the  medium  the  dispersion  medium. 

Coiioms  tall  into  3  quite  definite  classes:  ist,  those  consisting  of  extremely  finely  divided  particles  (Cu,  Au,  Ag, 
etc.)  capable  of  more  or  less  indefinite  suspension  against  gravity,  in  equilibrium  of  somewhat  the  same  aspect  as  the 
pases  of  the  atmosphere,  depending  as  in  the  Brownian  movement  upon  the  bombardment  of  the  molecules  of  the 
medium:  2nd,  those  resisting  precipitation  (haemoglobin,  etc.)  probably  because  of  charged  nuclei  and  which  maybe 
coagulated  and  precipitated  by  the  neutralization  of  the  charges;  3rd,  colloidal  as  distinguished  from  the  crystalloidal 
condition,  the  colloid  being  very  slowly  diffusible  and  incapable  unlike  crystalloids  of  penetrating  membranes  (gelatine, 
silicic  acid,  caramel,  glue,  white  of  egg,  gum,  etc.). 

Smallest  particle  of  Au  observed  by  Zsigmody  (ultraraicroscope)  i .  7  X  lo""7  cm. 

visible  in  ordinary  microscope  about  2.5  X  io~6  cm. 

"   ultramicroscope,  with  electric  arc  15  X  io~7  cm. 

with  direct  sunlight  i  X  io~7  cm. 

TABLE  523.  —  Molecular  Weights  of  Colloids. 


Determined  from  diffusion. 

Determined  from  freezing  point 

Gum  arabic  
Tannic  acid  (^22)* 

1750 
2730 

Glycogen  (162)  *  
Tungstic  acid  (250)  *  ... 

1625 
1750 

Egg  albumen  

7420 

Gum  

1800 

Caramel 

13200 

Albumose            

2400 

(Due  to  Graham) 

Ferric  hydrate  (107)  *  

oooo 

Egg  albumen  

14000 

Starch  (162)  * 

25000 

*  Formula  weight. 
TABLE  524.  —  Brownian  Movement. 

The  Brownian  movement  is  a  microscopically  observed  agitation  of  colloidal  particles.  It  is  caused  by  the  bom- 
bardment of  them  by  the  molecules  of  the  medium  and  may  be  used  to  determine  the  value  of  Avogadro's  number. 
Perrin,  Chaudesaignes.  Ehrenhaft  and  De  Broglie  found,  respectively,  70,  64,  63  and  64  X  io2*  as  the  value  of  this 
constant.  The  following  table  indicates  the  size  and  the  dependence  of  this  movement  on  the  magnitude  of  the  particles. 


Material. 

Diameter 
X  io»  cm 

Medium. 

Temp. 

Velocity 
X  10* 

cm/sec. 

Observer.                  < 

Dust  particles  
Gold 

2.0 

o  35 

Water 

20? 

none 
200 

Zsigmody 

Gold 

(i 

280 

a 

Gold  
Platinum  
Platinum  

0.06 
•  4  to  .5 

Acetone 
Water 

18 
20 

700. 
3900. 
3200. 

Svedberg,  1906-9 

Rubber  emulsion  
Mastic 

IO. 
IO 

i? 

20> 

124. 
i  55 

Henri,  1908 

Gamboge  

4-  5 

ti 

2O 

2  .  4 

Chaudesaignes,  1908. 

2   13 

it 

3  4 





The  movement  varies  inversely  as  the  size  of  the  particles;   in  water,  particles  of  diameter  greater  than  4^1  show  no 
perceptible  movement;  when  smaller  than  .I/JL,  lively  movement  begins,  while  at  10  ntfj.  the  trajectories  amount  up  to 


SMITHSONIAN  TABLES. 


TABLES  525-527.  4°7 

COLLOIDS. 
TABLE  525.  —  Adsorption  of  Gas  by  Finely  Divided  Particles.     See  also  p.  439 

Fine  division  means  great  surface  per  unit  weight.  All  substanct-  tcn.l  t.,  adsorb  gas  at  surface,  the  more  the  higher 
the  pressure  and  the  lower  the  temperature.  Since  different  gases  vary  in  tin-  adaption  fractional  separation  n 
possible.  Pt  black  can  absorb  100  vols.  Hz,  800  vols.  On,  Pd  3000  vols.  H».  In  I'd.  heated  to  100°,  is  used 

to  remove  Hz  (higher  temperature  used  for  faster  adsorption,  will  take  more  at  lower  temperature).  Pt  can  dissolve 
several  vols.  of  Hz,  Pd,  nearly  TOO  at  ordinary  temperatures;  but  it  seems  probable  that  the  bulk  of  the  100  vols.  of 
Hz  taken  by  Pt  and  the  3000  by  Pd  must  be  adsorbed.  In  1848  Rose  found  the  density  21  to  22  for  Pt  foil  but  26  for 
precipitated  Pt. 

The  film  of  adsorbed  air  entirely  changes  the  behavior  of  very  small  particles.  They  flow  like  a  liquid  (cf.  fog). 
With  substances  like  carbon  black  as  little  as  5  per  cent  of  the  bulk  is  C;  a  liter  of  C  black  may  contain  2.5  liters  of 
air.  Mitscherlich  calculated  that  when  CQz  at  atmospheric  pressure,  12°  C,  is  adsorbed  by  boxwood  charcoal,  it  occu- 
pies 1/56  original  vol.  Apparent  densities  of  gases  adsorbed  at  low  temperatures  by  cocoanut  charcoal  are  of  the  T^T 
order  (sometimes  greater)  as  liquids. 


Cm5  of  Gas  Adsorbed  by  a  Cm3  of  Synthetic  Charcoal  (corrected  to  o°  C,  76  cm?)  (Hemperl  and  Vater). 

°C 

H2 

Ar 

N2 

02 

CO 

CO2 

NO 

NjO 

Iff 

-185 

7-3 
19-5 
284.7 

12.6 

92.6 

21.0 
107-4 
632.2 

25-4 
122.4 

26.8 
139-4 
697.0 

83.8 
568.4 

103.6 
231-3 

109.4 
330.1 

CH, 

CzHe 

C2H4 

CzHi 

NHj 

H2S 

Cli 

SOj 

+  20° 
-78 

41.7 
174-3 

119.1 

275-5 

139    2 
360.7 

135-8 
488.5 

197.0 

213 

.0 

304  5 

337-8 

Cm3  of  Gas  Adsorbed  by  a  Cnv»  of  Cocoanut  Charcoal  (corrected  to  o°  C,  76  cm)  (Dewar). 

°C 

He 

H2 

N2                     O2 

CO 

Ar 

0° 

-185 

2 

IS 

4 
135 

15                        18 
155                       230 

21 
100 

12 
I7S 

See  Langmuir,  J.  Am.  Ch.  Soc.  40,  1361,  1918;  Richardson,  39,  1829,  1916. 
TABLE  526.  —  Heats  of  Adsorption. 


Adsorber. 

Amylene.  1 

4> 

• 

j 

M 

|3 

S  a 

11 

w*5 

j 

11 
|| 

11 

li 

u- 

% 

Carbon 
disulphidc.  1 

a  ,  «* 

i« 

I 

Fuller's  earth  *  

57-1 

30.2 

27-3 

21.8 

17.2 

13.4 

10.9 

10.  S 

8.4 

4.6 

4.6 

4.2 

3-9 

Bone  charcoal  *  

18.5 

19  3 

17.6 

16.5 

10.6 

14.0 

n.  i 

8.4 

13-9 

8.9 

Kaolin  *  

78.8 

27.6 

24-5 

— 

20.4 

— 

15-7 

9-9 

99 

94 

7.2 

Fuller's  earth  f  

.683 

.684 

.679 

.611 

.610 

.621 

.625 

*  Small  calories  liberated  when  i  g  of  the  adsorbent  is  added  to  a  relatively  large  quantity  of  the  liquid, 
t  Volume  adsorped  from  saturated  vapor  by  i  g  of  fuller's  earth. 
Gurvich,  J.  Russ.  Phys.  Ch.  Soc.  47,  805,  1915. 

TABLE  527.  —  Molecular  Heats  of  Adsorption  and  Liquefaction  (Favre). 


Molecular  heats  of 

Molecular  heats  of 

Adsorber. 

Gas. 

adsorption. 

lique- 
faction. 

Adsorl>er. 

adsorption. 

lique- 
faction. 

Platinum  

H2 

46200 

_ 

Charcoal  

IOOOO-IOOOO 

5600 

Palladium  
Charcoal  

H2 
NHs 

18000 
5000-8500 

(5000) 

Hd 
HBt 

020O-I0200 

15200-15800 

(3600) 
(4000) 

CO* 

6800-7800 

6250 

HI 

21000-23000 

(4400) 

NzO 

7100-10900 

4400 

SMITHSONIAN  TABLES- 


408 


TABLES  528-529. 
TABLE  528.  —  Miscellaneous  Constants  (Atomic,  Molecular,  etc.). 


Elementary  electrical  charge,  charge  on  electron,  i  charge  on  a  particle t  =  4-774  *  I0~10  esu  (M) 

=  1.591   X  io-2°emu 

=  i .  591  X  io-»  coulomb 

Mass  of  .an  electron i*  =  9 . 01  X  io~28  g 

Radius  of  an  electron about  2  X  io^13  cm 

Ratio  elm,  small  velocities e/m  =  i.  766  X  io7  emu.  g-1 

Number  of  molecules  per  gram  molecule  or  per  gram  molecular  weight  (Avogadro 

constant) N  =  6.062  X  io»  (M) 

Number  of  gas  molecules  per  cm3,  76  cm,  o°  C  (Loschmidt's  number) n  =  2.705  X  io19  (M) 

Number  of  gas  molecules  per  cmj,  o°  C  at  i  X  io6  bars 2 . 670  X  iolj 

Kinetic  energy  of  translation  of  a  molecule  at  o°  C Eo  —  5 . 621  X  io~14  erg  (M) 

Constant  of  molecular  energy,  Eo/T  -  change  of  translational  energy  per  °  C. . .  e  =  2.058  X  io~16  erg/6  C  (M! 

Mass  of  hydrogen  atom : =  i .  662  X  to"24  g  (M) 

Radius  of  hydrogen  molecule  about : .           io~8  cm 

Mean  free  path,  ditto,  76  cm,  o°  C,  about  Z,  =  i .  6  X  io~6  cm/sec. 

Sq.  rt.  mean  sq.  velocity,  ditto.  76  cm.  o°  C G  =  1.84  X  10*  cm/ sec. 

Arithmetical  average  velocity,  ditto.  76  cm.  o°  C 12  =  i .  70  X  io5  cm/sec. 

Average  distance  apart  of  molecules.  76  cm,  o°  C =  3  X  io~6  cm 

Boltzmann  gas  constant  =  constant  of  entropy  equation  =  R/N  =  poVo/TN  = 

(})« k  =  i  .372  X  io-"  erg/0  C 

Volume  per  mol(e)  or  gram-molecular  weight  of  ideal  gas,  76  cm,  o°  C  (i  .01323  X 

io6  bars) =22.412  liters 

Ditto,  i  X  io«  bars,  o°  C  (75  cm  Hg) =  22 . 708  liters 

Gas  constant:  PVm  =  RT.  Vm  =  vol.  molec.  wt.  in  g  when  P  in  g/cm2,  Vm  in  cm3  R  =  84.  780  g-cm/°  C 

when  P  in  atmospheres,  Vm  in  liters R  =  o.  08204  /-atm/°  C 

when  P  in  dynes,  Vm  in  cm3 R  =8.315  X  io7  ergs/0  C 

Absolute  zero  =  o°  Kelvin =  —273.13°  C 

i  Mega  bar  (=  Meteorological  "bar")  =  io«  dynes/cm2  =  1.013  kg/cm2 =0.987  atmosphere 

Mechanical  equivalent  of  heat,  i  g  (20°  C)  cal =  4. 184  X  io7  ergs 

=  4. 184  Joules 

Faraday  constant F  =  96494  coulombs 

Velocity  of  light  in  vacuo c  =  2. 99860  X  io10  cm/sec. 

Planck's  element  of  action h  =  6. 547  X  xo""27  erg.  sec.  (M) 

Rydberg's  fundamental  frequency Vo  =  3 .  28880  X  io15  sec."1 

Rydberg's  constant.  Vo/c N  =  109678 .  7 

\Vien's  constant  of  spectral  radiation ct  =  i. 4312  for  X  in  cm  (M) 

Stefan-Boltzmann  constant  of  total  radiation <r  =  5 .  72  X  io~12  watt/cm2  (M) 

Grating  space  in  calcite d  =  3 . 030  A 

Grating  space  in  rock-salt  (Uhler,  Cooksey) =  2 . 814  X  io~8  cm 

Potential  difference  in  volts  for  X-rays  of  wave-length  X  in  cm  =  FX  =  hc/e =  i.  241  X  io~4  volt,  cm 

Reference:   (M)  Millikan,  Phil.  Mag.  34,  i,  1917. 


TABLE  529.  —  Radiation  Wave-length  Limits. 

Hertzen  waves,  longest 2  coo  ooo. o  cm 

shortest 0.2  cm 

Infra-red,  longest, reststrahlung,  focal-isolation 0.03  cm 

Infra-red,  spectroscopically  studied 0.002  cm 

Visible,  longest 

shortest 

Ultra-violet,  Lyman,  shortest  * 

X-rays,  longest 

shortest 

7  rays,  longest 

shortest 


o .  ooo  08  cm 
o .  ooo  04  cm 
o .  ooo  006  cm 
o .  ooo  ooo  1 2  cm 
o.ooo  ooo  ooi  cm 
o.ooo  ooo  013  cm 
o.ooo  ooo  ooo  7  cm 


SMITHSONIAN  TABLES. 


*o.ooooo2o  cm  (Millikan-Sawyer,  1920) 


TABLE  530. 


TABLES  5SO-531. 
Periodic  System  of  the  Elements. 


409 


0 

I 

II 

III 

IV 

V 

VI 

VII 

1   ~" 

RsO 

RO 

RzO, 

RO, 

Rz04 

RO, 

RiOr 

R0«  -fit  Oxides,  j 

- 

- 

- 

— 

RH4 

RH, 

RH 

RH 

--«r  Hydrides. 

He 

Li 

Gl 

B 

C 

N 

0 

F 

4 

; 

9 

TI 

12 

14 

16                  19 

— 

\e 

\ 

Mg 

Al 

Si 

P 

S                  Cl 



20 

23 

24 

27 

28 

3i 

32     i             35 

— 

A 

K 

Ca 

Sc       ;     Ti 

V 

Cr 

Mn 

Fe     Ni      Co 

40 

39 

40 

44 

48 

Si 

52 

55 

56       59       59 



Cu 

Zn 

Ga 

Ge 

As 

Se 

Br 



— 

64 

OS 

70 

72 

75 

79 

80 

— 

Kr 

Rb 

Sr 

Yt 

Zr 

Cb 

Mo 

__ 

Ru     Rh     Pd 

82 

85 

88 

89 

9i 

94 

96 

— 

IO2       103       IO7 



Ag 

Cd 

In 

Sn 

Sb 

Te 

I 



— 

108 

112 

"5 

119 

120 

128 

127 



X 

Cs 

Ba 

La 

Ce 

Pr 

Nd 

— 



128 

133 

137 

139 

140 

141 

144 

— 



_ 

Sa 

Eu 

Gd 

Tb 

Ds 

Er              — 

__ 

— 

150 

'52 

157 

J59 

162 

168             — 

— 

_ 

Tm 

Yb 

Lu 



Ta 

W                   — 

Os      Ir       Pt 

— 

168 

*74 

175 

— 

181 

184                  — 

191     19.5     195 

_ 

Au 

Hg 

Tl 

Pb 

Bi 

Po 





— 

197 

201 

204 

207 

208 

2IO 

— 

— 

Em 



Ra 

Ac 

Th 

UrX; 

U 





(222) 

226 

(227) 

232 

234 

238 

TABLE  531.  —  Atomic  Numbers.* 


i  Hydrogen 

20  Calcium 

39  Yttrium 

58  Cerium 

76  Osmium 

2  Helium 

21  Scandium 

40  Zirconium 

59  Praseodymium 

77  Iridium 

3  Lithium 

22  Titanium 

41  Niobium  { 

60  Neodymium 

78  Platinum 

4  Beryllium 
5  Boron 

23  Vanadium 
24  Chromium 

42  Molybdenum 
43 

6! 

62  Samarium 

79  Gold 
80  Mercury 

6  Carbon 

25  Manganese 

44  Ruthenium 

63  Europium 

81  Thalium 

7  Nitrogen 

26  Iron 

45  Rhodium 

64  Gadolinium 

82  Lead 

8  Oxygen 

27  Cobalt 

46  Palladium 

65  Terbium 

83  Bismuth 

9  Fluorine 

28  Nickel 

47  Silver 

66  Dysprosium 

84  Polonium 

10  Neon 
ii  Sodium 

29  Copper 
30  Zinc 

48  Cadmium 
49  Indium 

67  Holmium 
68  Erbium 

85 
86  Emanation 

12  Magnesium 

31  Gallium 

50  Tin 

69  Thulium 

87  « 

13  Aluminum 

32  Germanium 

51  Antimony 

70  Ytterbium 

88  Radium 

14  Silicon 

33  Arsenic 

52  Tellurium 

71  Lutecium 

89  Actinium 

15  Phosphorus 

34  Selenium 

53  Iodine 

72 

90  Thorium 

1  6  Sulphur 
17  Chlorine 

35  Bromine 
36  Krypton 

54  Xenon 
55  Caesium 

73  Tantalum 
74  Tungsten 

91  Uranium  Xi 
92  Uranium 

i  8  Argon 

37  Rubidium 

56  Barium 

75 

19  Potassium 

38  Strontium 

57  Lanthanum 

*  Quoted  from  Millikan's  The  Electron,  1917. 
SMITHSONIAN  TABLES. 


t  Glucinium. 


t  Columbium. 


4io 


TABLE  632. 
PERODIC  SYSTEM   AND   THE  RADIOACTIVE   ISOTOPES.' 


4                   sA          6A         ?A 

0 

lA        2A         3A                 4 

Vb 

82 
Pb 

Non-metals. 

li    it    * 

Inert-gases. 
86 

Nt 

Light-metals. 
87          88          89 
—         Ra         Ac 

K 

VI 

IVb 

S 

&     ft     F 

Xe 

a   t   a 

g 

Va 

inb 

£34          35 
Se         Br 

36 
Kr 

a  g    v 

IVa 

lib 

14 

15          16          17 

18 

19               20                21 

22 

Ilia 

Si 

P           S           Cl 

Ar 

K          Ca         Sc 

Ti 

Ib 

6 
C 

8           9 
N          O          F 

10 

Ne 

II              12               13 

Na        Mg        Al 

s? 

Ha 

— 

i 
H 

2 

He 

L     1.     I 

6 
C 

la 

Heavy  metals. 

III' 

22 

Ti 

23         24         25          26         27         28        29        30        -51                     32 
V          Cr         Mn       Fe        Co       Ni        Cu       Zn        Ga             1     Ge 

III' 

IV 

40 

41          42           43           44          45          46         47          48         49                       50 

IV  ' 

Zr 

Cb       Mo       —         Ru       Rh       Pd       Ag       Cd       In 

Sn 

V 

58       59      60       61      62      63       64       65       66       67       68      69       70       71          72 
Ce      Pr      Nd     —      Sa      Eu      Gd      Tb      Dy      Ho      Er      Ad      Cp      Yb        Lu 

V 

V 

II 

73           74           75 
Ta         W          — 

76      77     78 
Os    Ir    Pt 

79          80           81 
Au        Hg         Tl 

82 
Pb 

V 

VI 

90 

91           92 

VI 

Th 

Bv         U 

4                     SB         6B          76                                            iB          26         36                  4 

Radioactive  isotopes. 

(Tl)          (Pb)        (Bi)         (Po)       (     )       (Nt)          (     )        (Ra)        (Ac)          (Th)         (Bv)         (U) 

81             82           83           84         85          86             87          88            89            90             91           g2 

1=1-    1=1 

PbRa                  I  RaF 

i  -  1  ' 

huti 

(PbTh 
\  PbAc 
[RaD 
[ThD  } 

}      «          {ThC'}            [ThEm]               (ThXl                   f  RaTh  ] 
'  *-      AcC'      v-       AcEm     «-          AcX       «-          \  RaAc 
\RaC-  j            [RaEmj              \  Ra    J           /      [lo        J       *-          U2 
InU                                                                             Msl 

\  AcD    \       <-       \  AcC                                                                       Ac             <-           Uz      ^ 

RaC"                     IRaC                                                                       *                                  Ux" 

JThB]     -             ThA]                                             MsT'  ^    «-            Th 

\  AcB  \  '   *-        AcA      «-                                                                        Uy          «-           Ui 

I  RaB  J                    RaA  J                                                                               Ux' 

<—  Indicates  the  loss  of  an  alpha  particle  (producing  He) ;  the  element  becomes  more  electro-positive  and  the  atomic 
weight  decreases  by  4,  position  changing  2  columns  to  the  left. 

/  Indicates  beta  radiation  (loss  of  electron);  the  element  becomes  more  electro-negative,  atomic  weight  remains 
the  same,  position  changes  one  column  to  the  right  and  up. 

Isotopes  of  an  element  have  the  same  valency  and  the  same  chemical  properties  (solubility,  reactivity,  etc.),  al- 
though their  atomic  weights  may  differ.  The  isotopes  of  Bi  are,  e.g.,  RaE,  ThC,  AcC,  RaC. 

In  the  upper  half  of  the  table  are  the  elements  possessing  high  electro-potential,  simple  spectra,  colorless  ions.  The 
properties  are  analogous  in  the  vertical  direction  (groups).  In  the  lower  half  are  the  elements  with  low  electro-poten- 
tial, complex  spectra,  colored  ions  and  tending  to  form  complex  double  salts,  the  general  properties  of  the  elements 
being  more  pronounced  in  the  horizontal  direction  (periods). 

On  the  left  side  of  the  table  are  the  electro-negative  elements,  those  of  the  upper  half  forming  strong  acids,  those 
of  the  lower  half  weak  oxyacids. 

On  the  right  side  of  the  table  are  the  electro-positive  elements,  forming  bases,  oxysalts,  sulfides,  etc. 

The  center  of  the  lower  half  is  occupied  by  the  amphoteric  elements  forming  weak  acids  and  bases,  many  complex 
compounds  and  double  salts,  many  insoluble  and  mostly  colored  compounds. 

A  very  striking  point,  however,  is,  as  already  mentioned,  that  the  similarity  among  the  elements  in  the  upper  half  is 
in  the  verticaUdirection,  and  in  the  lower  half  in  the  horizontal  direction.  This  justifies  the  use  of  the  expressions 
group-relation  and  period-relation. 

*  Table  adapted  from  Hackh,  J.  Am.  Chem.  Soc.  40,  1023,  1918,  Phys.  Rev.  13,  169,  1919. 

The  following  isotopes  have  been  determined  by  means  of  mass-spectra.  A  ••ton,  Phil.  Mag.  40,  633,  1920;  Na- 
ture, 106,  468,  1920.  The  columns  give  symbol,  min.  number  of  isotopes,  masses  in  order  of  intensity.  Numbers  in 
brackets  are  provisional. 

1.008  F  i         19  A 

As 


H 
He 
B 
C 

N 
O 


F 

Ne 
Si 
P 

s 

Cl 


19 

20,  22,  (21) 

28,  29,  (30) 

31 

32 

35.  37.  (39) 


36 


40, 

75 

Br      2  79,  81 

Kr      6  84,  86,  82,  83,  80,  78 

X         5,  (7)         129,  132,  131,  174,  136,  (128,  130?) 
Hg      (6)  (197-200),  202,  204 


SMITHSONIAN  TABLES. 


TABLES  533-535. 

ASTRONOMICAL   DATA. 
TABLE  533.  —  Stellar  Spectra  and  Related  Characteristics. 


411 


The  spectra  of  almost  all  the  stars  can  be  arranged  in  a  continuous  sequence,  the  various  types  connected  in  a  series 
of  imperceptible  gradations.    With  one  unimportant  exception,  the  sequence  is  linear,  the  transition  between  two  given 

Harvard  system  of 

.       OB,  ,dN.  —  and 

ween  classes  B  and  A  is  denoted  85,  while  those 
8  or  BQ.    In  Classes  M  and  O  the  notation  Ma, 
Mb,  Me,  etc.,  is  employed.     Classes  R  and  N  apparently  form  a  side  chain  branching  from  the  main  series  near  (  i 

The  colors  of  the  stars,  the  degree  to  which  they  are  concentrated  into  the  region  of  the  sky,  including  the  Milky 
Way,  and  the  average  magnitudes  of  their  peculiar  velocities  in  space,  referred  to  the  center  of  gravity  of  the  naked- 
eye  stars  as  a  whole,  all  show  important  correlations  with  the  spectral  type.    In  the  case  of  colors,  the  correl.r 
so  close  as  to  indicate  that  both  spectrum  and  color  depend  almost  entirely  on  the  surface  temperature  of  the  stars. 
The  correlation  in  the  other  two  cases,  though  statistically  important,  is  by  no  means  as  close. 

Examples  of  all  classes  from  O  to  M  are  found  among  the  bright  stars.    The  brightest  star  of  Class  N  is  of  magni- 
tude 5.3;  the  brightest  of  Class  R,  7.0. 


TABLE  534.  —  The  Harvard  Spectral  Classification. 


Class. 

Principal  spectral  lines 
(dark  unless  otherwise 
stated). 

Example. 

Number 
brighter 
than  6.25, 
mag. 

Per  cent 
in 
galactic 
region. 

Color 
index. 

Effective 
surface 
temperature, 
K 

Mean 
peculiar 
velocity, 

km  /sec. 

0 

Bright     H     lines,     bright 

spark  lines  of  He,  N,O,C 

7  Velorum 

20 

IOO 

—0.3 





B 

H,  He,  spark   lines  of  N 

and  O,  a  few  spark  lines 

of  metals. 

6  Orionis 

606 

82 

—  «  ?^ 

.  -  ryvio 

6 

A 

H  series  very  strong,  spark 

uyu 

u.  ,50 

lines  of  metals  

Sinus 

1885 

66 

0.00 

1  1,  OOO° 

10 

F 

H  lines  fainter.    Spark  and 

G 

arc  lines  of  metals  
Arc  lines  of  metals,  spark 

Canopus 

720 

57 

+0-33 

7,500° 

M 

lines  very  faint  

The  sun 

609 

58 

+0.70 

S.OOO0 

15 

K 

Arc  lines  of  metals,  spec- 

trum faint  in  violet  

Arcturus 

1719 

56 

+  I.I2 

4,2OO° 

i? 

M 

Bands  of  TiOz,  flame  and 

arc  lines  of  metals  

Antares 

457 

54 

+I.OO 

3.IO00 

17 

R 

Bands  of  carbon,  flame  and 

B.  D. 

arc  lines  of  metals  

—  10°  5057 

0 

63 

+1.7 

3,000° 

15 

N 

Bands   of   carbon,    bright 

lines,  very  little  violet 

light 

19  Piscium 

g 

87 

+2.5 

2,300° 

13 

Compiled  mainly  from  the  Harvard  Annals.  Temperatures  based  on  the  work  of  Wilsing  and  Scheiner.  Radial 
velocities  from  Campbell.  Data  for  classes  R  and  N  from  Curtis  and  Rufus.  The  color  indices  are  the  differences  of 
the  visual  and  photographic  magnitudes.  Negative  values  indicate  bluish  white  stars;  large  positive  values,  red  stars. 
The  peculiar  velocities  are  in  the  radial  direction  (towards  or  from  the  sun).  The  average  velocities  in  space  should 
be  twice  as  great. 

The  "galactic  region"  here  means  the  zone  between  galactic  latitudes  ±  30°,  and  including  half  the  area  of  the 
heavens. 

96%  of  the  stars  of  known  spectra  belong  to  classes  A,  F,  G,  K,  99. 7%  including  B  and  M  (Innes,  1919). 


TABLE  535.  —  Apex  and  Velocity  of  Solar  Motion. 


R.  A.  1900. 

Dec. 

Velocity, 
km/sec. 

Method. 

No.  of 
stars. 

Authority. 

i8A  02OT 
17     54 
18    oo 

+34-3 
25-1 
29.2 

19  5 
21.4 

Proper  motions 
Radial  velocities 

54U 
"03 
1405 

Boss,  Astron.  J.  614.  1910 
Campbell.  Lick  Hull.  196.  IQII 
StnimlHTi:.  A-troplns.  J.  1918. 

SMITHSONIAN  TABLES- 


412 


TABLES  536-537. 

ASTRONOMICAL   DATA. 

TABLE  536.  —  Motions  of  the  Stars. 


The  individual  stars  are  moving  in  all  directions,  but,  for  the  average  of  considerable  groups,  there  is  evidence  of  a 
drift  away  from  the  point  in  the  heavens  towards  which  the  sun  is  moving  (solar  apex).  The  best  determinations  of 
the  solar  motion,  relative  to  the  stars  as  a  whole,  are  given  in  Table  535.  In  round  numbers  this  motion  of  the  sun 
may  be  taken  as  20  km/sec,  towards  the  point  R.  A.  18  h.  om.,  Dec  +30.0°. 

After  allowance  is  made  for  the  solar  motion,  the  motions  of  the  stars  in  space,  relative  to  the  general  mean,  present 
marked  peculiarities.  If  from  an  arbitrary  origin  a  series  of  vectors  are  drawn,  representing  the  velocities  of  the  various 
stars,  the  ends  of  these  vectors  do  not  form  a  spherical  cluster  (as  would  occur  if  the  motions  of  the  stars  were  at  ran- 
dom), but  a  decidedly  elongated  cluster,  whose  form  can  be  approximately  represented  either  by  the  superposition  of 
two  intermingling  spherical  clusters  with  different  centers  (Kapteyn's  two-stream  hypothesis)  or  by  a  single  ellipsoidal 
cluster  (Schwarzschild),  the  actual  form,  however,  being  more  complicated  than  is  indicated  by  either  of  these  hy- 
potheses. The  direction  of  the  longest  axis  of  the  cluster  is  known  as  that  of  preferential  motion.  The  two  opposite 
points  in  the  heavens  at  the  extremities  of  this  axis  are  called  the  vertices.  The  components  of  velocity  of  the  stars 
parallel  to  this  axis  average  considerably  larger  than  those  parallel  to  any  axis  perpendicular  to  it. 

The  preferential  motion  varies  greatly  with '  spectral  type,  being  practically  absent  in  Class  B,  very  strong  in  Class 
A,  and  somewhat  less  conspicuous  in  Classes  F  to  M,  on  account  of  the  greater  mean  velocities  of  these  stars  in  all 
directions.  The  positions  of  the  vertices  are  nearly  the  same  for  all. 

Numerous  investigators,  from  the  more  distant  naked-eye  stars,  find  substantially  the  same  position  for  the 
vertex,  the  mean  being  R.  A.  6  h,  6  m.,  Dec.  +9°.  The  nearer  stars,  of  large  proper  motion,  give  a  mean  of  6  h.  i2m., 
+25°.  (See  Stromberg's  discussion,  cited  above.) 

In  addition  to  these  general  phenomena,  there  are  numerous  clusters  of  stars  whose  members  possess  almost  exactly 
equal  and  parallel  motions,  —  for  example,  the  Pleiades,  the  Hyades,  and  certain  large  groups  in  Ursa  Major,  Scorpius, 
and  Orion.  The  vertices,  and  the  directions  toward  which  these  clusters  are  moving,  are  all  in  the  plane  of  the  galaxy. 

Several  faint  stars  are  known  which  have  radial  velocities  between  300  and  350  km/sec,  (e.g.  A.  G.  Berlin  1366  R.A. 
looo  =  4*8»»6,  Dec.  1000  =  +22.7°,  mag.  8.Q  velocity  of  recession  339  km/sec.),  and  it  is  probable  that  the  actual 
velocity  in  space  exceeds  500  km/sec,  for  some  of  these. 

The  gth  magnitude  star  A.  G.  Berlin  1366  has  a  radial  velocity  of  404  km/sec. 

The  greatest  known  proper  motion  is  that  of  Barnard's  star  of  the  ninth  magnitude  in  Ophiuchus,  10.3"  per  year, 
position  angle  356°.  The  parallax  of  this  star  is  0.52".  and  its  radial  velocity  about  — 100  km/sec. 

The  average  radial  velocity  of  the  globular  clusters  is  100  km/sec,  and  that  of  the  spiral  nebulae  400  km.  The 
globular  clusters  as  a  class  are  approaching  the  sun.  The  spiral  nebulae,  with  a  few  exceptions,  are  receding.  The 
greatest  individual  values  are  —410  km  for  the  cluster  N.  G.  C.  6934  and  4-  1800  km  ~for  the  nebula  N.  G.  C.  584. 

Average  velocities  with  regard  to  center  of  gravity  of  the  stellar  system,  according  to  Campbell  (Stellar  Motion, 
IQI3): 


Type  B  Stars: 

A 


6 . 6  km  per  sec. 
10. 9     ' 
14.4     "      "      " 


Type  G  Stars: 

K 
"     M     " 


15.0  km.  per  sec. 
16. 8    " 

17.1  " 


For  radial  velocities  of  119  stars  see  Astrophysical  Journal,  48,  p.  261,  1918. 


TABLE  537.  —  Distances  of  the  Stars. 


Distances. 

Parsecs.* 

Light  years. 

Alpha  Centauri  (nearest  star)  
Barnard's  Star  

1.32 
1  .  9 

ft 

Sirius  . 

2   7 

8  7 

Arcturus.  .... 

13.0 

43.0 

The  Hyades.  . 

40. 

130. 

Nebula  of  Orion  (Kapteyn)  
Globular    Clusters     (Shapley):     omega 
Centauri  (nearest)  

185. 
6,500. 

600. 
21,000. 

N.  G.  C.  7006  (farthest)  

67,000. 

220,000. 

*  Parsec  =  206,265  astronomical  units  =  3.08  X  ion  km  =  3.26  light  years,  i  astronomical  unit  =  distance  sua 
to  earth. 

Practically  all  the  stars  visible  to  the  naked  eye  lie  within  1000  parsecs  of  the  sun,  and  most  of  them  are  more  than 
100  parsecs  distant.  In  the  vicinity  of  the  sun,  the  majority  of  the  stars  lie  within  two  or  three  hundred  parsecs  of  the 
galactic  plane;  but  along  this  plane  the  star-filled  region  extends  far  beyond  1000  parsecs  in  all  directions,  and 
may  reach  30,000  parsecs  in  the  great  southern  star  clouds  (Shapley). 

Average  parallax  6  planetary  nebulae,  0.018"  (van  Maanen,  Pr.  Nat.  Acad.  4,  p.  3941  1918). 

SMITHSONIAN  TABLES- 


TABLES  538-639  *  j  ^ 

ASTRONOMICAL    DATA- 

TABLE  538.—  Brightness  of  the  Stars. 

Stellar  magnitudes  give  the  apparent  brightness  of  the  stars  on  a  logarithmic  scale,  —  a  numerical  increase  of  one 
magnitude  corresponding  to  a  decrease  of  the  common  logarithm  of  the  light  by  0.400,  and  a  change  of  five  magnitudes 
to  a  factor  of  100.  The  brightest  objects  have  negative  stellar  magnitude  !  magnitude  of  the 

of  the  mean  full  Moon,  —12.5;  of  Venus  at  her  brightest,  —4.3;   of  Jupiter,  at  opposition,  rius,  — 1.6;  of 

Vega,  +0.2;  of  Polaris,  +2.1.  (The  stellar  magnitude  of  a  standard  candle  i  m  distant  is  -14.18.)  The  faintest  stars 
visible  with  the  naked  eye  on  a  clear  dark  night  are  of  about  the  sixth  magnitude  (though  a  single  luminous  point  as 
faint  as  the  eighth  magnitude  can  be  seen  on  a  perfectly  black  background).  The  faint-  .Me  with  a  telescope 

of  aperture  A  in.  are  approximately  of  magnitude  9  +  5  logic  A.  The  faintest  photographed  with  the  6o-inch  reflector 
at  Mt.  Wilson  are  of  about  the  2ist  magnitude,  A  standard  candle,  of  the  same  color  as  the  stars,  would  appear  of 
magnitude  +0.8  at  a  distance  of  one  kilometer. 

The  actual  luminosity  of  a  star  is  expressed  by  means  of  its  absolute  magnitude,  which  (Kapteyn's  definition)  is 
the  stellar  magnitude  which  the  star  would  appear  to  have  if  placed  at  a  distance  of  ten  parsecs.  The  absolute  mag- 
nitude of  the  sun  is  +4.8  (equal  to  that  of  0,2  Centauri);  of  Sirius  is  +1.3;  of  Arcturus,  —0.4.  The  faintest  star  at 
present  known  (Innes),  a  distant  companion  to  a  Centauri,  has  the  (visual)  absolute  magnitude  +15.4,  and  a  luminosity 
0.00006  that  of  the  sun.  The  brightest  so  far  definitely  measured,  ft  Orionis,  has  (Kapteyn)  the  abs.  mag.  —5.5  and 
a  luminosity  13,000  times  the  sun's.  Canopus,  and  some  other  stars,  may  be  still  brighter. 

Intrinsic  brightness  of  sun's  surface  =  57,000  candles  per  cm2  of  surface.     (Abbot-Fowle,  1920) 

The  absolute  magnitudes  of  6  planetary  nebulae  average  9.  i;  average  diameter,  4000  astronomical  units  (Solar 
system  to  Neptune  =  60  astr.  units),  van  Maanen,  Pr.  Nat.  Acad.  4,  p.  394,  1918. 

Giant  and  Dwarf  Stars. 

The  stars  of  Class  B  are  all  bright,  and  nearly  all  above  the  absolute  magnitude  zero.  Stars  of  comparable  bright- 
ness occur  in  all  the  other  spectral  classes,  but  the  inferior  limit  of  brightness  diminishes  steadily  for  the  "later  or 
redder  types.  The  distribution  of  absolute  magnitudes  conforms  to  the  superposition  of  two  series,  in  each  of  which 
the  individual  stars  of  each  spectral  class  range  through  one  or  two  magnitudes  on  each  side  of  the  mean  absolute 
magnitude.  In  one,  —  the  "giant  stars,"  —  this  mean  brightness  is  nearly  the  same  for  all  spectral  classes,  and  not 
far  from  absolute  magnitude  zero.  In  the  other,  —  the  "dwarf  stars,"  —  it  diminishes  steadily  from  about  abs.  mag. 
—  2  for  Class  Bp  to  +10  for  Class  M.  The  two  series  overlap  in  Classes  A  and  F,  are  fairly  well  separated  in  Class  K, 
and  sharply  so  in  Class  M.  Two  very  faint  stars  of  Classes  A  and  F  fall  into  neither  series. 

The  majority  of  the  stars  visible  to  the  naked  eye  are  giants,  since  these,  being  brighter,  can  be  seen  at  much  greater 
distances.  The  greatest  percentage  of  dwarf  stars  among  those  visible  to  the  eye  is  found  in  Classes  F  and  G.  The 
dwarf  stars  of  Classes  K  and  M  are  actually  much  more  numerous  per  unit  of  volume,  but  are  so  faint  that  few  of  the 
former,  and  none  of  the  latter,  are  visible  to  the  naked  eye. 

Adams  and  Stromberg  have  shown  that  the  mean  peculiar  velocities  of  the  giant  stars  are  all  small,  —  increasing 
only  from  about  6  km/sec,  for  Class  B  to  12  for  Class  M,  —  while  those  of  the  dwarf  stars  are  much  greater,  increas- 
ing within  each  spectral  class  by  about  1.5  km  per  unit  of  absolute  magnitude,  and  reaching  fully  30  km  for  stars  of 
Class  M  and  abs.  mag.  10.  Both  giant  and  dwarf  stars  show  the  phenomenon  of  preferential  motion. 


TABLE  539.  —  Masses  and  Densities. 

The  stars  differ  much  less  in  mass  than  in  any  other  characteristic.  The  greatest  definitely  determined  mass  is 
that  of  the  brighter  component  of  the  spectroscopic  binary  /3  Scorpii,  which  is  of  13  times  the  sun's  mass,  400  times 
its  luminosity,  and  spectrum  Bi.  The  smallest  known  mass  is  that  of  the  faint  component  of  the  visual  binary  Krueger 
60,  whose  mass  is  0.15,  and  luminosity  0.0004  of  the  sun's,  and  spectrum  M. 

The  giant  stars  are  in  general  more  massive  than  the  dwarfs.  According  to  Russell  (Publ.  Astron.  Soc.  America, 
3,  327,  1917)  the  mean  values  are: 


Spectrum.  ^™m-  Mass" 


62  12  X  Sun  Fa  dwarf  3.0  X  Sun 

Ao  6.5         "  G2      "  1.2 

FS  giant  8  K8      "  0.9         " 

KS     "  10 

The  densities  of  stars  can  be  determined  only  if  they  are  eclipsing  variables.  It  appears  that  the  stars  of  Classes 
B  and  A  have  densities  averaging  about  one  tenth  that  of  the  sun  and  showing  a  relatively  small  range  about  this  value, 
while  those  of  Classes  F  to  K  show  a  wide  range  in  density,  from  1.8  times  that  of  the  sun  (W  Urs.  Maj.)  to  0.000002 

The  surface  brightness  of  the  stars  probably  diminishes  by  at  least  one  magnitude  for  each  stop  ;ilmg  the  Harvard 
scale  from  B  to  M.  It  follows  that  the  dwarf  stars  are,  in  general,  closely  comparable  with  the  s  in  in  diameter,  while 
the  stars  of  Classes  B  and  A,  though  larger,  rarely  exceed  ten  times  the  sun's  diameter.  The  rol.U-r  k'hnt  stars,  how- 
ever, must  be  much  larger,  and  a  few,  such  as  An  tares,  may  have  diameters  exceeding  that  of  the  earth's  orbit.  The 
densities  of  these  stars  must  be  exceedingly  low. 

If  arranged  in  order  of  increasing  density,  the  giant  and  dwarf  stars  form  a  single  sequence  Stirling  with  the  giant 
stars  of  Class  M,  proceeding  up  that  series  to  Class  B,  and  then  down  the  dwarf  seri^  M  It  is  belu 

Russell  and  others  that  this  sequence  indicates  the  order  of  stellar  evolution,  —  a  star  at  fir-t  nperature  as 

it  contracts  and  then  cooling  off  again.    The  older  theory,  however,  regards  the  evolutionary  sequence  as  proceeding 
in  all  cases  from  Class  B  to  Class  M. 

SMITHSONIAN  TABLES. 


414 


TABLE  540. 
MISCELLANEOUS    ASTRONOMICAL    DATA- 


Tropical  (ordinary)  year 
Sidereal  year 
Anomalistic  year 
Eclipse  year 

Synodical  (ordinary)  month 
Sidereal  month 


=  {365.24219879  —  0.0000000614  (/  —  i9oo)}days 
=  {365.25636042  +  0.0000000011  (/  -  1900)} days 
=  {365.25964134  +  0.0000000304  (/  -  1900)} days 
=  {346.620000  +0.00000036  (/ -  i90o)}days 

{29.530588102  —  0.00000000294  (t  —  i9oo)}days 
{27.321660890  —  0.00000000252  (/  —  i9oo)}days 


Sidereal  day  (ordinary,  two  successive  transits 
of  vernal  equinox,  might  be  called  equinoctial 
day) 

Sidereal  day  (two  successive  transits  of  same 
fixed  star) 

1920,  Julian  Period  =  6633 

January  i,  1920,  Julian-day  number  =  2422325 


86164.09054  mean  solar  seconds 
=  23  h.  56  m.  4.09054  mean  solar  time 

=  86164.09966  mean  solar  seconds 


Solar  parallax    =  8. 7958"  ±  0.002"  (Weinberg) 

8.807    ±  0.0027  (Hincks,  Eros) 

8.799  (Sampson,  Jupiter  satellites;   Harvard  observations) 

8.80  Paris  conference 
Lunar  parallax  =  3422.63"  =  57'  2.63"  (Newcomb) 

Mean  distance  earth  to  sun     =  149500000  kilometers  =  92900000  miles 
Mean  distance  earth  to  moon  =  60. 2678  terrestrial  radii 

=  384411  kilometers  =  238862  miles 

Light  traverses  mean  radius  of  earth's  orbit  in  498. 580  seconds 

Velocity  of  light  (mean  value)  in  vacuo,  299860  kilometers/sec.  (Michelson-Newcomb) 
=  186324  statute  miles/sec. 
Constant  of  aberration  =  20.4874"  ±  0.005" 

20.47  Paris  conference  (work  of  Doolittle  and  others 

indicates  value  not  less  than  20.51) 

Light  year  =  9.5  X  io12  kilometers  =  5.9  X  io12  miles 

Parsec,  distance  star  whose  parallax  is  i  sec.  =  31  X  io12  km  =  19.  2  X  io12  m 


General  precession 
Obliquity  of  ecliptic 
Constant  of  nutation 
Gravitation  constant 
Eccentricity  earth's  orbit 

Eccentricity  moon's  orbit 
Inclination  moon's  orbit 
Delaunay's  y  =  sin  \I 
Lunar  inequality  of  earth 
Parallactic  inequality  moon 


50.  2564"  +  0.000222  (t  —  1900)"  (Newcomb) 
=  23°  27'  8.  26"  -  0.4684  (t  -  1900)"  (Newcomb) 
=  9.21"  (Paris  conference) 
=  666.07  X  io~10  cm3/g  sec2  *  o.  16  X  io~10 
=  e  =  0.01675104  —  0.0000004180  (t  —  1900)  — 

0.0000000000126  (/  —  1900)2 
=  e-i  =  0.05490056  (Brown) 
=  /=5°8'43.5"(Brown) 
=  0.04488716  (Brown) 
=  L  =  6.454" 
=  Q  =  124. 785"  (Brown) 


Pole  of  Milky  Way 


=  R.  A.,  12  h.  48  m.;  Dec.,  +27 


SMITHSONIAN   TABLES- 


TABLES  641-542. 
ASTRONOMICAL    DATA. 


415 


TABLE  541.  —  The  First-magnitude  Stars. 


No. 

Star. 

MUK- 

Spec- 
trum . 

R.A. 

1900. 

Dec. 
1900. 

Annual 
proper 
motion  , 
ft 

P.A. 
of 

M 

Parallax. 

Abs. 

ma>;. 

Radial 
velocity 
km. 

i 

Achernar  

0.6 

B5 

I*  34-0'" 

-57°  45' 

0.094" 

108° 

+0.051" 

-0.9 

2 

Aldebaran  J.  .  .  . 

1.  1 

K5 

4     30.2 

+  16     18 

0.203 

160 

+0.056 

-0.2 

+S5-I 

3 

Capellat  t  

0.  2 

G 

5       9-3 

+45     54 

0-437 

1  68 

+0.075 

-0-5 

+30.2 

4 

Rigel*f  

0.3 

B8 

5       97 

—8     19 

O.OOI 

135 

+0.007 

—  5-5 

+  22.6 

I 

Betelgeuse  t  §  •  • 
Canopus  

0.6-1.2 
-0.9 

Ma 
F 

5     49-8 
6     21.7 

+  7     23 
-52     38 

0.029 
0.018 

74 

+0.019 
+0.007 

-2.7 
-6.7 

+21.3 

+  20.8    1 

7 

Sinus*  

-1.6 

A 

6     40.7 

—  16    35 

1.316 

204 

+0.376 

+  1.2 

—  7-4  i 

8 

Procyon  *  

0.5 

FS 

7     34-1 

+5     29 

1.242 

214 

+0.309 

+3-0 

-3-5 

9 

Pollux  §  .  . 

I  .  2 

K 

7     39-2 

+28     16 

o.  625 

264 

+o  .  064 

+0.2 

+3-9 

10 

Regulus  {  

1-3 

B8 

10       3.0 

+  12     27 

0.247 

269 

+0.033 

—  I.I 

-9.1 

II 

a  Crucis*  

I.I 

Bi 

12       21.  O 

-62     33 

0.048 

240 

+0.047 

-0.5 

+7- 

12 

0  Crucis  t  

I-  5 

Bi 

12       41.  Q 

-59      9 

0.056 

240 

+0.008 

-4.0 

+  13- 

13 

Spica  t  

1.2 

B2 

13       19-9 

-io    38 

0.055 

229 

—  O.OI2 

+  1.6 

14 

/8  Centauri  t  .  .  . 

0-9 

B! 

13      56.8 

—  59     53 

0.041 

219 

+0.037 

—X-3 

-7- 

15 

Arcturus  

0.  2 

K 

14     II.  I 

+  19    42 

2.282 

209 

+  0-075 

-0.5 

—39 

16 

a  Centauri  *  

0.3 

G 

14     32.8 

-60    25 

3.680 

281 

+0-759 

+4-7 

-21.6 

17 

Antares  1  1  •  •  •  • 

I.  2 

Ma 

16     23.3 

—  26     13 

0.034 

192 

+0.029 

-1-5 

—3i 

18 
iQ 

Vega  §  
Altair§  

O.I 

0.9 

A 

A5 

18     33-6 
19     45-9 

+38    41 
+8    36 

0.346 
0.655 

36 

54 

+0.091 
+0.214 

—  O.I 

+  2-5 

-13-8 
-33- 

20 

Deneb  §  

i-3 

A2 

20     38.0 

+44    55 

O.OOI 

180 

+O.002 

-7.2 

-4- 

21 

Fomalhaut  

i-3 

A3 

22       52.1 

-30      9 

0.365 

117 

+0.138 

+  2.0 

+6.7 

*  Visual  binary.          t  Spectroscopic  binary.          {  Pair  with  common  proper  motion. 

§  Wide  pair  probably  optical. 

Mass  relative  to  sun  of  (7)  is  3.1;  of  (8),  1.5;  of  (16),  2.0.  For  description  of  types,  see  Table  534  or  Annals  of 
Harvard  College  Observatory,  28,  p.  146,  or  more  concisely  56,  p.  66,  and  91,  p.  5.  The  light  ratio  between  successive 
stellar  magnitudes  is  "V^ioo  or  the  number  whose  logarithm  is  0.4000,  viz.,  2.512.  The  absolute  magnitude  of  a  star 
is  its  magnitude  reduced  to  a  distance  corresponding  to  o.i"  parallax. 


TABLE  542.  —  Wolf's  Observed  Sun-spot  Numbers.    Annual  Means. 

Sun-spot  number  =  k(io  X  number  of  groups  and  single  spots  observed  +  total  number  of  spots  in  groups  and 
single  spots),  k  depends  on  condition  of  observation  and  telescope,  equaling  unity  for  Wolf  with  3-in.  telescope  and 
power  of  64.  Wolf's  numbers  are  closely  proportional  to  spotted  area  on  sun.  100  corresponds  to  about  1/500  of 
visible  disk  covered  (umbras  and  penumbras).  Periodicity:  mean,  11.13,  extremes,  7.3  and  17.1  years.  Monthly 
Weather  Review,  30,  p.  171,  1002;  monthly  means,  revised,  1749-1901;  see  A.  Wolfer  in  Astronomische  Mitteilungen 
and  Zeitschrift  fur  Meteorologie,  daily  and  monthly  values. 


Year. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

1750 

83 

48 

48 

31 

12 

IO 

IO 

32 

48 

j. 

1760 

63 

86 

61 

45 

36 

21 

// 

38 

70 

106 

1770 

IOI 

82 

66 

35 

31 

7 

20 

92 

154 

i  jf> 

1780 

85 

68 

38 

23 

IO 

24 

83 

132 

I31 

118 

7790 

90 

67 

60 

47 

41 

21 

16 

6 

4 

7 

1800 

14 

34 

45 

43 

48 

42 

28 

10 

8 

1 

1810 

o 

i 

5 

12 

14 

35 

46 

41 

30 

24 

1820 
1830 

16 

7 
48 

,1 

2 

8 

8 
13 

17 
57 

36 

122 

50 
138 

62 
103 

67 
86 

1840 

63 

37 

24 

it 

15 

40 

62 

98 

124 

96 

1850 

66 

64 

54 

39 

21 

7 

4 

23 

55 

94 

1860 

96 

77 

59 

44 

47 

30 

16 

7 

37 

1870 
1880 

139 

32 

ill 

54 

102 
60 

66 
64 

8 

17 

52 

ii 

25 

12 

u 

3 

7 

6 
6 

1890 
1900 

7 

IO 

36 
3 

73 
5 

85 

24 

78 
42 

64 

42 
54 

26 
62 

I 

12 

44 

1910 

19 

6 

4 

10 

46 

55 

99 

78 

NOTE:  The  sun's  apparent  magnitude  is  —26.5,  sending  the  earth  00,000,000,000  times  as  much  light  as  the  star 
Aldebaran.    Its  absolute  magnitude  is  +4-8. 

Ratio  of  total  radiation  of  sun  to  that  of  moon  about  100,000  to  i  1  T  ,npicv 
"      "      light          "     "     "  '      400,000  to  i  / 


SMITHSONIAN  TABLES. 


416 


TABLES  543-545. 


GEODETICAL  AND   ASTRONOMICAL  TABLES. 

TABLE  543. — Length,  of  Degrees  on  the  Earth's  Surface. 


Miles  per  degree 

Km.  per  degree 

Miles  per  degree 

Km.  per  degree 

At 

At 

Lat. 

L^t. 

of  Long. 

of  Lat. 

of  Long. 

of  Lat. 

of  Lon^. 

of  Lat. 

of  Long. 

of  Lat. 

0° 
10 

69.17 
68.13 

68.70 
68.72 

111.32 
109.64 

110.57 
II0.60 

S 

39-77 
34.67 

69.17 
69.23 

64.00 
55.80 

111.42 

2O 

3° 

65-03 
59-96 

68.79 

63.88 

104.65 
96.49 

110.70 
110.85 

65 

70 

29.32 
2373 

69.28 
69.32 

47.18 
33.19 

111.50 
III.S7 

40 
4<5 

49.00 

68.99 
69.05 

85.40 
78.85 

111.03 
III.I3 

L5 

17.96 
12.05 

69-36 

28.90 
19.39 

111.62 
111.67 

44-55 

69.11 

71.70 

111.23 

90 

0.00 

69.41 

o.oo 

III.7O 

For  more  complete  table  see  "  Smithsonian  Geographical  Tables.' 


TABLE  544.— Equation  of  Time. 

The  equation  of  time  when  -f-  is  to  be  added  to  the  apparent  solar  time  to  give  mean  time. 
When  the  place  is  not  on  a  standard  meridian  (75th,  etc.)  its  difference  in  longitude  in  time 
from  that  meridian  must  be  subtracted  when  east,  added  when  west  to  get  standard  time  (75  th 
meridian  time,  etc.).  The  equation  varies  from  year  to  year  cyclically,  and  the  figure  following 
the  -I-  sign  gives  a  rough  idea  of  this  variation. 


M.          S. 

M.         S. 

M.        S. 

M.        S. 

Jan.   I 

t3  26-j 

f-T4 

Apr.   i 

+4     2J 

-  7 

July    i 

+3  3'J 

:S 

Oct.   i 

10    12- 

U  8 

Feb.  i 

9  25i 

r  9 
-  4 

15 

May    I 

+o    8Z 

!=  5 
L  3 

Aug.  i 

t!  42^ 

+6     9^ 

L3 
1=3 

15 
Nov.  i 

—  16  i9: 

:  6 

I    2 

Ma/i 

-f-14   20- 

+  12    34rj 

-   2 

~-  4 

*5 
June  I 

—3  49d 

—2    28- 

-  I 
=  3 

Sept.  I 

+4  24- 
-fo     2- 

tz5 
-7 

Dec.  I 

—  15    22  J 

-io  5s: 

^8 

IS 

+  9    9a 

E  6 

15 

+°  83 

t  4 

15 

—4  4iz 

L9 

15 

—  4  53d 

t-IO 

TABLE  545.— Planetary  Data. 


Body. 

Reciprocals 
of  masses. 

Mean  distance 
from  the  sun. 
K  m  . 

Sidereal 
period. 
Mean  days. 

Equatorial 
diameter. 
Km. 

Inclination 
of  orbit. 

Mean 
density. 

HoO  =  I 

Gravity 
at 
surface. 

Sun 

I. 

I39H07 

1.42 

28.0 

Mercury 

60000OO. 

S8xio« 

87-97 

4842 

7°.  003 

5-6l 

0.4 

Venus 

408OOO. 

108' 

244.70 

I2I9I 

3-393 

5-16 

0.9 

Earth  * 

329390. 

149' 

365-26 

12757 

5.52 

I.OO 

Mars 

3093500. 

228  ' 

686.98 

6784 

1.850 

3-95 

0.4 

Jupiter 

1047.35 

778' 

4332.59 

142745 

1.308 

2.7 

Saturn 
Uranus 

3501.6 
22869. 

1426' 
2869' 

10759.20 
30685.93 

120798 
49093 

2.492 
0-773 

I  '-3§ 

1.2 
1.0 

Neptune 

19700. 

4495  " 

60187.64 

52999 

1.778 

1-30 

1.0 

Moon 

t  81.45 

38  x  io4 

27.32 

3476 

5-145 

3-36 

0.17 

1 

*Earth  and  moon,  t  Relative  to  earth.  Inclination  of  axes:  Sun  7°. 25;  Earth  23°.45;  Mars  24*.6; 
Tupiters'.i;  Saturn  26°. 8;  Neptune  27°.2.  Others  doubtful.  Approximate  rates  if  rotation:  SunaSid; 
Moon27jd;  Mercury  88d;  Venus  225d;  Mars  24""  37"' ;  Jupiter  9h  55'"  ;  Saturn  ioh  I4m. 

SMITHSONIAN  TABLE*. 


TABLES  646-648. 
ASTRONOMICAL  DATA. 


417 


TABLE  546.  —  Numbers  and  Equivalent  Light  of  the  Stars. 

The  total  of  starlight  is  a  sensible  but  very  small  amount.  This  table,  taken  from  a  paper  by  Chapman,  shows 
that  up  to  the  2oth  magnitude  the  total  light  emitted  is  equivalent  to  687  ist-magnitude  stars,  equal  to  about  the 
hundredth  rnrt  of  full  moonlight.  If  all  the  remaining  stars  are  included,  following  the  formula,  the  equivalent  addi- 
tion would  be  only  three  more  ist-magnitude  stars.  The  summation  leaves  off  at  a  point  whfcre  each  additional  magni- 
tude is  adding  more  stars  than  the  last.  But,  according  to  the  formula,  between  the  23d  and  24th  magnitudes  there 
is  a  turning  point,  after  which  each  new  magnitude  adds  less  than  before.  The  actual  counts  have  been  carried  so 
near  this  turning  point  that  there  is  no  reasonable  doubt  of  its  existence.  Given  its  existence,  the  number  of  stars  is 
probably  finite,  a  conclusion  open  to  very  little  doubt.  All  the  indications  of  the  earlier  terms  must  be  misleading  if 
the  margin  between  i  and  2  thousand  millions  is  not  enough  to  cover  the  whole.  (Census  of  the  Sky,  Sampson,  Observ- 
atory, 1915-) 


Equivalent 

Equivalent 

Magnitude, 
m 

Number. 

number 
of  ist- 
magnitude 

Totals  to 
magnitude, 
m 

Magnitude, 
m 

Number. 

number 
of  ist- 
magnitude 

Totals  to 
magnitude, 
m 

stars. 

stars. 

-1.6.  ... 

Sirius 

ii 

9.0-10.0  

174,000 

69 

380 

6 



10  o—  ii  o  . 

426  ooo 

68 

448 

II    O—  12    O 

60 

508 

o.o-i.o.  .  .  . 

8 

14 

33 

12.0-13.0  

2,020,000 

Si 

559 

1.0-2.0.  .  .  . 
2  .  O~3  .  0  .... 

27 
73 

17 
18 

So 
68 

13.0-14.0  
14.0-15.0  

3,960,000 
7,820,000 

40 

630 

3.0-4.0.  .  .  . 

189 

19 

87 

15.0-16.0  

14,040,000 

22 

652 

4-0-5.0.... 

650 

26 

H3 

16.0-17.0  

25,400,000 

16 

668 

5  .  0-6  .  o  .... 

2,200 

35 

148 

17.0-18.0  

38,400,000 

10 

678 

6  .  0-7  .  o  .... 

6,600 

42 

190 

18.0-19.0  

54,600,000 

6 

684 

56 

246 

76,000,000 

3 

687 

8  .  0-9  .  o  .... 

65,000 

65 

All  stars  fainter  than  20.0 

3 

690 

TABLE  547.  -  Albedos. 

The  albedo,  according  to  Bond,  is  defined  as  follows:  "Let  a  sphere  5  be  exposed  to  parallel  light.  Then  its  Albedo 
is  the  ratio  of.  the  whole  amount  reflected  from  S  to  the  whole  amount  of  light  incident  on  it."  In  the  following  table, 
m  =  the  stellar  magnitude  at  mean  opposition;  g  =  magnitude  it  would  have  at  full  phase  and  unit  distance  from 
earth  and  sun;  ff  =  assumed  mean  semi-diameter  at  unit  distance;  p  =  ratio  of  observed  brightness  at  full  phase  to 


that  of  a  flat  disk  of  same  size  and  same  position,  illuminated  and  viewed  normally  and  reflecting  all  the  incident  light 
according  to  Lambert's  law;   g  depends  on  law  of  variation  of  light  with  phase;   albedo  =  pq.    Russell,  Astrophysical 
Journal,  43,  p.  173,  1916. 
Albedo  of  the  earth:  A  reduction  of  Very's  observations  by  Russell  gives  0.45  in  close  agreement  with  the  recent 
value  of  Aldrich  of  0.43  (see  Aldrich,  Smithsonian  Misc.  Collections,  69,  1919). 

Object. 

m 

g 

ff 

P 

q 

Visual 
albedo. 

Color 
index. 

Photo- 
graphic 
albedo. 

Moon  ....    
Mercury  

Venus      

-i    -55 
-    -94 

—     .12 

—    -77 
-    -85 
-   .29 
+0.89 
+5-74 
+7-65 

+0.40 
-0.88 
—0.06 
-4.06 
-1.36 
-8.99 
-8.67 
-6.98 
-7.06 

2.40" 
3-45 
3-45 
8-55 
4.67 
95-23 
77-95 
36.0 
34-5 

0.105 
.164 
.077 
.492 
•  139 
•  375 
.420 
.42 
•49 

0.694 
0.42 
0.72 
.20 
.  ii 
•  S- 
•S: 
•5: 
-S: 

0.073 
.069 
•  055 
•  59 
•'54 
•56: 
.63: 
-63: 
•73: 

+1.18 

+0.78 
+1.38 
+0.50 

+  I.I2 

0.051 

.60 
.090 
•  73  = 
0.47: 

Jupiter  
Saturn  
Uranus  
Neptune  

TABLE  548.  —  Duration  of  Sunshine. 


Declination 

-23°  27' 

—  15° 

—  10° 

—  5° 

0° 

+5° 

+10° 

+15° 

+  20° 

+  23°  27' 

ot  sun: 
approx.  date: 

Dec.  22. 

Feb.  9 

Nov.  3. 

Feb.  23 
Oct.  19. 

Mar.  8 
Oct.  6. 

Mar.  21 
Sept.  23- 

Sept.  10 
Apr.  3. 

Apr.  1  6 
Aug.  28. 

May  i 
Aug.  13- 

May  20 
Jan.  24. 

June  21 

Latitude. 

h  m 

h  m 

h  m 

h  m 

h  m 

h  m 

h  m 

h  m 

h  m 

h  m 

o° 

12  07 

12  07 

12  07 

12  07 

12  07 

12  07 

12  07 

12  07 

12  07 

12  07 

II  32 

ii  45 

ii  53 

12  00 

12  07 

12  14 

12  21 

12  29 

12  36 

12  43 

20° 

10  55 

II  22 

ii  38 

ii  53 

12  07 

12  22 

12  37 

12  52 

13  08 

13  20 

30° 

10  13 

10  57 

II  21 

ii  44 

12  08 

12  31 

12  55 

13  19 

13  46 

14  05 

40° 

9  19 

10  25 

II  01 

ii  35 

12  O9 

12  43 

13  17 

13  53 

14  32 

15  01 

50° 
55° 

8  04 
7  09 

9  43 

9  12 

10  34 
10  15 

ii  23 
ii  14 

12  10 
12  12 

12  58 
13  09 

13  48 
14  09 

14  40 
IS  13 

15  38 
16  26 

16  23 
17  23 

60° 

5  52 

8  34 

9  52 

ii  04 

12  13 

13  23 

14  36 

IS  57 

17  31 

18  52 

6=;° 

3  34 

7  39 

9  19 

10  50 

12  16 

13  43 

IS  IS 

17  oi 

19  19 

22  03 

70° 

6  10 

8  31 

10  29 

12  19 

14  II 

16  15 

18  50 

— 



75° 

— 

2  37 

7  04 

9  '55 

12  26 

15  oo 

1  8  05 

— 

— 



80° 

3  10 

8  46 

12  38 

16  44 



For  more  extensive  table,  see  Smithsonian  Meteorological  Tables. 


SMITHSONIAN  TABLES- 


TABLES  649-552.-SOLAR  ENERGY. 
TABLE  649. -The  Solar  Constant. 

Solar  constant  (amount  of  energy  falling  at  normal  incidence  on  one  square  centimeter  per 
minute  on  body  at  earth's  mean  distance)  =  1.932  calories  ==  mean  696  determinations  1902—12. 
Apparently  subject  to  variations,  usually  within  the  range  of  7  per  cent,  and  occurring  irregularly 
in  periods  of  a  week  qr  ten  days. 

Computed  effective  temperature  of  the  sun :  from  form  of  black-body  curves,  6000°  to  7000° 
Absolute  ;  from  Amax.  =  2930  and  max.  =  0.470/11, 6230° ;  from  total  radiation,  J  =  76.8xio-ia  X  T4, 
58300. 

TABLE  650.  —  Solar  spectrum  energy  (arbitrary  units)  and  its  transmission  by  the  earth's  atmosphere. 
Values  computed  from  eni=  e0ain,  where  em  is  the  intensity  of  solar  energy  after  transmission: 
through  a  mass  of  air  m ;  m  is  unity  when  the  sun  is  in  the  zenith,  and  approximately  =  sec. 
zenith  distance  for  other  positions  (see  table  5 5$) ',  e0=the  energy  which  would  have  been  ob- 
served had  there  been  no  absorbing  atmosphere;  a  is  the  fractional  amount  observed  when  the 
sun  is  in  the  zenith. 


Transmission  coef- 

Intensity Solar  Energy.    A{jb^ry 

ficients,  a. 

M 

>. 

r 

j 

*  *** 

i'l 

Mount  Wilson. 

Washington. 

£ 

if 

§  •- 

=  '•=       u  "  S 

~.  " 

2 

s^ 

c  ~ 

0 

m  —  i 

m  =  i 

2 

4 

6 

m=  i 

2 

3 

4 

6 

0.30 



(.460) 

(.550) 



54 

30 

25 

II 

2 

i 

_ 









•32 

— 

.520 

6*5 

in 

68 

58 

30 

B 

2 

— 



— 

— 

— 

•34 

— 

.580 

.692 

232 

160 

'35 

78 

26 

9 

— 



— 

— 

— 

.36 
•38 

(.380) 

.635 

.676 

£ 

.562 

302 
354 

278 

192 

239 

122 
162 

49 

74 

20 

34 

i34 

51 

'9 

7 

3 

.40 
.46 

.560 
.090 

.729    .809 
.83--    .887 

.768 
.829 

414 

618 

III 

302 

2  2O 
428 

117 
206 

62 
205 

232 
426 

130 
294 

73 
203 

41 
140 

67 

•  SO 

.733  .862  .919 

.850 

606 

557 

522 

450 

334 

248 

441 

323 

237 

17.4 

94 

.60 

.779  .900  .940 

.866 

504 

474 

454 

409 

331 

268 

393 

306 

238 

185 

112 

.     -70 

•858  .950  .964 

•903 

364 

35i 

346 

329 

297 

268 

312 

268 

230 

197 

J45 

.80 

.886    ;    .970        .976 

•915 

266 

260 

2S8 

250 

235 

221 

236 

209 

185 

,64 

145 

1.  00 

.922        .980 

•975 

.941 

1  66 

162 

163 

160 

154 

147 

J53 

141 

130 

I2O 

1  02 

1.50 

.938       .976* 

.965 

.961 

63 

61 

61* 

60* 

,S7* 

ss* 

59 

55 

52 

49 

43 

2.00 

.912       .970* 

•932 

.940 

25 

23 

24* 

23* 

21* 

19* 

23 

21 

17 

| 

Transmission  coefficients  are  for  period  when  there  was  apparently  no  volcanic  dust  in  the  air. 
*  Possibly  too  high  because  of  increased  humidity  towards  noon. 

TABLE  551.  —  The  intensity  of  Solar  Radiation  in  different  sections  of  the  spectrum,  ultra-violet,  visual 

infra-red.    Calories. 


Wave-length. 

Mount  Whitney. 

Mount  Wilson. 

Washington. 

M            /* 

m=o 

m=  i 

2 

3 

4 

m=  i 

2 

3 

4 

m  =  i 

2 

3 

4 

o.oo   to  0.45 

•31 

•25 

.19 

.16 

•13 

•23 

.16 

.12 

.09 

•13 

.06 

.04 

.02 

0.45   to  0.70 
0.70    to        oo 
o.oo   to       oo 

•7' 
.91 
i-93 

.67 

3 

.62 
-85 

1.66 

t 

1.56 

•54 
.80 
1.47 

•65 
.69 
i-57 

11 

I.42 

£ 

1.28 

•45 
•63 
1.17 

« 

'•35 

.40 
.62 

1.08 

•3° 
•57 
.90 

•24 
•53 
•79 

TABLE   552.  -  Distribution  of  brightness  (Radiation)  over  the  Solar  Disk. 
(These  observations  extend  over  only  a  small  portion  of  a  sun-spot  cycle.) 


Wave- 
length. 

M 

0323 

0.386 

0-433 

0.456 

0.481 

M 
0.501 

0-534 

0.604 

0.670 

M 
0.699 

0.866 

I.03I 

1.225 

M 
1-655 

2.097 

3 

0.00 

0.40 

13 

338 
312 

456 
423 

486 

5" 

483 

489 
463 

463 
440 

399 

382 

333 
320 

307 
295 

169 

III 

108 

77.6 
75-7 

39-5 
38-9 

14.0 
13-8 

1 

0.55 
0.65 

120 
112 

289 
267 

395 
368 

455 
428 

456 
430 

437 
414 

4'7 
396 

365 
348 

308 
295 

284 
273 

,63 
'59 

103 

73-8 
72.2 

38-2 
37-6 

13-6 
13-4 

I' 

0.75 
0.825 

99 
86 

240 
214 

333 
296 

39° 
35' 

394 
358 

38o 
347 

366 

337 

326 
304 

281 
262 

258 
243 

152 
'45 

99 
94-5 

69.8 
67.1 

36-7 
35-7 

13-1 

12.8 

1 

0.875 

0.92 

f 

64 

1  88 
163 

266 
233 

3'7 
277 

324 
290 

323 
286 

3'2 

281 

284 
259 

247 
227 

229 

212 

•38 

If5 

64.7 
61.6 

34-7 
33-6 

12.5 

12.2 

fc  1  0.95 

49 

141 

205 

242 

255 

254 

254 

237 

210 

195 

122 

Si 

58.7 

32-3 

II.7 

Taken  from  vols.  II  and  III  and  unpublished  data  of  the  Astrophysical  Observatory  of  the 
Smithsonian  Institution.   Schwartzchild  and  Villiger :  Astrophysical  Journal,  23,  1906. 
SMITHSONIAN  TABLES. 


TABLES   553-556.  419 

ATMOSPHERIC    TRANSPARENCY    AND    SOLAR    RADIATION. 

TABLE  553.— Transmission  of  Radiation  Through  Moist  and  Dry  Air. 

This  table  gives  the  wave-length,  A;  a  the  transmission  of  radiation  by  dry  air  above  Mount 
Wilson  (altitude  =  1730  m.  barometer,  620  mm.)  for  a  body  in  the  zenith  ;  finally  a  correction  fac- 
tor, aw,  due  to  such  a  quantity  of  aqueous  vapor  in  the  air  that  if  condensed  it  would  form  a  layer 
i  cm.  thick.  Except  in  the  bands  of  selective  absorption  due  to  the  air,  a  agrees  very  closely  with 
what  would  be  expected  from  purely  molecular  scattering.  aw  is  very  much  smaller  than  would  be 
correspondingly  expected,  due  possibly  to  the  formation  of  ions  by  the  ultra-violet  light  from  the 
sun.  The  transmission  varies  from  day  to  day.  However,  values  for  clear  days  computed  as  fol- 
lows agree  within  a  per  cent  or  two  of  those  observed  when  the  altitude  of  the  place  is  such  that 
the  effect  clue  to  dust  may  be  neglected,  e.g.  for  altitudes  greater  than  1000  meters.  If  B=s 

the  barometric  pressure  in  mm.,  w,  the  amount  of  precipitable  water  in  cm.,  then  aB  =  a*20  a*,  w  is 
best  determined  spectroscopically  (Astrophysical  Journal,  35,  p.  149,  1912,37,  p.  359,  1913)  other- 
wise by  formula  derived  from  Ilann,  w=  2-3ewio  2200°,  ew  being  the  vapor  pressure  in  cm.  at  the 
station,  h,  the  altitude  in  meters.  See  Table  377  for  long-wave  transmission. 


A  (/*) 
a 
a\v 

.360 
(.660) 
•95° 

•384 

•713 
.960 

413 
.783 
•965 

•452 
.840 
.967 

•5°3 
&s 

•977 

I 

•574 
•905 
•974 

.624 
.929 

.978 

.653 
•938 

.720 
.970 
.988 

.986 
.986 
.990 

1.74 
.990 
.990 

•  Fowle,  Astrophysical  Journal,  38,  1913. 

TABLE  554.  -Brightness  of  (radiation  from)  Sky  at  Mt.  Wilson  (1730  m.)  and  Flint  Island  (sea  level). 


Zenith  dist.  of  zone  .....            ;  o-ii;0 

15-35° 

35-50° 

So-  60° 

60-70° 

70-80° 

80-90°                Sun. 

i  o8  X  mean  ratio  sky/sun    Mt.  Wilson      . 
Flint  Island     . 

15oo* 
IJ5 

400 

122 

520 
128 

610 

150 

660 

700 

210 

720 
46o  ; 

Ditto  X  area  of  zone           Mt  Wilson 

51.0 

S8.8 

91-5 

87.2 

104.3 

117.6 

125.3       -    '     636 

Flint  Island     . 

3-9 

17.9 

22.5 

21.4 

29.2 

35-3 

80.0 

210 

Altitude  of  sun    

_ 

_ 

5° 

15° 

25° 

35° 

47*° 

65°  ;  82*° 

Sun's  brightness,  cal.  per  cm.2  per  min.    . 

_ 

- 

•533 

.900 

1-233 

1.358 

«.4i3 

T)ittn  rm  linriyontal  surface 

780 

Mean  brightness  on  normal  surface  sky  X  io8/sun 
Total  sky  radiation  on  horizontal  cal.  per  cm.2  • 

- 

- 

423 

403 

•385 

365 

346 

320          310 

per  m.         ....... 

— 

_ 

.056 

.  I  IO 

.162 

.189 

.205       .226       .240 

Total  sun  -f  sky,  ditto         

™ 

.102 

•343 

.686 

.969 

1.246 

1.581  i  1.747 

*  Includes  allowance  for  bright  region  near  sun.    For  the  dates  upon  which  the  observation  of  the  upper  portion  of 
table  were  taken,  the  mean  ratios  of  total  radiation  sky/sun,  for  equal  angular  areas,  at  normal  incidence,  at  the  island 
and  on  the  mountain,  respectively,  were  636  X  10—  &  and  210  X  10—  8,  on  a  horizontal  surface,  305  X  10— *>  and  77  > 
for  the  whole  sky,  at  normal  incidence,  0.57  and  0.20;  on  a  horizontal  surface  0.27  and  0.07.     Annals  of  the  Astro- 
physical  Observatory  of  the  Smithsonian  Institution,  vols.  II  and  III,  and  unpublished  researches  (Abbot). 

TABLE  555.  -Relative  Distribution  In  Normal  Spectrum  of  Sunlight  and  Sky-light  at  Mount  Wilson. 

Zenith  distance  about  50°. 


^ 

ft 

)" 

M           H 

/* 

C 

D 

b 

F 

Place  in  Spectrum 

0.422 

0-457 

0.491 

0.566 

0.614 

0.660 

Intensity  Sunlight 

186 

227 

21  F 

191 

166 

Intensity  Sky-light 

1194 

986 

701 

395 

23  I 

174 

Ratio  at  Mt.  Wilson 

642 

4^5 

309 

187 

121 

105 

102 

'43 

Ratio  computed  by  Rayleigh 
Ratio  observed  by  Kayleigh 

- 

- 

- 

102 

102 

| 

258 

3S 

TABLE  556.  -Air  Masses. 

See  Table  174  for  definition.  Besides  values  derived  from  the  pure  secant  formula,  the  tuHe 
contains  those  derived  from  various  other  more  complex  formula,  taking  into  account  the  curva- 
ture of  the  earth,  refraction,  etc.  The  most  recent  is  that  of  Bemporad. 


Zenith   Dist. 

0° 

20° 

40° 

60° 

70° 

75° 

80° 

85° 

88° 

Secant 

1.00 

1.064 

1.305 

2.000 

2.924 

3.864 

5-76 

11.47 

P'orbes 

I.OO 

1.065 

1.306 

T-995 

2.902       vs°o 

5-57 

IO.22 

I8.9 

Bouguer 
Laplace 
Bemporad 

I.OO 
I.OO 
I.OO 

1.064 

'•3°5 

1.990 

'•993 
1.995 

2.900 
2.899 
2.904 

3.805 

5.56            10.20 
5.56             10.20 
5.60      '      IO-39 

19.0 
19.8 

The  Laplace  and  Bemporad  values,  Lindholm,  Nova  Acta  R.  Soc.  Upsal.  3,  1913  ;  the  others,  Radat 
metric,  1877. 
SMITHSONIAN  TABLES. 


420 


TABLES  557-558. 
RELATIVE   INTENSITY  OF  SOLAR   RADIATION, 


TABLE  557.  —  Mean  Intensity ./  lor  24  hours  of  solar  radiation  on  a  horizontal  surface  at  the  top  of  the 

atmosphere  and  the  solar  radiation  A  ,  In  terms  of  the  solar  radiation,    t  , 

at  earth's  mean  distance  from  the  son. 


RELATIVE  MEAN  VERTICAL  INTENSITY  (~7~r 

Motion  of 

°' 

the  sun 

^ 

Date. 

in 

LATITUDE   NORTH. 

—  . 

longi- 

AQ 

tude. 

0° 

10° 

2O 

30° 

40° 

50^ 

00° 

70° 

80° 

90° 

Jan. 

0 

0.99 

0.303 

0.265 

O.22O 

0.169 

0.117 

0.066 

0.018 

I.O335 

Feb. 

31-54 

.312 

.282 

.244 

.200 

.150 

.100 

.048 

0.006 

I.O288 

Mar.      \      59.14 

.320 

•303 

.279 

•245 

.204 

.158 

.108 

.056 

0.013 

I.OI73 

Apr. 

89.70 

•3'7 

•3'9 

.312 

•295 

.269 

•235 

•195 

.148 

.101 

0.082 

1.0009 

May 

119.29 

•303 

.318 

•330 

•329 

.320 

.302 

.278 

•253 

.255 

.259 

0.(>S4I 

flint 

149.82 

.287 

•31.  s 

•334 

•345 

•349 

•345 

•337 

•344 

.360 

.366 

O.97I4 

July 

179-39 

•283 

.312 

•333 

•347 

•352 

.351 

•345 

.356 

•373 

•379 

0.9666 

Aug. 

209.94 

.294 

.316 

•33° 

•334 

•330 

.318 

.300 

.282 

•295 

.300 

O.97O9 

Sept.  i 

240.50 

.310 

.318 

.316 

•305 

.285 

•256 

.220 

.180 

•139 

.140 

0.9828 

Oct. 

270.07 

•3*7 

.308 

.289 

.261 

.225 

.183 

.135 

.084 

.obS 

i 

0-9995 

Now. 

300.63 

.312 

.286 

•251 

.211 

.164 

.114 

.063 

.018 

I.OI64 

Dec. 

330.19 

•3°4 

.267 

.224 

•175 

.124 

.072 

.024 

1.0288 

Year.... 

0.305 

0.301 

0.289 

0.268 

0.241 

0.209 

0-173 

0.144 

0-133 

0.126 

TABLE  558,  —  Mean  Monthly  and  Yearly  Temperatures. 

Mean  temperatures  of  a  few  selected  American  stations,  also  of  a  station  of  very  high,  two  of  very  low  temperature, 
and  one  of  very  great  and  one  of  very  small  range  of  temperature. 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Year. 

i  Hebron-Rama  (Labr.) 

—  20.9 

-15-6 

-  6.9 

+    0.2 

+  4-S 

+  7-6 

+  8.0 

. 

—  0.8 

—   6.2 

—16.2 

—  5-2 

2  Winnipeg  (Canada)     . 

—21.6 

—  18.8 

II.  0 

+   1.9 

+  10.9 

+  17.1 

+  18.9 

+  17.6 

--ii.  6 

+  4-1 

-7.6 

—  '5-7 

+  0.6 

3  Montreal 

—  10.9 

—  9.1 

—  4-3 

+   4-8 

+  12.6+18.3 

+20.  S 

+  19-1 

--14.7+  7.8 

—    0.2 

—  7.1 

+  5-5 

4  Boston 

—   2.8 

—    2.2 

+  1.2 

f  7-1 

+13.6+19.1 

+21.8 

+20.6 

--16.9  +  11.1 

+  4-8 

—  °-5 

+  9-2 

5  Chicago 

-4-8 

—   2.9 

+    1-2 

4-7-9 

+  I3-4  +  I9-7 

+22.2 

+21.6 

--17.9+,,.! 

+  1-6 

—  i-5 

+  9.i 

6  Denver 

2.  I 

-f-  o.i 

+  1-8 

+  8.3 

+13.6+19.1 

+  22.1 

+  21.2 

+  16.6+10.3 

+  3-3 

0.0+  9.7 

7  Washington 

+   0.7 

+    2.1 

+    S2 

+11.7 

+  I7-7 

+22.9 

+  24.9 

+21-7 

+  19-9  +'3-4i+  6.9 

+  2.3+12.6 

8  Pikes  Peak 

—  l6.4 

—  IS.6 

—  13-4 

—10.4 

—  5-1 

+  0.4 

+  4-5 

+  3-6 

—  0.3  —  5.8—11.8 

—14.41—  7.1 

g  St.  Louis 

—  0.8 

+  i.7 

+    6.2 

+H.4 

+18.8 

+24.0 

+26.0 

+24.9 

+20.8  +14.2'+  6.4 

+  2.0+13.1 

10  San  Francisco 

-j-io.  i 

+10.9 

+  12.0 

+  12.6 

4-IJ.7 

+M-7 

+  .4-6 

+  14.8  +158  +  15-2  +  .  3.5 

+  10.8+13.2 

ii  Yuma   . 
12  New  Orleans 

+12.3 

-}-I2.  I 

+  u-9 

+I4-S 

+  18.1 
+  .6.7 

+21.0 

4-20.6 

fas-i 
+23-7 

+29.4 
+26.8 

+33-1 

+27.9 

+32-6 
+275 

+29.1  +22.8+16.6 
+25.7  +  21.01  +  15.9 

+  13.3+22.3 
+  13.1  +20.4 

13  Massaua 

+2S.6 

+26.0 

+27.1 

+29.0 

+.V.  T 

+11.  S 

+34-8 

+34-7 

+33-3  +31-71+29.0 

+27-0+30.3 

14  Ft.  Conger  (Greenl'd) 

—39-° 

—40.1 

—33-5 

—25.3 

—  10.0 

+  0.4 

+    2.8 

+    1.0 

—  9.0 

—22.7—30.9 

—33-4 

20.0 

15  Werchojansk 
16  Batavia 

-51.0 
+25-3 

—45-3 
+254 

—32.5 
+25-8 

—13.7 
+26.3 

+    2.0 
+26.4 

+12.3 
+26.0 

+  '5-5 
+25-7 

+  10.  1 

+25.9 

+  2.5—  iso1—  37.8 
+26.3+26.4+26.2 

—  47.0  —  16.7 
+25.6+25.9 

Lat.,  Long.,  Alt.  respectively:  (i)  +58°.5,63°.o  W,  — ;  (2)  +49.9,  97-r  W,  233m.;  (3)  +45.5,  73-6  W,  57m. ; 
(4)  -[-42.3,71.1  W)38m.;  (5)  +  41  9,  87.6  W,  25im.;  (6)  +39.7,  105.0  W,  i6i3m.;  (7)  +38.9,  77-o  W,  34m.;  (8) 
+  38.8,  105.0  W,  43o8m.  ;  (9)  +  38.6,  00.2  W,  1731".;  (10)  +37.8,  122.5  W,  47m.;  (n)+32.7,  114.6  W,  43m. ; 
(12)  +30.0,  90.1  W,  i6m.;  (13)  +  15.6,  37.5  E,  901.5  (14) +81.7,  64.7  W.,—;  (15) +67.6,  133.8  E,  i4om. ;  (16)  — 6.2, 
106.8  E,  7m. 

Taken  from  Hann's  Lehrbuch  der  Meteorologie,  2!nd  edition,  which  see  for  further  data. 
Note:     Highest  recorded  temperature  in  world  =  57°  C  in  Death  Valley,  California,  July  10,  1913. 

Lowest  recorded  temperature  in  world  =  -68°  C  at  Verkhoyansk,  Feb.  1892. 
SMITHSONIAN  TABLES. 


TABLES  559-561. 

THE   EARTH'S  ATMOSPHERE. 
TABLE  559.  -    Miscellaneous  Data.    Variation  with  Latitude. 


421 


Optical  ev.dence  of  atmosphere's  extent:  twilight  63  km,  luminous  clouds  83,  meteors  200,  aurora  44-360.  Jeans 
•computes  a  density  at  170  km  of  2  X  io13  molecules  per  cm3,  nearly  all  H  (5%  He);  at  810  km,  3  X  10"  molecule* 
per  cm3  abnost  all  H.  When  in  equilibrium,  each  gas  forms  an  atmosphere  whose  density  decrease  with  altitude  is 
independent  of  the  other  components  (Dalton's  law,  HzO  vapor  does  not).  The  lighter  the  gas,  the  smaller  the  decrease 
rate.  A  homogeneous  atmosphere,  76  cm  pressure  at  sea-level,  of  sea-level  density,  would  be  7091  m  high.  Average 
sea-level  barometer  is  74  cm;  corresponding  homogeneous  atmosphere  (truncated  cone)  7790  m,  weighs  (base,  m») 
10,120  kg;  this  times  earth's  area  is  52  X  io14  metric  tons  or  io~6  of  earth's  mass.  The  percentage  by  vol.  and  the 
partial  pressures  of  the  dry-air  components  at  sea-level  are:  Nj,  78.03,  593.02  mm;  Oi,  20.99,  J59-52J  A,  0.94,  7.144; 
COj,  0.03,  0.228;  H2,  o.oi,  0.076;  Ne,  p.ooi2,  0.009;  He,  0.0004,  0.003  (Hann).  The  following  table  gives  the  varia- 
tion of  the  mean  composition  of  moist  air  with  the  latitude  (Hann). 


N2  75-99 
77-32 
77.87 

O2  20.44 
20.80 
20.94 

A,  0.92 
0.94 
Q-94 

HiO  2.63 
0.92 

0.22 

COl   0.02 
O.O2 
O.O3 

so°N  
70°  N  

TABLE  560.  —  Variation  of  Percentage  Composition  with  Altitude  (Humphreys). 

Computed  on  assumptions:    sea -level  temperature  11°  C;    temperature  uniformly  decreasing  6°  per  km  up  to 
ii  km,  from  there  constant  with  elevation  at  —55°.     J.  Franklin  Inst.  184,  p.  388,  1917. 


Height, 
km 

Argon. 

Nitrogen. 

Water 
vapor. 

Oxygen. 

Carbon 
dioxide. 

Hydrogen. 

Helium. 

Total 

pressure,  mm 

140 

O.OI 

99  15 

0.84 

0.0040 

120 

— 

o.  19 

— 

— 

— 

98.74 

1.07 

0.0052 

100 

— 

2.9S 

0.05 

O.II 

— 

95.58 

1.31 

0.0067 

80 

— 

32-18 

0.17 

1.85 

— 

64.70 

I.  10 

0.0123 

60 

0.03 

81.22 

0.15 

7.69 

— 

10.68 

0.23 

0-0935 

5° 

0.12 

86.78 

O.IO 

io.  17 

— 

2.76 

0.07 

0.403 

40 

O.  22 

86.42 

0.06 

12.  6l 

— 

0.67 

0.02 

1.84 

30 

0-35 

84.26 

0.03 

15.18 

O.OI 

0.16 

O.OI 

8.63 

20 

0-59 

81.24 

0.02 

18.10 

O.OI 

0.04 



40.99 

IS 

0.77 

79-52 

O.OI 

19.66 

0.02 

0.02 



89-66 

II 

0.94 

78.02 

O.OI 

20.99 

O.O3 

O.OI 



168.00 

5 

0-94 

77.89 

0.18 

20.95 

0.03 

O.OI 



405- 

0 

0-93 

77-08 

I.  20 

20.75 

0.03 

O.OI 

760. 

TABLE  561.  —  Variation  of  Temperature,  Pressure  and  Density  with  Altitude. 

Average  data  from  sounding  balloon  flights  (65  for  summer,  52  for  winter  data)  made  at  Trappes  (near  Paris), 
Uccle  (near  Brussels),  Strassburg  and  Munich.    Compiled  by  Humphreys,  16  to  20  m  chiefly  extrapolated. 


Summer. 

Winter. 

Elevation, 
km 

Temp.  °  C 

Pressure, 
mm  of  Hg. 

Density, 
dry  air, 
g/cm3 

Temp.  °  C 

Pressure, 
mm  of  Hg. 

Density, 
dry  air, 
g/cm1 

20.0 

—  51-0 

44.1 

0.000092 

-57-0 

39-5 

0.000085 

19.0 

—51-0 

Si-5 

.000108 

—  57-0 

46-3 

.000100 

18.0 

—51-0 

60.0 

.000126 

-57-0 

54-2 

.000117 

17.0 

—  51-0 

70.0 

.000146 

-57-0 

63-5 

.000137 

16.0 

—  51.0 

81.7 

.000171 

—  57-0 

74-0 

.000160 

15-0 

-51-0 

95-3 

.000199 

-57-0 

87.1 

.000187 

14.0 

-51-0 

in.  i 

.000232 

-57-0 

102.  I 

.000220 

13-0 

—  51.0 

129.  6 

.000270 

-57-o 

"9-5 

.000257 

12.0 

-51.0 

151-2 

.000316 

-57-0 

140.0 

.000301 

II.  0 

-49-5 

176.  2 

.000366 

—  57-0 

164.0 

•000353 

10.  0 

—45-5 

205.1 

.000419 

-54-5 

192.0 

.000408 

9.0 

-37-8 

237.8 

.000470 

-49-5 

224.1 

.000466 

8.0 

—  29.7 

274-3 

.000524 

-43-0 

260.6 

.000526 

7-0 

—  22.1 

314.9 

.  000583 

-35-4 

301.6 

.000590 

6.0 

—  IS-I 

360.2 

.000649 

-28.1 

347-5 

.000659 

5-0 

-8.9 

410.6 

.000722 

—  21.2 

398.7 

.000735 

4.0 

—3-0 

466.6 

.  000803 

-15-0 

455-9 

.000821 

3-0 

+  2.4 

528.9 

.000892 

-9-3 

5I9.7 

.000915 

2.5 

+5-0 

562.5 

.000942 

-6.7 

554-3 

.000067 

2.  O 

+7-5 

598.0 

.000990 

-4-7 

590.8 

.001023 

i-5 

+  10.0 

635.4 

.001043 

-3-0 

629  6 

.001083 

1.0 

+  12.0 

674.8 

.001100 

—  1-3 

670.6 

.001146 

0.5 

+  14-5 

716.3 

.001157 

0.0 

71-4.0 

.001215 

0.0 

+  15-7 

760.0 

.001223 

+0.7 

760.0 

.001290 

760  mm  =  29.921  in.  =  1013.3  millibars,     i  mm  =  1.33322387  millibars,     i  bar  =  1,000,000  dynes;    this  value, 
sanctioned  by  International  Meteorological  Conferences,  is  1,000,000  times  that  sometimes  used  by  physicists. 
SMITHSONIAN  TABLES. 


422 


TABLES  562  563. 

TERRESTRIAL  TEMPERATURES- 
TABLE  562.  —  Temperature  Variation  over  Earth's  Surface  (Hann). 


Temperatures  °  C 

Mean     !     Land 

Jan. 

Apr. 

July. 

Oct. 

Year. 

Range. 

temp. 

North  pole 

-41.0 

—  28.0 

—  i.o 

-24.0 

—  22.7 

10.0 

—  i.  7 



+80° 

-32.2 

—  22.7 

+  2.0 

-19.1 

-17.1 

34-2 

—  I    7 

20 

70 

00 

-26.3 
-16.1 

-14.0. 

-2.8 

7-3 
14.1 

—9-3 
+0.3 

—  10.7 
—  i.i 

33-6 

30.2 

+0.7 
4.8 

e 

50 

-7.2 

+5-2 

17.9 

6.9 

+5-8 

25-1 

79 

58 

40 

+5-5 

I3-I 

24.0 

15-  7 

14.1 

18.3 

14.1 

45 

30 
20 

14.7 
21.9 

20.1 

25.2 

27.3 
28.0 

21.8 

26.4 

20.4 
25-3 

12.6 

6.1 

21-3 
25-4 

43-5 
31-5 

+  10 

25.8 

27.2 

27.0 

26.9 

26.8 

1.4 

27.2 

24 

Equator 

26.5 

26.6 

25-7 

26.5 

26.3 

0.9 

27.1 

22 

—  10 

26.4 

25.9 

23.0 

25-7 

25-5 

3-4 

25-8 

20 

20 

25-3 

24.0 

19.8 

22.8 

23-0 

5-5 

24.0 

24 

30 

21.6 

18.7 

14-5 

18.0 

18.4 

7-1 

19-5 

20 

40 

iS-4 

12.5 

8.8 

ii.  7 

ix.  9 

6.6 

13-3 

4 

50 

8.4 

5-4 

3-o 

4.8 

5-4 

5-4 

+6.4 

2 

60 

3-2 

— 

-9-3 

— 

—3-2 

"•S 

o.o 

0 

70 

—  I.  2 

— 

—  21.0 

— 

—  12.0 

19.8 

—  1.3 

71 

80 
South  pole 

(-4-3) 

(-6.0) 

— 

(-28.7) 
(-33-0) 

— 

(-20.6) 

(-25.0) 

(24.4) 
(27.0) 



100 

(100) 

TABLE  563.  —  Temperature  Variation  with  Depth  (Land  and  Ocean), 

Table  illustrates  temperature  changes  underground  at  moderate  depths  due  to  surface  warming  (read  from  plot 
for  Tiflis,  Lehrbuch  der  Meteorologie,  Hann  and  Siiring,  1915).  Below  20-30  m  (nearer  the  surface  in  tropics)  there 
is  no  annual  variation.  Increase  downwards  at  greater  depths,  0.03  =*=  °  C  per  m  (i°  per  35  m)  1.  c.  At  Pittsburgh, 
1524  m,  49.4°,  .0294  per  m;  Oberschlesien,  2003  m,  70°,  .0294  per  m;  or  W.  Virginia,  2200  m,  70°,  .034°  per  m  (Van 
Orstrand).  Mean  value  outflow  heat  from  earth's  center,  0.00000172  g-cal/cm2/sec.  or  54  g-cal/cm2/year  (39  Laby). 
Open  ocean  temperatures:  Greatest  mean  annual  range  (Schott)  40°  N,  4.2°  C;  30°  S,  5.1°;  but  io*N,  only  2.2°; 
50°  S,  2.9°.  Mean  surface  temp,  whole  ocean  (Kriimmel)  17.4°;  all  depths,  3.9°.  Below  i  km  nearly  isothermal  with 
depth.  In  tropics,  surface  28°;  at  183  m,  11°,  80%  all  water  less  than  4.4°.  Deep-sea  (bottom)  temps,  range  —0.5°  to 
+2.6°.  Soundings  in  S.  Atlantic:  o  km,  18.9°;  .25  km,  15°;  .5  km,  8.3°;  i  km,  3.3°;  3  km,  1.7°;  4.5  km,  0.6°. 


Temperature,  centigrade. 

Depth, 

m 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

0 

, 

4 

10 

14 

21 

29 

32 

32 

24 

16 

9 

4 

o-S 

4 

4 

9 

13 

18 

23 

26 

28 

24 

18 

12 

6 

I.O 

6 

6 

8 

12 

15 

20 

24 

26 

23 

18 

14 

IO 

i  .  5 

9 

8 

9 

II 

14 

18 

21 

23 

22 

18 

15 

12 

2.0 

ii 

10 

IO 

II 

16 

19 

21 

21 

18 

16 

14 

3-0 

14 

12 

12 

II 

13 

14 

16 

17 

18 

18 

17 

15 

4.0 

15 

13 

12 

12 

12 

14 

16 

16 

17 

17 

16 

5-0 

IS 

14 

13 

13 

13 

13 

14 

14 

15 

16 

16 

16 

6.0 

15 

14 

14 

14 

14 

14 

14 

14 

14 

IS 

15 

IS 

SMITHSONIAN  TABLES. 


TABLE  564. 

GEOCHEMICAL  DATA. 


423 


Eighty-three  chemical  elements  (86  including  Po,  Ac  and  UrX..,)  are  found  on  the  earth.  Besides  the  eight  occur- 
ring uncombined  as  gases,  23  may  be  found  native,  Sb,  As,  Bi,  L,  Cu,  Au,  Ir,  Fe,  Pb?,  Hg,  Ni,  Os,  Pd,  Pt,  Rh,  Ru, 
Se,  Ag,  S,  Ta  ?,  Te,  Sn  ?,  Zn  ?.  Combined  the  elements  form  about  1000  known  mineral  species.  Rocks  are  in  genera! 
aggregates  of  these  species.  Some  few  (e.  g.,  quartzite,  limestone,  etc.)  consist  of  one  specie.  We  have  some  knowl- 
edge of  the  earth  to  a  depth  of  10  miles.  This  portion  may  be  divided  into  three  parts :  the  innermost  of  crystalline  or 
plutonic  rocks,  the  middle,  of  sedimentary  or  fragmentary  rocks,  the  outer  of  clays,  gravels,  etc.  93%  of  it  is  solid  mat- 
ter, f/,i  liquid,  and  the  atmosphere  amounts  by  weight  to  0.03%  of  it.  Besides  the  9  major  constituents  of  igneous  rock 
(see  7th  col.  of  table)  3  are  notable  by  their  almost  universal  occurrence,  TiO2,  PaOg,  and  MnO.  Bo,  Gl,  and  Sc  are  also 
widely  distributed. 

The  density  of  the  earth  as  a  whole  is  5.52  (Burgess);  continental  surface,  2.67  and  outer  10  miles  of  crust,  2.40 
(Harkness).  Computed  from  average  chernjcal  composition:  outer  ten  miles  as  a  whole,  2.77;  northern  continents 

rvey,    1916;   Washington,  J.   Franklin.    Inst.   190, 


2.73;  southern,  2.76  ;  Atlantic  basin,  2.^3  ;   Pacific  basin,  2.88. 

Data  of  Geochemistry,  Clarke,  Bui.  616,  U.  S.  Geological  Su 


AVERAGE  COMPOSITION  OF  KNOWN  TERRESTRIAL  MATTER. 


Average  composition. 

Average  composition  of  lithosphere. 

Atomic 
number 
and 
element. 

Litho- 
sphere, 
93% 

Hydro- 
sphere, 

7% 

Average 
includ- 
ing 
atmos- 

Igneous 
rocks. 

Compound. 

Igneous 
rocks, 

95% 

Shale, 

4% 

Sand- 
stone, 
o.75% 

Lime- 
stone, 

0.25% 

Weighted 
average. 

phere. 

8  O 

47-33 

85  .  79 

46.43 

47  •  29 

SiOz 

59.09 

58.10 

78.33 

C      IQ 

eg    77 

14  Si 

27.74 

27.77 

28.02 

AhOa  

iS-35 

15-40 

4-77 

O  •  AV 

0.81 

ov  *  /  / 

14.89 

13  Al 
26  Fe 

7-85 
4-50 

— 

8.14 
5.12 

7.96 
4-56 

FC2G-3  

FeO  

3.08 
3.80 

4.02 
2-45 

1.07 
•  30 

•54 

2.69 
3-39 

30  Ca 

3-47 

0.05 

3-63 

3-47 

MgO  

3-49 

2.44 

1.16 

7.  89 

12    Mg 

2.24 

0.14 

2.09 

2.29 

CaO  

5-08 

5-50 

42-57 

4.86 

ii  Na 
19  K 

2.46 
2.46 

1.14 
0.04 

2.85 
2.60 

2.50 
2-47 

Na20  
K20  

3-84 
3-13 

1.30 
3.24 

•45 

•05 
•  33 

3-25 
2.98 

i  H 

0.22 

10.67 

0.127 

o.  16 

H20  

1.14 

5.00 

1.63 

•  77 

2.02 

22    Ti 

0.46 

.629 

.46 

TiO2... 

1.05 

.65 

•25 

.06 

•77 

6  C 

.19 

O.O02 

.027 

•  13 

ZrO2  

0.039 

— 

.02 

17  Cl 

.06 

2.07 

.055 

.063 

C02  

.102 

2.63 

5-03 

41-54 

•70 

35  Br 



0.008 

— 

P2O5  

•30 

•  17 

.08 

•04 

.28 

15  P 

.  12 



-  I3O 

.13 

S. 

•°53 



.09 

.  IO 

16  S 

.  12 

.09 

.052 

.103 

SG-3  

~64 

•07 

•  05 

•  03 

56  Ba 

.08 

.048 

.092 

Cl  

.056 

.02 

.06 

25  Mn 

.08 



.006 

.078 

F  

.078 

— 

— 



•09 

38  Sr 

.02 



.018 

•  033 

BaO  

•055 

•  05 

•05 



.09 

7  N 





SrO  

.022 



.04 

9F1 

.IO 



.077 

.10 

MnO.  . 

.125 

— 

— 

•05 

.09 

etc. 

•50 



.in 

.091 

NiO  

.025 

— 

— 

.025 

CivOa 

.056 

— 

— 



•  05 

VzOs.  '.'.'.'.'.'. 

.032 

— 

— 



.025 

Li20  

.007 

— 

— 

__ 

.  .01 

C  

.80 

•  03 

AVERAGE  COMPOSITION  OF  METEORITES:  The  following  figures  give  in  succession  the  element,  atomic  number 
(bracketed),  and  the  percentage  amount  in  stony  meteorites  (Merrill,  Mem.  Nat.  Acad.  Sc.  14,  p.  28,  1916).  The 
"iron"  meteorites  contain  a  much  larger  percentage  of  iron  and  nickel,  but  there  is  a  tendency  to  believe  that  with 
such  meteorites  the  composition  is  altered  by  the  volatilization  or  burning  up  of  the  other  material  in  passing  through 
the  air.  Note  the  greater  abundance  of  elements  of  even  atomic  number  (97.2  per  cent). 


O     (8) 
S      (16) 

36.53 
i.  80 

Fe   (26) 
Ca  (20) 

23-32 
1.72 

Si      (14) 
Al     (13) 

18.03 
1-53 

Mg    (12) 

Ni    (28) 

13.60 
1-52 

Na  (11) 

1.64 

Cr    (24) 

0.32 

Mn  (25) 

0.23 

K     (19) 

0.17 

C     (6) 

0.15 

Co  (27) 

O.  12 

Ti       (22) 

O.II 

P      ds) 

0.  II 

H     (i) 

0.09 

Cu  (29) 

O.OI 

Cl     (17) 

0.09 

V      (23) 

tr. 

Ru  (44) 

tr. 

Pd  (46) 

tr. 

Pt     (78) 

tr. 

Ir     (77) 

tr. 

SMITHSONIAN  TABLES. 


424 


TABLE  666- 

ACCELERATION  OF  GRAVITY- 
For  Sea  Level  and  Different  Altitudes. 


Calculated  from  U.  S.  Coast  and  Geodetic  Survey  formula,  p.  134  of  Special  Publication  No.  40  of  that  Bureau. 
g  =  0.78039  (i  +  0.005 294  sin2  0  -  0.000007  sin2  2  0)m 
g  =  32-08783  (i  +  0.005294  sin*. <£  -o. 000007  sin*  20)  ft. 


Latitude 

cm/sec1 

log  S 

ft/sec» 

Latitude 

cm/  sec2 

... 

ft./sec2 

0° 

5 

978.039 

2-9003562 
•9903735 

32.0878 
.0891 

50° 
51 

981.071 
-159 

2.9917004 
•9917394 

32.1873 
.1902 

10 

12 

U 

.195 
.262 

•340 

.9904  .'5  4 
9904552 
.9004808 

.0929 
.0951 
.0977 

52 
53 
54 

.247 
.336 
.422 

.9917784 
.9918177 
.9918558 

•  1931 
.1960 
.1988 

U 

16 
17 

978.384 
•  430 
.480 

2.0905094 
.9905298 
.9905520 

32.0991 
.1007 
.1023 

a 

57 

981.507 
.592 
-675 

2.9918934 
.9919310 
.9919677. 

32.2016 
.2044 
.  2071 

18 

-532 

.0905750 

.1040 

58 

•  757 

.9920040 

.2098 

.585 

-9905985 

.1057 

59 

.839 

.9920403 

-2125 

20 

978  641 

2.9906234 

32.1076 

60 

981.918 

2.9920752 

32-2151 

21 

.701 

.9906500 

.1095 

61 

•995 

.9921073 

.2176 

22 
23 

.763 
.825 

.9906775 
.  9907050 

.1116 
.1136 

62 
63 

982.070 
•  145 

.9921424 
.9921756 

.  2201 
-2225 

24 

.892 

.  9907348 

.1158 

64 

.218 

.9922079 

.2249 

25 

978.960 

2  .  9907649 

32.1180 

65 

982.288 

2.9922388 

32.2272 

26 

979.030 

.  990/960 

.1203 

66 

•  356 

.9922689 

.2295 

27 

.101 

.9908275 

.1227 

67 

.422 

.9922981 

.2316 

28 

•  175 

.9908603 

.1251 

68 

•  487 

.9923268 

.2338 

29 

-251 

.9908940 

.1276 

69 

•549 

•9923542 

•2358 

30 

979-329 

2.9909286 

32.1302 

70 

982.608 

2.9923803 

32.2377 

31 

.407 

.9909632 

•  1327 

71 

.665 

.9924055 

.2396 

.487 

.  9909987 

.1353 

72 

.720 

.9924298 

.2414 

33 

-569 

.9910350 

•  1380 

73 

•  772 

.9924528 

•2431 

34 

.652 

.99IO7I8 

.1407 

74 

.822 

.9924749 

.2448 

35 

979-737 

2.99II095 

32.1435 

75 

982.868 

2.9924952 

32.2463 

36 

.822 

.9911472 

.1463 

76 

.912 

•9925147 

.2477 

37 

.908 

.1491 

77 

•  954 

.9925332 

.2491 

38 

•  995 

.9912238 

.1520 

78 

•  992 

.9925500 

•2503 

39 

980.083 

.9912628 

•  1549 

79 

983-027 

.9925655 

•2515 

40 

980.171 

2.99I3OI8 

32.1578 

80 

983-059 

2.9925796 

32.2525 

.261 

.0913417 

.  1607 

81 

.089 

.9925929 

•2535 

42 

•  350 

.9913812 

-1636 

82 

•US 

.  9926043 

-2544 

43 

.440 

.9914210 

.1666 

83 

•  139 

.9926149 

-2552 

44 

•  531 

.9914613 

.1696 

84 

.160 

.9926242 

.2558 

8 

980.621 
.711 

2.99I50II 
.9915410 

32.1725 
-1755 

85 
86 

983-178 
.191 

2.9926321 
.9926379 

32-2564 
.2569 

47 

.802 

.9915814 

-1785 

87 

.203 

.9926432 

.2572 

48 

.892 

.9916212 

.1814 

88 

.211 

.9926467 

•2575 

49 

.98! 

.9916606 

.1844 

90 

983.217 

.9926494 

•2577 

To  reduce  log  g  (cm.  per  sec.  per  sec.)  to  log  g  (ft.  per  sec.  per  sec.)  add  log  0.03280833  =  8.5159842  —  10. 
The  standard  value  of  gravity,  used  in  barometer  reductions,  etc.,  is  980.665.    It  was  adopted  by  the  International 
Committee  on  Weights  and  Measures  in  1901.    It  corresponds  nearly  to  latitude  45°  and  sea-level. 

FREE-AIR  CORRECTION  FOR  ALTITUDE. 

—0.0003086  cm/sec2/m  when  altitude  is  in  meters. 
— o .  000003086  ft/ sec2/ ft  when  altitude  is  in  feet. 


Altitude. 

Correction. 

Altitude. 

Correction. 

200  m. 

—0.0617  cm/sec2 

200  ft. 

-0.000617  ft.  /sec2 

300 

.0926 

300 

.  000926 

400 

•  1234 

400 

.001234 

500 

000 

•1543 
.1852 

500 
600 

.001543 
.001852 

700 

.2160 

700 

.002160 

800 

.2469 

800 

.  002469 

000 

•2777 

900 

.002777 

SMITHSONIAN  TABLES- 


TABLE  566. 
GRAVITY. 


425 


The  following  more  recent  gravity  determinations  (Potsdam  System)  serve  to  show  the  accuracy  which  may  be 
assumed  for  the  values  in  Table  565,  except  for  the  three  stations  in  the  Arctic  Ocean.  The  error  in  the  observed  gravity 
is  probably  not  greater  than  o.oio  cm/ sec2,  as  the  observations  were  made  with  the  half -second  invariable  pendulum, 
using  modern  methods. 

In  recent  years  the  Coast  and  Geodetic  Survey  has  corrected  the  computed  value  of  gravity  for  the  effect  of  ma- 
terial above  sea-level,  the  deficiency  of  matter  in  the  oceans,  the  deficiency  of  density  in  the  material  below  sea-level 
under  the  continents  and  the  excess  of  density  in  the  earth's  crust  under  the  ocean,  in  addition  to  the  reduction  for 
elevation.  Such  corrections  make  the  computed  values  agree  more  closely  with  those  observed.  See  special  publica- 
tion No.  40  of  the  U.  S.  Coast  and  Geodetic  Survey  entitled,  "Investigations  of  Gravity  and  Isostasy,"  by  William 
Bowie,  1917;  also  Special  Publication  No.  10  of  same  bureau  entitled,  "Effect  of  Topography  and  Isostatic  Compen- 
sation upon  the  Intensity  of  Gravity,"  by  J.  F.  Hayford  and  William  Bowie,  1912. 


Name. 


Latitude. 


Elevation, 
meters. 


Gravity,  cm/sec2 


Observed. 


Reduced  to 
sea-level. 


Refer- 


Kodaikanal,  India 10°  14' 

Ootacamund,  India n  25 

Madras,  India 13  4 

Jamestown,  St.  Helena — 15  55 

Cuttack,  India 20  29 

Amraoti,  India 20  56 

Sibbulpur,  India 23  9 

aya,  India 24  48 

Siliguri,  India 26  42 

Kuhrja,  India 28  14 

Galveston,  Texas 29  18 

Rajpur,  India 30  24 

Alexandria,  La 31  19 

St.  Georges,  Bermuda 32  21 

McCormick,  S.  C 33  55 

Shamrock ,  Texas 35  13 

Cloudland,  Tenn 36  6 

Mount  Hamilton,  Cal 37  20 

Kala-i-Chumb,  Turkestan 38  27 

Denver,  Col 39  41 

Hachinohe,  Japan 40  31 

Chicago,  111 41  47 

Albany,  N.  Y 42  39 

Florence,  Italy » 43  45 

Minneapolis,  Minn 44  59 

Simplon  Hospice,  Switzerland 46  15 

Fort  Kent,  Me 47  15 

Sandpoint,  Idaho 48  16 

Medicine  Hat,  Canada 50  2 

Field,  Canada 51  24 

Magleby ,  Denmark 54  47 

Copenhagen ,  Denmark 55  41 

St.  Paul  Island,  Alaska 57  7 

Fredericksvarn ,  Norway 59  o 

Christiania,  Norway 59  55 

Ashe  Inlet,  Hudson  Strait 62  33 

St.  Michael,  Alaska 63  28 

Hatnarfjordr,  Iceland 64  3 

Niantilik,  Cumberland  Sound 64  54 

Glaesibaer,  Iceland 65  46 

Sorvagen,  Norway 67  54 

Umanak,  Greenland 70  40 

Danes  Island ,  Spitzbergen 79  46 

Arctic  Sea 84  12 

Arctic  Sea 84  52 

Arctic  Sea 85  55 


2336 

2254 

6 

10 

28 

342 

447 

no 

118 

198 

3 

1012 

24 

2 

163 

708 

1890 

1282 

1345 

1638 

21 

182 

61 

184 

256 

1998 

1 60 

637 

664 

1239 

14 

14 

10 

10 

28 

IS 

i 
4 
7 

10 
19 

10 

3 
o 
o 
o 


977-645 

977-735 
978.279 
978.712 
978.659 
978.609 
978.719 
978.884 
978.887 
979.082 
979.272 
979.002 
979.429 
979.806 
979.624 
979-577 
979-383 
979.660 
979.462 
979.609 
980.359 
980.278 
980.344 
980.491 
980.597 
980.202 
980.765 
980.680 
980.865 
980.745 
981.502 
98i.559 
981.726 
981.874 
981.927 
982.105 
982. 192 
982.266 
982.273 
982.342 
982.622 
982.590 
983-078 
983-109 
983-174 
983-155 


978.366 
978.427 
978.281 
978.715 
978.668 
978.714 
978.856 
978.918 
978.923 
979-143 
979-273 
979.313 
979-436 
979.807 
979.674 
979-795 
979.966 
980.056 
979.877 
980.114 
980.365 
980.334 
980.363 
980.548 
980.676 
980.819 
980.814 
980.877 
981.070 
981.127 
981 . 506 
981-563 
981.729 
981.877 
981-936 
982 .  no 
982.192 
982. 267 
982.275 
982.345 
982.628 
982.593 
983.079 
983.109 
983.174 
983.155 


References:  (i)  Report  i6th  General  Conference  International  Geodetic  Association,  London  and  Cambridge, 
1909.  3d  Vol.  by  Dr.  E.  Borrass,  1911;  (2)  U.  S.  Coast  and  Geodetic  Survey,  Special  Publ.  No.  40;  *  (3)  U.  S.  Coast 
and  Geodetic  Survey,  Report  for  1897,  Appendix  6.* 

*  For  references  (2)  and  (3),  values  were  derived  from  comparative  experiments  with  invariable  pendulums,  the 
value  for  Washington  being  taken  as  980.112.  For  the  latter,  Appendix  5  of  the  Coast  and  Geodetic  Survey  Report 
for  1901,  and  pages  25  and  244  of  the  3d  vol.  by  Dr.  E.  Borrass  in  1911  of  the  Report  of  the  i6th  General  Conference 
of  the  Intern.  Geodetic  Association,  London  and  Cambridge,  1909.  As  a  result  of  the  adjustment  of  the  net  of  gravity 
base  stations  throughout  the  world  by  the  Central  Bureau  of  the  Intern.  Geodetic  Association,  the  value  of  the  Wash- 
ington base  station  was  changed  to  980.112. 

SMITHSONIAN  TABLES. 


426 


TABLE  567. 

ACCELERATION   OF  GRAVITY   (0)    IN   THE  UNITED  STATES- 


The  following  table  is  abridged  from  one  for  219  stations  given  on  pp.  50  to  52,  Special  Publication  No.  40,  U.  S. 

nirvey.    The  observed  values  depend  on  relative  determinations  and  on  adopted  value  of  980.112 

for  Washington  (Toast  and  C.etxlctic  Survey  Office,  see  footnote,  Table  566).    There  are  also  given  terms  necessary 

in  reducing  the  theoretical  value  (Table  565)  to  the  proper  elevation  (free-air)  and  to  allow  for  topography  and  isostatic 

compensation  by  the  Hayford  method  (see  introductory  note  to  Table  566). 

To  a  certain  extent,  the  greater  the  bulk  of  material  below  any  station,  the  less  its  average  density.  This  phenomenon 
is  knov.  c  compensation.  The  depth  below  sea-level  to  which  this  compensation  extends  is  about  96  km. 

Below  this  depth  any  mass  element  is  subject  to  equal  (fluid)  pressure  from  all  directions. 


lion. 

Latitude. 

Longitude. 

Eleva- 
tion, 
meters. 

Observed 

cm/sec2 

Correction. 

Elevation, 
cm/sec2 

Topography 
and  com- 
pensation, 
cm/sec2 

Key  West.  Fla  

24°  33-6' 
29     57-0 
30    17-2 
31     46-3 
32     43-3 
32     47-2 
33     30.8 
33     36.5 
33    45-0 
34    43-1 
34    45-0 
35       8.8 
35     13-8 
35    35-8 
35     57-7 
36       5-3 
36      6.2 
37     20.4 
37    32-2 
37    47-5 
38    38.0 
38     50.3 
38     50.7 
38    56.3 
38     54-7 
38     59-4 
39       8.3 
39     I/-  8 
39     28.7 
39     40.6 
39     57-1 
40       4.0 
40     21.0 
40     27.4 
40    46  .  I 
40    48-5 
40    58.4 
41     30.4 
41     47-4 
42     16.5 

42      22.8 

42    27.1 

42    30.8 
42     58.0 
43       4-6 
43     37-2 
43     41-8 
44     29.5 
44    43-3 
44     58.7 
45     I  I-  2 
46     24.2 
47     39-6 
48     58.1 

81°  48.4' 
90      4-2 
97    44-2 
106     29.0 
114    37-0 
79    56.0 
86    48.8 
91     12.2 
84    23.3 
76    39-8 
92     16.4 
90      3-3 
80    50.8 

IO5       12.  I 

83    55. 
112      6.8 
82      7.9 

121      38.6 

77    26.1 

122       25.7 
90      12.2 
105         2.0 
104     49.0 

77      4-0 
ioi     35-4 
no      9.9 
84    25.3 
76    37-3 
87     23-8 
104     56.9 
75     n.  7 
80    43-4 
74    39-5 
80      0.6 
in     53-8 
73     57-7 
117    43-8 
81     36.6 
87    36.1 
71     48-5 
71       7-8 
76     29.0 
94     II.  4 
85     40.8 
89     24.0 
116    12.3 
98      1.8 
7i     34-3 
no    29.7 
93     13-9 
67     16.9 
105     50. 

122       18.3 

97     14-9 

i 

2 
189 
1146 

M6 
179 

44 
324 

I 

89 
80 
228 
1960 
280 
849 
1890 
1282 
30 
H4 
154 
4293 
1841 
103 
1005 
1243 
245 
30 
151 
1638 
16 
205 
64 
235 
1322 
38 
1311 

2IO 

182 
170 

14 
247 

340 
236 
270 
821 
408 
261 
2386 
256 
38 
7i8 
58 
243 

978.970 
979-324 
979-  283 
979.124 
979.529 
979.546 
979-536 
979.600 
979-524 
979.729 
979-721 
979-740 
979-727 
979.204 
979-712 
979.463 
979.383 
979.660 
979.960 
979-965 
980.001 
978.954 
979-490 
980.095 
979-755 
979-636 
980.004 
980.097 
980.072 
979-609 
980.196 
980.085 
980.178 
980.118 
979-803 
980.267 
979-844 
980.241 
980.278 
980.324 
980.398 
980.300 
980.311 
980.372 
980.365 
980.212 
980.375 
980.486 
979.899 
980.597 
980.631 
980.539 
980.733 
980.917 

0.000 

—  .001 
—  .058 
—  •354 
-.017 
—  .002 
-•055 
-.014 

—  .100 

—  .000 
-.027 
-.025 
—  .070 
-.605 
-.086 
-.262 
-.583 
—  •396 
-.009 
-.035 
—  .048 
-1.325 
-.568 
-.032 
-.310 
-.384 
—  .076 
-.009 
-.047 
-.505 
-.005 
-.063 

—  .020 

-.073 
-.408 
—  .012 
-.404 
-.065 
-.056 
—  .052 
—  .004 
—  .076 
-.105 
--073 
-.083 
-.253 
-.126 
-.081 
-.736 
—  .079 
—  .012 

—  .  222 
-.018 

--075 

+0.035 
+  .013 

—  .001 
+  .OOI 

—  .010 

+.016 

+  .011 

+  .005 
+  .014 

+.036 

+  .001 
+  .OO2 

+  .015 
+  .017 
—  .001 

-.096 

+  .130 

+  .120 
+  .010 
+  •045 
+  .OOI 

+.187 

—  .007 

+  .012 
.000 
-  •  043 
+  .002 
+  .006 
+  .001 

—  .015 
+  .009 
—  .003 
+  .013 

.000 

-.041 

+  .011 

—  .004 

.000 

+  •007 

+.018 

+  -OIO 

+  .005 

+  .002 

+  .003 
+  -003 
—  .042 
-.006 

+  .007 

+.038 
-.005 

+  .010 

—  .020 

—  .  O2O 
-.009 

New  Orleans,  La  
Austin,  Tex.  university  
El  Paso,  Tex 

Yuma,  Ariz  

Charleston,  S.  C  

Birmingham,  Ala 

Arkansas  City,  Ark  
Atlanta,  Ga.  capitol  
Beaufort,  N.  C 

Little  Rock,  Ark  
Memphis,  Tenn  
Charlotte,  N.  C. 

,     Las  Vegas,  N.  Mex  
'     KnoxvUle,  Tenn  
Grand  Canyon,  Ariz  
Cloudland,Tenn  

Mount  Hamilton,  Cal.,  Obs'y. 
Richmond,  Va.  . 

San  Francisco,  Cal  
St.  Louis,  Mo.,  university  
Pike's  Peak,  Col.  . 

Colorado  Springs,  Col.  ... 
Washington,  D.  C.,  Bur.  St'ds. 
Wallace,  Kans  
Green  River,  Utah  
Cincinnati,  Ohio,  obs'y  
Baltimore,  Md.,  university.  .  . 
Terre  Haute,  Ind  
Denver,  Co!.,  university  obs'y. 
Philadelphia,  Pa.,  university  . 
Wheeling,  W.  Va.  
Princeton,  N.  J.  .  .  . 

Pittsburg,  Pa.  .  .'. 
Salt  Lake  City,  Utah  
New  York,  N.  Y.,  university. 
Winnemucca,  Nev... 
Cleveland,  Ohio  '. 
Chicago,  111.,  university  
Worcester,  Mass  
Cambridge,  Mass,  observatory 
Ithaca,  N.  Y.,  university  .  .  . 
Fort  Dodge,  Iowa  
Grand  Rapids,  Mich  
Madison,  Wis.,  university.  . 
Boise,  Idaho  
MitcheU,  S.  Dak.  university.  . 
Lancaster,  N.  H  . 
Grand  Canyon  ,  Wyo  
Minneapolis,  Minn. 

Calais,  Me  
Miles  City,  Mont  
Seattle,  Wash,  university.  . 
Pembina,  N.  Dak  

SMITHSONIAN  TABLES. 


TABLES  668-569.  427 

TABLE  568.  —  Length  of  Seconds  Pendulum  at  Sea  Level  and  for  Different  Latitudes. 


Length 

Log. 

Length 
in 

Log. 

Length 

Log. 

Length 
in 

inches. 

inches. 

0 

99.0961 

1.996056 

39.0141 

1.591222 

So 

99-4033 

i  .  997401 

39.1351 

1.592566 

5 

.  IOOO 

.  996074 

.0157 

.591239 

55 

•4475 

•997594 

•  1525 

.592760 

10 

.  1119 

.996126 

.0204 

.591292 

60 

.4891 

•997776 

.1689 

.  592941 

15 

.  1310 

.996210 

.0279 

-59I375 

65 

-5266 

•997939 

.1836 

•593104 

20 

•  1571 

.996324 

.0382 

.591490 

70 

•  5590 

.998081 

.1964 

•593246 

25 

99.1894 

i  .  996465 

39.0509 

1.591631 

75 

99.5854 

1.998196 

39.2068 

i.59336i 

30 

.2268 

.996629 

.0656 

.591794 

80 

.6047 

.998280 

.2144 

.  593446 

35 

.2681 

.996810 

.0819 

.591976 

85 

.6168 

•998332 

.2191 

•  593498 

40 

.3121 

.997002 

.0992 

.592168 

90 

.6207 

•998350 

.  2207 

•593515 

45 

-3577 

.997201 

.1171 

•592367 

Calculated  from  Table  565  by  the  formula  /  =  g/7T2.    For  each  100  ft.  of  elevation  subtract  0.000953  cm 
or  0.000375  in.  or  0.0000313  ft.    This  table  could  also  have  been  computed  by  either  of  the  following  formu- 

lae derived  from  the  gravity  formula  at  the  top  of  Table  565. 
/  =    0.990961(1  +  0.005294  sin2</>  —  0.000007  sin220)  meters 

/  =    0.990961  +  0.005246  sin20  —  0.000007  sin220  meters 

/  =  39.014135(1  +  0.005294  sin20  —  0.000007  sin220)  inches. 
/  =  39.014135  +  0.206535  sin20  —  0.000276  sin220  inches. 

TABLE  569.  —  Miscellaneous  Geodetic  Data. 


Equatorial  radius  =  a  =  6378206  meters; 

3963.  225  miles. 
Polar  semi-diameter        =  b  =  6356584  meters; 

3949 . 790  miles. 

Reciprocal  of  flattening  = -:  =  295 .  o 


Square  of  eccentricity     =  e2 


a2  -i* 


=  0.006768658 


6378388  =fc  1 8  meters; 
3963-339  miles. 
6356909  meters; 
3949.992  miles. 

297.0  =*=  0.5 
0.0067237  ±  0.0000120 


Difference  between  geographical  and  geocentric  latitude  =  0  —  </>'  = 

688.2242"  sin  20  —  1. 1482"  sin  40  +  0.0026"  sin  60. 

Mean  density  of  the  earth  =  5.5247  =*=  0.0013  (Burgess  Phys.  Rev.  1902). 

Continental  surface  density  of  the  earth  =  2.67  \  TT    i  _„       <;„,>  -icr>  r>a«r«  ttt 

Mean  density  outer  ten  miles  of  earth's  crust  =  2.40  )  Harkness-  Se 

Constant  of  gravity,  6.66  X  io~8  c.g.s.  units. 

Rigidity  =  n  =  8.6  X  lo11  c.g.s.  units.  \  A.  A.  Michelson,  Astrophysical  Journal,  39, 

Viscosity  =  e  =  10.9  X  io16  c.g.s.  units  (comparable  to  steel),  j      p.  105,  1914. 

Moments  of  inertia  of  the  earth;  the  principal  moments  being  taken  as  A,  B,  and  C,  and  C  the  greatest: 

C  -A  i 

— 7: —  =  0.00326521  =  — ; 

C  306.259 

C  —  A  =  0.001064767  £<i2; 
A  =  B  =  0.325029  Eaz; 
C  =  0.326094  Ea2; 
where  E  is  the  mass  of  the  earth  and  a  its  equatorial  semi-diameter. 


SMITHSONIAN  TABLES. 


428 


TABLE  570. 
TERRESTRIAL    MAGNETISM. 


Secular  Change  of  Declination. 

Changes  in  the  magnetic  declination  between  1810,  the  date  of  the  earliest  available  observations,  and  1920.  Based 
on  tables  in  "Distribution  of  the  Magnetic  Declination  in  Alaska  and  Adjacent  Regions  in  1910"  and  "Distribution 
of  the  Magnetic  Declination  in  tin-  United  States  for  January  i,  1915,"  published  by  the  United  States  Coast  and 
Geodetic  Survey.  For  a  somewhat  different  set  of  stations,  see  6th  Revised  Edition  of  the  Smithsonian  Physical  Tables. 


Station. 

1810 

1820 

,30 

1840 

1850 

1860 

1870 

1880 

1890 

1900 

1910 

1920 

Ala. 

Ashland.  .  . 

6.0E 

6.2E 

6.  IE 

S-9E 

5-6E 

S-2E 

4-7E 

4.1  E 

3-4E 

3-OE 

2.9E 

3-OE 

Tuscaloosa.... 

7.  IE 

7-3E 

7-3E 

7!2E 

6.9E 

6.6E 

6.  IE 

S-SE 

4.8E 

4-4E 

4-4E 

4.6E 

Alas. 

Sitka  

— 

28.7  E 

29.  O  E 

29.  3  F 

29.5  E 

29.  7  E 

3O.  2  E 

30.  4  E 

Kodiak 











26.  2  E 

25.  7  E 

25.  2  1 

24.  8  E 

24   5  E 

24.  2  E 

24.  2  E 

Unalaska.  .  .  . 









— 

2O.  4  E 

20.  I  E 

19.  6E 

19.  OE 

i8.3E 

17-  SE 

17-  2E 

St.  Michael.  .  . 





__ 

^_ 



__ 



24.7  E 

23.1  E 

22.1  E 

21-5  E 

2I.OE 

Ariz. 

Holbrook  

— 

— 

— 

— 

13-  SE 

I3-7E 

13.  8  E 

13.  6E 

13.  4E 

13-  5E 

14-  IE 

I4-5E 

Prescott  

— 

— 

— 

— 

13-  3E 

13.  6  E 

13-7  E 

I3-7E 

13-  6E 

13.  7E 

I4-4E 

I4-9E 

Ark. 

Augusta  

7-7E 

7-9E 

8.0E 

S.OE 

7.8E 

7-SE 

7.1  E 

6.SE 

5-9E 

5-SE 

5-6E 

S-SE 

Danville  

9-3E 

9-3E 

9.2E 

9.0E 

8.6E 

8.  IE 

7.6E 

7.2E 

7-4E 

7-7E 

Cal. 

Bagdad  

— 

— 

13.1  >• 

13-  SE 

13.9  E 

14.  IE 

I4-3E 

14.  4E 

14.  4E 

14.  6E 

I5-3E 

IS-  7E 

Mojave  

12.  4E 

12  .9  E 

13-  4E 

13-  SE 

14-  2E 

14.  4E 

14.  6E 

14-  9E 

14.  9E 

IS-  IE 

IS.SE 

16.3  E 

Modesto  .  .  , 

13-  8E 

14.21 

14-  7E 

IS-  IE 

15-5  E 

IS.SE 

16.  i  E 

16.  i  E 

16.  2E 

i6.6E 

17-  3E 

17-  7E 

Redding  

IS-  6E 

16.  I  E 

I6.6E 

17.  OE 

17.  4E 

17.  SE 

I8.IE 

I8.2E 

I8.3E 

i8.7E 

19.  4E 

I9-7E 

Colo. 

Pueblo 

__ 







13-  7  E 

13.  SE 

13  •  7  E 

13  •  S  E 

13  .  O  E 

12  .  8  E 

13  .  3  E 

13.  7  E 

Our.iv.  .  . 

__ 







IS  •  O  E 

IS    2  E 

IS  .  2  E 

IS.OE 

14  6  E 

14.  6  E 

IS.  I  E 

IS  •  5  E 

Conn. 

Hartford  

5-iW 

5-SW 

6.iw 

6.8w 

7-5W 

l£.  «  A 

S.iw 

8.7W 

9-4W 

^    if 

9.8w 

10.  4W 

II.2W 

12.  IW 

Del. 

Dover  

i.6w 

i  .  9\v 

2-3W 

2.8w 

3-4W 

4.0W 

4-7W 

5-3W 

S-9W 

6.5w 

7-2W 

8.ow 

D.  C. 

Washington..  . 

O.SE 

0-3E 

0.0 

o.sw 

LOW 

i.7W 

2.4W 

3-OW 

3-6W 

4.2W 

4-9W 

5.6w 

Fla. 

Miami  

S-8E 

5-7E 

S-3E 

4.9E 

4-4E 

3-9E 

3-3E 

2.7E 

2.2E 

I.7E 

I-5E 

Bartow  

S-5E 

5-4E 

5-2E 

4.8E 

4-4E 

3-SE 

3-2E 

2.6E 

2.1  E 

I.6E 

I.4E 

I-3E 

Jacksonville.  .  . 

S.OE 

S.OE 

4-9E 

4-6E 

4.2E 

3-6E 

3-OE 

2.4E 

I.8E 

L3E 

LIE 

Tallahassee.  .  . 

5-8E 

5-SE 

5-7E 

5-SE 

5-2E 

4.8E 

4.2E 

3-6E 

3-OE 

2.SE 

2.4E 

2!4E 

Ga. 

Millen  

4-9E 

4.8E 

4.6E 

4-3E 

3-9E 

3-4E 

2.?E 

2.1  E 

I.SE 

0-9E 

0.7E 

0-5E 

Americus  

S-9E 

6.0E 

5-9E 

S-6E 

5-2E 

4-7E 

4-1  E 

3-SE 

2.9E 

2.4E 

2.2  E 

2.2E 

Haw. 

Honolulu  

— 

9-4E 

9-4E 

9-SE 

9.8E 

10.  I  L 

IO-4E 

10.  7  E 

J.I.  I  E 

Idaho 

Pocatello  

— 

— 

— 

— 

17.  7E 

17.  9E 

iS.OE 

I7-9E 

17.  SE 

I7-9E 

18.  s  E 

iS.SE 

Boise  

— 

— 

— 

— 

iS.OE 

iS.SE 

iS.SE 

i8.6E 

iS.SE 

19-  SE 

19.  SE 

Pierce  

_ 



__ 

2O.  2  E 

2O.  6  E 

21    O  E 

21.2  E 

21.  I  E 

21  .  2  E 

21.4  E 

22  .  0  E 

22.  2  E 

111. 

Kankakee  .... 

6.6E 

6.8E 

6.8E 

6.6E 

5-8E 

S-3E 

4.8E 

4.  IE 

3-SE 

3-3E 

3-  IE 

Ind. 

Rushville  
Indianapolis  .  . 

7-7E 
S.OE 

8.0E 

S-IE 

8.  IE 

S.OE 

8.0E 

4-7E 

7:sE 

4-3E 

7-4E 
3-SE 

7-OE 
3-3E 

6.4E 

2.7E 

5-7E 
2.1  E 

5-2E 

LSE 

5-  IE 
LIE 

5.  IE 
O.9E 

Iowa 

Walker  

8.9E 

9.  IE 

9.1  E 

8.9E 

8.6E 

8.2E 

7-SE 

6.8E 

6.2E 

6.2E 

6.2E 

Kans. 

Sac  City  
Emporia  

— 

IO.4E 

10-7  E 

10.  SE 

10.  SE 
n-SE 

10.  SE 
II.4E 

10.2  E 
II.  2  E 

9.6E 
10.  SE 

8.8E 

10.  2  E 

8.4E 
9-9E 

8.6E 

IO.I  E 

8.6E 
10.  3E 

Ness  City  

— 

— 

— 

— 

12.  4E 

12  .4  E 

12.  2  E 

II.  9E 

II.  3  E 

II.  2  E 

II.4E 

II.7E 

Ky. 

Manchester.  .  . 

3-SE 

3-6E 

3-4E 

3-  IE 

2.8E 

2.2E 

I.6E 

I.OE 

0.3E 

O.3W 

o.6w 

o.8w 

Louisville  4.8E 
Princeton  |  6.8E 

4-9E 
6.9E 

4.8E 
6.9E 

4.6E 

6.8E 

4-3E 
6.5E 

3-8E 

6.0E 

3-2E 
S-SE 

2.5E 
4.8E 

I.9E 

4.2E 

I-SE 
3-9E 

L3E 
3-7E 

I.2E 

3-SE 

La. 

Winfield  

8.6E 

8.9E 

9.0E 

9.0E 

8.9E 

8.6E 

8.2E 

7.6E 

7.1  E 

6.8E 

7-OE 

7-4E 

Me. 

Eastport  

13.  9W 

14.  7W 

IS-SW 

i6.3W 

I7.2W 

iS.ow 

iS.sw 

iS.Sw 

19.  ow 

19-  3W 

20.  OW 

21.  OW 

Bangor  >  1  1.  8w 

12.  4W 

13-  2W 

13.  9W 

14.  7W 

IS-4W 

IS-  9W 

i6.4W 

i6.7W 

17.  iw 

i7.8w 

iS.Sw 

Md. 

Portland  
Baltimore  

9-3W 

9-9W 
LIW 

10.  6w 
L4W 

II.2W 
I.QW 

ii.gw 

2.4W 

1  2  .  6W 

3-iw 

13.  iw 
3-8w 

13.  6w 

4.4W 

14.  iw 

S-OW 

14-  SW 

S-6w 

IS-  3W 
6.3W 

7.ow 

Mass. 

Boston  

7-3W 

7.8w 

8.4W 

9.iw 

9.8w 

10.  sw 

II.OW 

I2.0W 

I2.6W 

13.  4W 

14.  4W 

Mich. 

Pittsfield  
Marquette  

S-7W 

6.2W 

6.7E 

6.7W 
6.7E 

7-4W 
6.SE 

S.iw 
6.  IE 

8.7W 
5-SE 

9-3W 
4-7E 

IO.OW 

3-8E 

IO.4W 
3-OE 

II.OW 

2.4E 

n.8w 

2.  IE 

12.  7W 
I.7E 

Minn. 

Lapeer  
Grand  Haven. 
St.  Paul  

E 

2.6E 

5.  IE 
II.6E 

2.4E 

S.OE 
ii.  SE 

2.1  E 

4-8E 

II.  QE 

I.6E 
4-4E 

I.OE 

3-SE 

II.  4E 

0.3E 
3-  IE 
IO-9E 

o.sw 

2.4E 
10.  3E 

I.2W 
I.6E 

9-SE 

i.8w 

LIE 
8.9E 

2-3W 
0    7E 

8.8E 

2.8W 

0.3  « 

8.7E 

Marshall  . 

— 

— 

— 

II.  7E 

L6E 

II.4E 

II.OE 

10.5  E 

9.8E 

9-3E 

9-4E 

9-4E 

Hibbing  

— 

10.  SE 

10.  7  E 

10.  SE 

0.6E 

10.  3  E 

9-7E 

9.0E 

8.2E 

7.6E 

7-7E 

7-SE 

Meridian... 
Vicksburg.... 

7-3E 

8.2E 

7-4E 
8.4E 

13-  OE 

7-SE 
S.SE 

3-  IE 
7-4E 

8.4E 

3-IE 
7.2E. 
8.2E 

12.  SE 
6.9E 
S.OE 

12.3  E 

6.5E 
7.6E 

II.  7E 
5-9E 
7.  IE 

I.OE 
5-2  E 
6.4E 

0.4E 

4.8E 

6.0E 

0.6E 
4-9E 
6.  IE 

10.  SE 

S-IE 
6.4E 

SMITHSONIAN  TABLES. 


TABLE  570. 

TERRESTRIAL   MAGNETISM   (continued). 
Secular  Change  of  Declination  (concluded'). 


429 


State. 

Station. 

1810 

1820 

1830 

1840 

l8SO 

1860 

1870 

1880 

1800 

1900 

1910 

1920 

Mo. 

Hcrmajui  

_ 

Q.2E 

9-3E 

Q.2E 

Q.OE 

8.7E 

8.3E 

7-7E 

7.0E 

6.5E 

6.5E 

6.6E 

Sedalia  



Q.QE 

IO.OE 

IO.OE 

g.gE 

g.6E 

9-3E 

8.7E 

8.0E 

7.0E 

7.8E 

S.OE 

Mont. 

Miles  City  

— 

17.  OE 

17.  SE 

17.  7E 

17.  4E 

I6.0E 

i6.gE 

I7-3E 

17.  6E 

Lewis  town.  .  .  . 

— 



— 

IQ.5  E 

IQ.SE 

2O.  I  E 

20.  IE 

19.  gE 

IQ.OE 

ig.6E 

2O.  I  E 

20-4  E 

Ovando  

— 



— 

20.  4  E 

20.  8  E 

21.  I  E 

21.2  E 

21.  1  E 

20.  QE 

21.  I  E 

21.  6E 

22.  OE 

Nebr. 

Albion  

— 

12.  4E 

12.  7  E 

12.  QE 

12.  QE 

12.  SE 

12.  SE 

12.  OE 

II.  4  E 

II.  OE 

II.  2E 

II.  5  E 

Valentine  

— 

— 

— 



I4.I  E 

14.  IE 

13.  QE 

13.  4  E 

12.  SE 

12.  6E 

12.  SE 

13-  IE 

Alliance  

— 

— 

— 



15.  4E 

15.  4E 

IS-  3E 

14.  8  E 

14.  3E 

14.  2  E 

14.  SE 

14.  SE 

Nev. 

Elko        .    . 



— 





17.3  E 

17  .  6  E 

17.7  E 

17.  7  E 

17  .  6  E 

17.  SE 

i8.4E 

iS.QE 

Hawthorne  .  .  . 



— 





l6.  2  E 

i6.6E 

i6.8E 

17.  OE 

17.  OE 

17-  3E 

I8.0E 

l8.4E 

N.  H. 

Hanover  

7.iw 

7-5W 

8.2W 

S.QW 

9-7W 

10.  sw 

II.IW 

n.6w 

I2.OW 

I2.6W 

13-  2W 

14.  2W 

N.J. 

Trenton  

2.8W 

3.IW 

3-5W 

4.  iw 

4-7W 

S-4W 

6.ow 

6.7W 

7-2W 

7-8w 

8.6w 

9-4W 

N.  M. 

Santa  Rosa  .  .  . 

— 

— 



12.7  E 

12.  SE 

12.  7E 

12.  4E 

12.  OE 

ii.  gE 

12.  SE 

12.  gE 

Laguna  

— 

— 

— 



13.  4  E 

1^.6  E 

I3-6E 

13.  4E 

13-  OE 

13-  OE 

13-6  E 

14.  IE 

N.  Y 

Albany  

S-7W 

S.QW 

6.4W 

7.ow 

7-Sw 

8.5W 

Q.2W 

10.  OW 

10.  3W 

10.  gw 

n.6w 

12.  SW 

Elmira  

2.2W 

2.4W 

2.8w 

3-3W 

4.ow 

4.8w 

5-4W 

6.3W 

7-ow 

7-SW 

8.2W 

g.ow 

Buffalo 

I  .OW 

I  .  IW 

T    AW 

i  .  ow 

2.4W 

3  •  2W 

3.8w 

4.  7W 

5  .  4\V 

Sow 

6.  sw 

7  .  2W 

N.  C. 

Newbern  

I.7E 

I.6E 

A  .  4-W 

I-3E 

O.SE 

0.3E 

O.^W 

LOW 

I.7W 

2-3W 

.  y  w 

2.gw 

3-4W 

4.0W 

Greensboro  .  .  . 

3-SE 

3-4E 

3-  IE 

2.7E 

2.2E 

1.61 

I.OE 

0.3E 

0.3W 

o.8w 

I-3W 

i.Sw 

Asheville  

4.2E 

4.2E 

4.0E 

3-6E 

3-IE 

2.6E 

2.0E 

I.3E 

0.7E 

0.2E 

0.2W 

o.sw 

N.  D. 

Jamestown  .  .  . 

14.  OE 

14.  2  E 

14.  2  E 

14.  OE 

13-  7  E 

13-  2  E 

12.5  E 

12.  2E 

12.  4E 

12.  SE 

Bismarck  

— 

— 

— 



i6.4E 

16.3  E 

16.1  E 

IS-  6E 

IS-OE 

14.  7  E 

IS.OE 

IS-  2E 

Dickinson  .... 

— 

— 

— 



17-  7E 

17.  7E 

I7-5E 

17.  IE 

i6.SE 

16.3  E 

i6.7E 

i6.gE 

Ohio 

Canton  

2.3E 

2.  2  E 

2.0E 

I.7E 

I.2E 

0.6E 

0.0 

o.7W 

I-3W 

I.QW 

2.SW 

3-iW 

Urbana  

4-4E 

4-4E 

4-3E 

4.0E 

3-SE 

3.0E 

2.4E 

I.8E 

I.I  E 

O.SE 

O.IE 

0.3W 

Okla. 

Okmulgee  .... 

— 

IO.2  E 

IO.  I  E 

g.8E 

9-5E 

g.iE 

8.7E 

S.QE 

g.2E 

Enid  



— 

__ 



II.  2E 

II.  2  E 

II.  OE 

10.  6E 

10.  2  E 

Q.SE 

10.  I  E 

10.  SE 

Ore. 

Sumpter  

— 

— 





IQ.3E 

I9-7E 

2O.  OE 

20.2  E 

2O.  2  E 

2O.  4  E 

21.  1  E 

21.  4E 

Detroit  

16.7  E 

17.  4E 

iS.OE 

i8.6E 

ig.  2  E 

ig.7E 

2O.  I  E 

20.3  E 

20.5  E 

20.  SE 

21.  6E 

21.  QE 

Pa. 

Wilkes-Barre.  . 

2.3W 

2.5W 

2.g\v 

3.4W 

4.ow 

4-7W 

S-3W 

6.ow 

6.6w 

7-2W 

8.0W 

S.Sw 

Lockhaven.  .  .  . 

I.4W 

i.SW 

I  .  QW 

2.4W 

3.ow 

3-6w 

4-3W 

S-ow 

5-6w 

6.3w 

7-ow 

7-7W 

Indiana  

0.6E 

O.SE 

0-3E 

O.IW 

o.7W 

i-3W 

2.0W 

2.6W 

3-3W 

3.gw 

4.6w 

5.2W 

P.  R. 

San  Juan  

— 

— 

— 

— 

— 

— 

I  .  OW 

2.OW 

3-4W 

R.  I. 

Newport  

6.6w 

7.iw 

7-7W 

8.4W 

g.iw 

g.8w 

10.  3W 

10.  8w 

H.3W 

n.gw 

1  2  .  7W 

13.  7W 

S.  C. 

Marion  

3-4E 

3-3E 

3-OE 

2.6E 

2.1  E 

I.6E 

o.gE 

0.3E 

O.4W 

LOW 

I.4W 

i.Sw 

Aiken  

4.8E 

4-7E 

4-SE 

4.2E 

3-7E 

3-IE 

2-SE 

I.QE 

I-3E 

0.7E 

0.4E 

O.I  E 

S.  D. 

Huron  

— 

13-2  E 

13-  2E 

13.  OE 

12.  7E 

12.  3E 

II.  7E 

II.  2  E 

II.  SE 

II.  7E 

Murdo  

— 

— 

— 

— 

IS.OE 

14.  gE 

I4-7E 

14-  3  E 

I3-7E 

13.  4E 

13-  7  E 

13.  9E 

Rapid  City  ... 

— 

— 

— 

— 

IO-4E 

i6.4E 

i6.3E 

IS-8E 

IS-3E 

IS-  IE 

15.  4E 

IS-  7E 

Tenn. 

Knoxville  

3-8E 

3-8E 

3-6E 

3-3E 

2.QE 

2.4E 

I.SE 

LIE 

O.SE 

o.o 

o.3W 

o.sw 

Shelbyville.... 

6.4E 

6.5E 

6.4E 

6.2  E 

S-9E 

5-SE 

4-9E 

4-3E 

3-7E 

3-2E 

3-OE 

2.QE 

Huntingdon.  .  . 

7-3E 

7-4E 

7-4E 

7-3E 

7.0E 

6.6E 

6.  IE 

5-SE 

4.QE 

4-4E 

4-3E 

4-4E 

Tex. 

Houston  

Q.OE 

g.2E 

9-4E 

Q.4E 

9-3E 

8.QE 

8.4E 

7-9E 

7-7E 

8.  IE 

8.6E 

San  Antonio  .  . 

— 



9-SE 

9-7E 

g.8E 

9-7E 

9-5E 

Q.2E 

8.yE 

8.7E 

Q.2E 

9-7E 

Pecos  

— 



10.7  E 

II.  OE 

II.  I  E 

II.  I  E 

II.  OE 

10.  SE 

IO.4E 

10.  3E 

10.  8  E 

II.  3E 

Wytheville.... 

2.9E 

2.QE 

2.7E 

2.4E 

2.0E 

I.4E 

o.8E 

O.IE 

o.sw 

I.IW 

i.SW 

I.QW 

Wash. 

Wilson  Creek.. 

21.2  E 

21.  6E 

21.  SE 

21.  QE 

22.1  E 

22:4E 

23.  OE 

23.  3  E 

Seattle  

I8.QE 

IQ.  SE 

20.1  E 

20.  7  E 

21.  2E 

21.  6E 

22.  OE 

22.  2E 

22.  4E 

22.  SE 

23-  SE 

23.  SE 

W.  Va. 

Sutton  

I.QE 

I.8E 

I.6E 

I.2E 

O.SE 

0.2E 

0.4W 

I.IW 

i.8w 

2.4W 

2.gw 

3-4W 

Wis. 

Shawamo  

7-4E 

7-4E 

7-3E 

7.0E 

6-SE 

S.QE 

S.OE 

4-3E 

3-7E 

3-4E 

3-  IE 

Floydada  

— 

— 

II  .  2  E 

II.  3  E 

II  .  2  E 

10.  QE 

10.  4E 

10.3  E 

10.  7  E 

II.  IE 

Utah 

Manti  

— 

— 

— 

— 

i6.4E 

16.7  E 

i6.8E 

16.7  E 

i6.4E 

i6.SE 

17-  IE 

17-  SE 

Vt. 

Rutland  

6.6w 

7.iw 

7.6w 

8.3W 

g.iw 

Q.8W 

10.  sw 

II.2W 

n.6w 

12.  IW 

12.  8W 

13-  Sw 

Va. 

Richmond.  .  .  . 

O.SE 

0.6E 

0.3E 

O.IW 

o.6w 

I.2W 

i.8w 

2.5W 

3-iw 

3-7W 

4-2W 

4.QW 

Lynchburg..  .  . 

I.6E 

I-5E 

I.3E 

O.gE 

O.SE 

O.IW 

o.7W 

I.4W 

2.OW 

2.6w 

3-iw 

3-7W 

Stanley  

— 

8.QE 

Q.OE 

Q.OE 

8.8E 

8.4E 

7.8E 

7.  IE 

6.3E 

S.8E 

5-6E 

5-4E 

Wyo. 

Douglas  

— 

— 

— 



IS-8E 

I6.0E 

I6.0E 

15.  SE 

IS-3E 

IS.2E 

IS-  7E 

I6.0E 

Green  River  .  . 

i6.8E 

17.  OE 

17.  OE 

i6.8E 

l6.5  E 

i6.6E 

I7.  2E 

17-  5E 

SMITHSONIAN  TABLES. 


4.^0 


TABLES  571  572. 

TERRESTRIAL   MAGNETISM   (continued). 
TABLE  571.  —  Dip  or  Inclination. 


This  table  gives  for  the  epoch  January  i,  1915.  the  values  of  the  magnetic  dip,  /,  corresponding  to  the  longitudes 
Greenwich  in  the  heading  and  the  north  latitudes  in  the  first  column. 


X 

0 

65 

7° 

75 

80 

85 

90 

95 

100 

105 

no 

"5 

1  20 

125 

19 





50-4 

49-4 

48-5 

47.2 

46.1 

45-1 

44-1 

— 







21 

— 

— 

52.7 

51.9 

51-1 

50.1 

48.9 

47-9 

46.9 

— 

— 

— 

— 

23 

— 

— 

55-i 

54  2 

53-7 

52.8 

51-7 

50.4 

49-7 

48.7 

— 

— 

— 

as 
27 

— 

— 

57-6 
59-8 

56.8 
59-3 

56-1 
58.3 

55-2 
57-6 

54-2 
56.6 

53.1 
55-6 

52.2 
54-6 

Si.  a 

53-6 

50.1 
52-4 

— 

— 

29 





61.9 

6i.3 

6o.| 

59-7 

58.9 

57-9 

56.8 

55-8 

54-6 

53-8 

— 

31 
33 
35 

= 

63.6 
65.4 
67.2 

63.8 
65.6 
67.3 

63.4 
65-3 
67.2 

62.8 
64-7 
66.6 

62.0 
64.0 
66.1 

61.1 
63.1 
65-3 

60.  i 
62.4 
64-3 

59-0 
61.2 
63.2 

i 

62. 

57-0 
59-1 
61.0 

55-8 
fc? 

- 

37 

— 

gil 

69.2 

69.0 

68.9 

68.1 

67.3 

66.4 

65.2 

64. 

63.1 

62.! 

— 

39 



70.6 

70.8 

70.6 

70.  6 

70.0 

69.2 

68.3 

67.3 

66. 

64.9 

63-9 

62.5 

41 

_„ 

72.2 

72.3 

72.5 

72.2 

71.7 

71.0 

70.1 

69.0 

68. 

66.6 

65.5 

64.3 

43 

— 

73.6 

74.0 

74.1 

74.0 

73-5 

72.6 

71.8 

70.7 

6o-7 

68.4 

67.2 

65-9 

45 

47 

74-3 
75-6 

74-9 
76.3 

ll'i 

75-5 
76.9 

75-5 
76.9 

75-2 
77.0 

74-5 
76.1 

73-5 
75-1 

72.4 
74-2 

71-3 
72.9 

70.2 
71.7 

69.0 
70.5 

67.8 
69-5 

49 

76.5 

77-4 

78.2 

78-5 

78.5 

78-3 

77-7 

76.7 

75-7 

74-5 

73-2 

72.1 

71.2 

TABLE  572.  — Secular  Change  of  Dip. 

Values  of  the  magnetic  dip  for  places  designated  by  the  north  latitudes  and  longitudes  west  of  Greenwich  in  the 
first  two  columns  for  January  i  of  the  years  in  the  heading.  The  degrees  are  given  in  the  third  column  and  the  minutes 
in  the  suceeding  columns. 


Latitude. 

Long- 
itude. 

1855 

1860 

1865 

1870 

1875 

-1880 

1885 

I890 

1895 

1000 

1905 

1910 

1915 

25 

80 

55  + 

32 

32 

31 

29 

26 

23 

18 

18 

22 

31 

43 

73 

108 

25 

no 

49  + 

14 

26 

36 

45 

52 

61 

67 

74 

82 

92 

IO2 

116 

132 

30 

83 

60+ 

66 

70 

73 

74 

73 

67 

57 

51 

53 

61 

78 

101 

126 

30 

IOO 

57+ 

4i 

46 

55 

64 

67 

62 

57 

58 

6s 

74 

87 

103 

I2O 

30 

"5 

54+ 

47 

56 

63 

65 

64 

66 

69 

73 

79 

85 

90 

06 

102 

35 
35 
35 
35 

80 
90 
i°S 

120 

66+ 

65  + 
62  + 
59+ 

67 
67 

56 

68 
61 

59 

67 

53 

61 

64 
46 
47 
61 

55 
39 
45 
60 

45 
34 
39 
59 

36 
28 
39 
61 

3i 
27 
39 
64 

30 
27 
43 
66 

32 

29 

£ 

$ 

57 
66 

55 

i 

8 

72 
66 

40 

75 

7i  + 

82 

82 

78 

73 

65 

55 

43 

33 

27 

24 

24 

29 

36 

40 

90 

70+ 

30 

31 

34 

37 

36 

32 

29 

26 

25 

26 

30 

38 

48 

40 

105 

67  + 

— 

S6 

S3 

51 

Si 

Si 

52 

S6 

60 

63 

66 

40 
45 

120 

65 

64+ 
74+ 

118 

112 

103 

51 
94 

II 

54 
70 

57 
59 

i 

58 
37 

54 
30 

50 
26 

45 

22 

42 
18 

45 

75 

75  + 

9i 

87 

83 

78 

73 

6z 

50 

41 

31 

26 

24 

24 

24 

45 

90 

74+ 

86 

86 

86 

84 

82 

80 

73 

68 

66 

64 

6s 

68 

72 

45 

105 

72  + 

— 

— 

— 

— 

30 

28 

27 

26 

26 

25 

25 

24 

45 
49 

122.  5 
92 

68+ 
77+ 

& 

44 
79 

47 
78 

50 
76 

50 

74 

49 
74 

8 

44 
66 

40 
6S 

37 
6^ 

g 

3 

21 
60 

49 

120 

72  + 

27 

25 

24 

23 

22 

21 

20 

20 

19 

17 

12 

06 

SMITHSONIAN  TABLES. 


TABLES  573-574. 

TERRESTRIAL    MAGNETISM  (continued). 
TABLE  673.  —  Horizontal  Intensity. 


431 


This  table  gives  for  the  epoch  January  i,  1915,  the  horizontal  intensity,  H,  expressed  in  cgs  units,  corresponding  to 
the  longitudes  in  the  heading  and  the  latitudes  in  the  first  column. 


X 
4> 

65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

i°5° 

110° 

"5° 

120° 

125° 

19 

•  297 

•  303 

•  311 

-3i6 

.321 

.325 

•325 

21 



— 

.290 

.  206 

.303 

.310 

•  315 

•  320 

•  320 



— 





23 



— 

.283 

.288 

•  294 

•  301 

•  307 

•  3" 

•  3" 

•311 

— 





25 



— 

•  273 

.281 

.286 

.292 

.298 

.302 

•303 

•303 

•  304 





27 

— 

— 

.264 

.271 

.276 

.281 

.288 

.292 

•295 

.296 

.297 





29 
31 

- 

•  237 

•  253 

.242 

.258 

.247 

.265 

•  254 

.272 
.260 

.277 
.266 

.283 

.272 

.286 
.276 

.287 
.279 

.288 
.280 

.288 
.280 

~ 

33 

— 

.225 

.230 

.236 

.242 

.248 

•  255 

.259 

.264 

.270 

.271 

.272 



35 

— 

.213 

.217 

.223 

.232 

•  235 

.241 

•  249 

•  251 

.256 

.260 

.263 



37 

— 

.202 

.205 

.210 

.213 

.222 

.227 

•  234 

.240 

.244 

.250 

•  253 



3Q 
41 

— 

.191 
.178 

.193 
.178 

.196 
.182 

.200 
.185 

.206 
.191 

.212 
.197 

.218 
.204 

.226 

.212 

.232 
.218 

•3 

.242 
.232 

•245 
.236 

43 

— 

.166 

.166 

.165 

.171 

.174 

.182 

.189 

.198 

.207 

.214 

.221 

.227  ' 

45 

•  159 

•154 

.153 

•153 

•155 

.160 

.167 

.174 

.185 

.192 

.202 

.210 

.216 

47 

.146 

•143 

.139 

.139 

.141 

.142 

•  ISO 

•  159 

.168 

.ISO 

.187 

•195 

.202 

49 

•  135 

.130 

.126 

-123 

.123 

.129 

.136 

.144 

-153 

.'164 

.174 

.182 

.189 

TABLE  574.  — Secular  Change  of 'Horizontal  Intensity. 

Values  of  horizontal  intensity,  H,  in  cgs  units  for  the  places  designated  by  the  latitude  and  longitude  in  the  first 
^wo  columns  for  January  i  of  the  years  in  the  heading. 


u, 

Long. 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

1895 

1900 

1905 

1910 

1915 

o 

25 

80 

.3086 

•  3073 

.3057 

.3042 

•  3025 

.3008 

.2990 

.2970 

.2949 

.2917 

.2870 

.2810 

25 

no 

.3216 

.3202 

•  3187 

.3168 

.3153 

•3141 

.3128 

.3115 

.3102 

.3088 

•  3063 

.3030 

30 

83 

•  2775 

.2768 

.2760 

.2752 

•  2743 

.2732 

.2720 

.2705 

.2686 

.2658 

.2614 

.2560 

30 

IOO 

.2978 

•  2959 

.2941 

.2924 

.2908 

'.2894 

.2882 

.2867 

•  2847 

.2817 

.2780 

30 

"5 

.2996 

.2981 

.2966 

.2949 

•  2934 

.2922 

.2910 

.2899 

.2890 

.2880 

.2863 

.2840 

35 

80 

.2367 

.2362 

•  2357 

•2355 

•2351 

•  2347 

.2340 

•  2335 

•  2325 

.2306 

.2272 

.2230 

35 

90 

— 

.2460 

.2460 

•  2459 

.2456 

•  2453 

•  2445 

•  2435 

.2418 

.2387 

•2350 

35 
35 

105 
1  20 

~ 

* 

.2727 

.  2619 
.2714 

.2607 
.2702 

.2598 
.2690 

.2589 
.2679 

.2582 
.2670 

.2572 
.2663 

.2559 
.2657 

•  2537 
.2645 

.2510 
.2630 

40 

75 

.1876 

.1884 

.1895 

.1904 

.1912 

.1918 

.1923 

.1924 

.1921 

.1911 

.1889 

.i860 

40 

go 

.2080 

.2076 

.2073 

.2070 

.2069 

.2068 

.2066 

.2062 

.2054 

.2042 

.2019 

.1990 

40 

105 

— 

— 

.2269 

.2263 

.2258 

.2254 

.2250 

.2245 

.2237 

.2227 

.2210 

.  2I9O 

40 

1  20 

— 

— 

•  2439 

.2430 

.2422 

.2416 

.2409 

.2402 

.2396 

.2390 

.2381 

.2370 

45 

65 

.1504 

•  1515 

•  1527 

•  1543 

•  1557 

.1568 

•  1579 

.1590 

.1598 

.1600 

.1596 

•1590 

45 

75 

.1487 

.1490 

.1497 

.1508 

.1518 

.1529 

.1540 

.1548 

.1552 

•  1552 

•1543 

•1530 

45 

90 

.1648 

.1646 

.1644 

.1641 

.1639 

•  1637 

.16^6 

.1637 

.1636 

•  1633 

.1620 

.I60O 

45 

105 

— 

— 

.1895 

.1894 

.1893 

.1891 

.1888 

.1885 

.1881 

.1875 

.1864 

.1850 

45 

122.5 

.2183 

•  2175 

.2166 

.2158 

.2148 

.2140 

.2134 

.2130 

.2128 

.2128 

.2125 

.2I2O 

49 

92 

•  1336 

•  1334 

.1330 

•  1327 

•  1325 

•  1324 

.1324 

.1327 

•  1330 

.1^6 

.1330 

.1320 

49 

1  20 

.1846 

.1845 

.1844 

.1841 

.1836 

.1831 

.1826 

.1824 

.1825 

.1825 

.1823 

.1820 

SMITHSONIAN  TABLES. 


TABLES  575-576. 
TERRESTRIAL   MAGNETISM    (.continued). 

TABLE  575.  —  Total  Intensity. 

This  Uble  rives  for  the  epoch  January  i.  HJI.S.  tin-  values  of  the  total  intensity,  F,  expressed  in  cgs  units  corre- 
sponding to  the  longitudes  in  the  heading  ar.«l  tin-  latitudes  in  the  first  column. 


X 

65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

«• 

120° 

125° 

10 

.466 

.469 

•  465 

.463 

.461 

•  453 

_ 

: 

21 

— 

— 

.480 

.482 

•  483 

•  479 

•  477 

.468 

— 

— 



— 

>3 



— 

•  495 

•  492 

•  497 

.498 

•495 

.488 

.481 

.471 

— 



— 

25 
27 

— 

— 

•  509 

•  513 
•  531 

•  513 
•525 

•  512 

.524 

•  Sio 
.523 

•  503 
.517 

•494 
•509 

.484 
•499 

•474 
•487 

— 

' 

. 

29 
31 
33 
35 

E 

•533 

•  540 

1 

•  537 

•  552 

•  576 

•  538 
.556 
.566 
•  584 

•  539 

•  536 
•  550 
•  564 

.533 
.546 
•  559 

•  574 

.522 
.536 
.548 
•  557 

^528 
•  543 
•  549 

•497 
•514 
•  528 
-536 

.488 
.498 
•513 
•  528 

37 

— 

.566 

•  577 

.586 

-592 

•  595 

.588 

.585 

•572 

•  561 

•552 

•541 

— 

39 

_ 

575 

.587 

•  590 

.602 

.602 

•  597 

•590 

•  586 

•  575 

-559 

-550 

•  531 



582 

•  585 

.605 

.605 

.608 

605 

•  599 

•  592 

•  582 

•569 

•559 

•544 

43 
45 
47 

.588 
.587 

.588 

.602 
.607 
.609 

.602 
.611 
.613 

.620 
.619 
.622 

•  613 
.626 
.631 

.609 
•  625 
.624 

.605 
.613 
.618 

•  599 
.612 
.617 

•  597 
•  599 
.612 

•  S8i 
•  596 
•  596 

•  570 
•  586 

.584 

•556 

•  572 
•577 

49 

.578 

.596 

.'616  • 

.617 

.617 

.636 

.638 

.626 

.  619 

.614 

.602 

-592 

•587 

TABLE  576. -Secular  Change  of  Total  Intensity. 

Values  of  total  intensity,  F,  in  cgs  units  for  places  designated  by  the  latitudes  and  longitudes  in  the  first  two  columns 
for  January  i  of  the  years  in  the  heading. 


Lat. 

Long. 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

1895 

1900 

1905 

1910 

1915 

0 

0 

25 

80 

.5476 

•  5453 

•5427 

.5396 

.5363 

•5324 

•5285 

.5253 

•  5227 

.5208 

.5178 

.5160 

.5131 

25 

no 

•4941 

.4946 

.4941 

•  4933 

.4914 

.4906 

.4900 

.4889 

.4884 

•  4879 

.4876 

.4861 

.4836 

30 

83 

•5758 

•  5755 

•5749 

•  5735 

.5716 

.5678 

•  5625 

.5584 

•  5559 

•5549 

•  5534 

•  5510 

•5471 

30 

100 

•  5608 

•  5595 

.5567 

•  5523 

•5479 

•5455 

•5450 

•  5444 

•  5441 

.5426 

•  5399 

30 

"5 

•5219 

.5216 

•  5205 

.5182 

•  5149 

•5129 

•5114 

.5101 

•5°94 

.5092 

-5086 

.5068 

•5041 

35 

80 

.6lOI 

.6000 

•  6075 

.6048 

.6008 

.5955 

.5910 

.5873 

•  5856 

.5838 

•  5823 

.5796 

.5756 

35 

90 



— 

— 

•5993 

•  5966 

.5946 

•  5914 

•  5904 

•  5885 

.5868 

.5861 

•  5834 

.5800 

35 
35 
40 

105 

120 

.6183 

.6193 

.6196 

•  5457 
.6204 

.5720 
.5428 
.6190 

•  5675 
•  5401 
.6160 

•  5656 
.5383 
.6115 

•  5636 
•  5369 
.6077 

•5634 
•  5356 
.6047 

•  5630 
•  5342 

.0022 

.5627 
-5330 
•  5991 

•  5604 
.5306 
•  5948 

•5567 
•  5276 
.5892 

40 

00 

— 

.6236 

.6240 

.6246 

.6233 

.6209 

.6190 

.6169 

•  6151 

.6133 

.6118 

.6089 

.6052 

40 

105 

— 

— 

— 

.6040 

.6011 

.5988 

•5978 

.5967 

•5958 

•  5955 

•  5944 

•5912 

•  5871 

40 

120 



— 

— 

•  5739 

•  5720 

•  5709 

•  5707 

•  5692 

.5676 

•  5647 

.5621 

.5581 

.5546 

45 

65 

.6l6l 

.6x59 

.6140 

.6126 

.6107 

.6082 

.6052 

.6022 

•5994 

•  5980 

.5962 

•  5923 

.5875 

45 

75 

.6369 

•  6347 

-6330 

.6320 

.6329 

.6281 

.6247 

.6228 

.6189 

.6171 

•  6157 

.6121 

.6070 

45 

90 

— 

•  6552 

.6544 

.6522 

•6495 

.6474 

.6415 

•  6377 

.6366 

•6349 

•  6344 

•  6315 

.6264 

45 

105 



— 

— 

— 

.6296 

.6276 

.6261 

.6245 

.6232 

.6206 

.6170 

.6n8  ! 

45 

122-5 

.6037 

.6019 

.6010 

.6000 

.5978 

•  5944 

•5913 

•  5883 

•5855 

•5837 

•  5820 

.5784 

•  5745 

49 

92 

.6616 

.6597 

•  6578 

.6540 

.6508 

.6498 

.6448 

.6421 

.6427 

.6424 

.6426 

.6380 

•  6349 

49 

120 

.6121 

.6107 

.6098 

•  6083 

.6061 

•  6039 

.6017 

.6010 

.6008 

•  5997 

•5963 

.5922 

SMITHSONIAN  TABLES- 


TABLES  577-578. 

TERRESTRIAL   MAGNETISM   (continued). 
TABLE  577.  — Agonic  Line. 


433 


The  line  of  no  declination  appears  to  be  still  moving  westward  in  the  United  States,  but,  as  the  line  of  no  annual 
change  is  only  a  short  distance  to  the  west  of  it,  it  is  probable  that  the  extreme  westerly  position  will  soon  be  reached. 


Lat 

N. 

Longitudes  of  the  agonic  line  for  the  years 

1800 

1850 

1875 

1890 

1905 

1915 

25 

• 

• 

• 

75-5 

76.1 

77-4 

30 

— 

— 

— 

78.6 

79-7 

80.0 

35 



76.7 

79.0 

79-9 

81.7 

82.7 

6 

75-  2 

77-3 

79-7 

80.5 

82.8 

84-4 

7 

76  3 

77-7 

80.6 

82.2 

83-5 

84.0 

8 

76.7 

78.3 

81.3 

82.6 

83-6 

84.1 

9 

76.9 

78.7 

81.6 

82.2 

83.6 

83-9 

40 

77-o 

79-3 

81.6 

82.7 

84.0 

84.3 

i 

2 

77-9 
79-i 

80.4 
81.0 

81.8 
82.6 

82.8 
83.7 

84.6 
84.8 

85-1 
85-3 

3 

79-4 

81.2 

83-1 

84-3 

85.0 

85-4 

4 

79-8 

— 

83-3 

84-9 

85-S 

85.8 

45 





83-6 

85-2 

86.0 

86.2 

6 

— 

— 

84-2 

84-8 

86.4 

86.3 

7 

— 

— 

85.1 

85-4 

86.4 

86.6 

8 

— 

— 

86.0 

85-9 

86.5 

87.2 

9 

86.5 

86.3 

87.2 

88.0 

TABLE  578.  —  Mean  Magnetic  Character  of  Each  Month  in  the  Years  1906  to  1917.* 

Means  derived  from  daily  magnetic  characters  based  upon  the  following  scale:   o,  no  disturbance;  i,  moderate 
disturbance,  and  2,  large  disturbance. 


Year. 

Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Year 
Mean. 

1906 

0.45 

o.  90 

0.68 

0.63 

0.58 

0.56 

o.  69 

0.63 

0.79 

o-59 

0-55 

0.71 

0.65 

1907 

0.69 

0.83 

0.58 

o-SS 

0.72 

0.67 

0:67 

0.66 

0.68 

0.71 

0.61 

0.53 

0.66 

1908 

0.64 

0.71 

0.87 

0.68 

0.82 

0.66 

0.49 

0.77 

0.89 

0.53 

0.60 

0.47 

0.68 

1909 

o.  76 

0.63 

0.79 

0.49 

0-S9 

o-54 

0.53 

0.65 

0.70 

0.69 

0.49 

0.58 

0.62 

1910 

0.58 

0.71 

0.81 

0.68 

0.72 

0-53 

0.55 

0.81 

0.80 

0.96 

0.77 

0.76 

0.72 

1911 

0.78 

0.89 

0.78 

o.  76 

0.70 

0-53 

0.61 

0-53 

0.50 

0.59 

0.49 

0-45 

0.63 

1912 

0.42 

0.49 

o-45 

Q-45 

o-47 

0.47 

0.41 

0.49 

0.47 

0.46 

0-45 

0.43 

0.46 

1913 

0.51 

0-53 

0-53 

0-54 

0-45 

0-45 

0.42 

0.46 

0.58 

0.57 

0.42 

0.36 

0.48 

1914 

0.46 

0.50 

0.62 

0.50 

0-37 

0.52 

0.61 

0.61 

0-53 

0.64 

0.60 

0.46 

0-54 

1915 

0-53 

0.64 

0.68 

0.61 

0.58 

0.61 

0.47 

0.60 

o.S9 

0.77 

0.82 

o-54 

0.62 

1916 

0.61 

0.56 

0.86 

0.68 

0.75 

0.67 

0.62 

0-75 

0.75 

o.  76 

0.83 

0.65 

0.71 

1917 

0.81 

o.  69 

0-59 

0.63 

0.66 

0-55 

0.61 

0.85 

0.61 

0-74 

0-53 

0.72 

0.67 

*  Compiled  from  annual  reviews  of  the  "Caractere  magnetique  de  chaque  jour"  prepared  by  the  Royal  Meteoro- 
logical Institute  of  the  Netherlands  for  the  International  Commission  for  Terrestrial  Magnetism.  The  number  of 
stations  supplying  complete  data  for  the  above  years  were  respectively,  30,  32,  36,  38,  34,  39,  43,  42,  37,  35,  35,  35- 
Data  from  Sitka,  Ekaterinburg,  Stonyhurst,  Wilhelmshaven,  Potsdam-Seddin,  De  Bilt,  Greenwich,  Kew,  Val  Joyeux, 
Pola,  Cheltenham,  Honolulu,  Bombay,  Porto  Rico,  and  Buitenzorg  were  employed  for  all  of  the  years. 

SMITHSONIAN  TABLES. 


434  TABLE  573' 

RECENT  VALUES  OF  THE   MAGNETIC   ELEMENTS  AT   MAGNETIC  OBSERVATORIES. 

pilot  l.y  tin-  Dop.irtmcnt  of  Terrestrial  Magnetism,  Carnegie  Institution  of  Washington.) 


Latitude 

Longitude 

Middl 
of 
year. 

Magnetic  elements. 

Declination 

Inclination 

Intensity  (cgs  units). 

Hor'l 

Ver'l. 

Total. 

Pavlovsk.  .  . 

O           / 

57  o.<  N 
56  50  N 
55  5i  N 
55  47  N 
55  19  N 
S3  Si  N 
5332N 
52  23  N 
52  17  N 
52  i6N 
52  06  N 
51  56  N 
51  48  N 
51  29  N 
51  28  N 
51  28  N 
So48N 
So  46  N 
50  21  N 
50  09  N 
50  05  N 
50  04  N 
48  49  X 
48  09  N 
48  03  N 
47  53  N 
46  26  N 
4452N 
43  47  N 
42  42  N 
41   43  N 
40  52  N 
40  49  N 
40  12  N 
38  47  N 
38  44  N 
36  28  X 
354IN 
.32    15  X 

31  19  N 
30  19  N 

29  52  N 

22    46  N 
22    18  N 

21  19  N 
1  8  (6  X 

18  38  N 
18  09  N 
I436N 
10  14  N 
6  ii  S 
8  48  S 
13  488 
18  558 
20  06  S 
31  40  S 
33  278 
43  328 
54  45  S  J 
60  45  S 

o         / 

30  29  E 
135  20  W 
60  38  E 
12  27  E 
49  08  E 
3  12  W 

2    28  W 

8  ogE 
13  04  E 
13  01  E 
104  16  E 
5  ii  E 
10  15  W 

10    20  E 

7  14  E 
o  19  W 
o  oo 
4  21  E 
16  14  E 
18  55  E 
5o5W 
14  25  E 
19  58  E 

2    01   E 

ii  37  E 
14  08  E 
18  12  E 
30  46  E 
13  Si  E 
79  16  W 
2  53  E 
44  48  E 
14  15  E 
o  31  E 
8  25  W 
95  10  W 
76  50  W  ' 
6  12  W 
139  45  E 
no  50  W 

121    02  E 

78  03  E 

31    20  E 

88  22  E 
114  10  E 
158  04  W 
96  27  E 
72  52  E 
65  26  W 

121    10  E 

77  28  E 
106  49  E 
13  13  E 
171  46  W 
47  32  E 
57  33  E 
63  53  W 
70  42  W 
172  37  E 
64  03  W} 
42  32  W 

1907 
1916 
1907 
1915 
1912 
1913 
1915 
1911 
1916 
1916 
1905 
1914 
1913 
1905 
1912 
I9i5 
1916 
1911 
1913 
1908 
1912 
1912 
1913 
1913 
1911 
1904 
1912 
1910 
1915 
1916 
1910 
1913 

IQII 
1914 
1915 
1909 
I9l6 
1913 
1912 
I9l6 
1909 
1914 
1913 
1914 
I9l6 
I9l6 
1914 
1915 
I9l6 
I9II 
1914 
1912 
1910 
I9l6 
1907 
I9l6 
1914 
1909 
1914 
1906 
1912 

0              / 

i  09.9  E 
30  24.0  E 
10  35-  5  E 
8  44-3  W 
8  09.1  E 
17  54-9  W 
16  38.0  W 
ii  28.2  W 
8  07.6  W 
8  08.9  W 
i  58.1  E 

12    22.6    W 
20    19.6    W 

10  40.3  W 
ii  39-4  W 
15  18.4  W 
14  46.9  W 
13  13-9  W 
6  58.2  W 
6  12.3  W 
17  24.2  W 
7  50.3  W 
5  03.3  W 
13  59-2  W 
9  23.8  W 
9  02.4  W 
6  17.5  W 
3  35-9  W 
7  39-o  W 
6  33-4  W 
12  44.8  W 
3  09.1  E 

12  51.6  W 
15  57-5  W 
8  34.0  E 
6  07.6  W 
1451-7  W 
5  03.4  W 
13  44-4  E 
2  59-6  W 
2  18.8  E 
2  17.0  W 
o  32.2  E 
o  13.8  W 
9  43-8  E 
o  02.6  E 
o  40.6  E 
3  19-4  W 
o  40.9  E 
i  17.  i  W 
o  47-3  E 
16  12.3  W 
9  59-9  E 
9  29.7  W 
9  47-6  W 
8  40.4  E 
13  57-9  E 
16  44.8  E 
15  41-6  E 
4  46.5  E 

0              / 

70  37-7  K 
74  26.0  K 
70  52.2  K 
68  50.  6  N 
69  17-3  M 
69  37-3  N 
68  41.  4  N 
67  30.7  N 
66  27.  i  N 
66  24.1  N 
70  25.0  N 
66  46.  5  N 
68  09.  2  N 

66  56.  6  N 
66  52.  8  N 
66  oo.  i  N 

66  26.  6  N 

64  i8.4N 
64  38.  9  N 
63  06.2  N 

62  26.  9  N 
60  05  .  i  N 
74  43-5  N 

56  51.  i  N 
56  11.7  N 
57  47-5  N 
58  34-  7  N 
68  50.  2  N 
70  49-  9  N 
54  26  6  N 
48  53.  7  N 
59  26.1  N 
45  34-  9  N 
44  22.9  N 
40  47  .  6  N 
30  58.9  N 
30  51.  8  N 
39  29.2  N 
23  06.  i  N 
24  21.  i  N 
50  56.7  N 
16  i8.2N 
4  ii.  2  N 
31  19-48 
35  32-2  S 
29  54-5  S 
54  05.7  S 
52  54-68 
25  41-5  S 
29  57-2  S 
67  59-  8  S 
50  03.6  S 
54  26.  oS 

•  1650 
.1558 
.1762 
.1726 
.1802 
.1682 
•1734 
.1811 
.1870 
•1874 

.2001 
.l85I 
.1789 

.1846 
.1849 
.I9O2 

.l8oO 

•1974 
.2063 

.2IO6 

.2171 
.2217 
•1599 

.2522 

•2330 
•2305 
.2167 
•1934 
.2494 
.3000 
.2706 
•3323 
•3316 
-3003 
•3740 
.37X6 
.2896 
.3898 
•3637 
.2315 
.3820 

•3757 
.3668 

.2012 
•3536 
•2533 
.2320 
.2560 

.2241 
•2717 
•2534 

.4694 
•  5592 
.5081 
•4459 
•476S 
•4528 
.4446 
•4375 
.4290 
.4289 
•5625 
•4314 
•4463 

.4338 
•4332 
•4273 

•4312 

•4167 
.4068 

.4161 
.3853 
.5854 

•  376i 

•  3"6~98 
•3773 
.5596 
.5662 
.3489 
.3438 
.4582 
•  3391 
•3246 
.2592 
.2246 

.2220 
.2386 
.1663 
.1669 
•3470 
.1117 
•0275 
.2232 
•1437 
.2034 

•3499 
3069 
1232 

5546 
3244 
3544 

•4975 
.5805 
•  5378 
•  4781 
•5094 
•4831 
.4772 
•4735 
.4680 
.4680 
•5970 
.4694 
.4808 

•4714 
•4710 
•4677 

•4704 

.4611 
.4561 

•4693 

•4445 
.6068 

•4528 

•4371 
•  4422 
.6001 
.5889 
.4289 
•4563 

•5322 

•4747 
.4641 
•3967 
.4363 
.4328 
•3752 
.4238 
.4047 
.4468 
•3981 
•3767 
.4229 
•2473 
.4080 
•4319 
•3847 
.2841 

•  5982 
•4231 
•4357 

Sitka  
Katharinenhurg  
Rude  Skov  
Kasan  .  .  . 

EskdaJemuir. 

Stonvhurst  

Wilhelmshaven.  .  . 

Potsdam 

Scddin  

Irkutsk. 

De  Bill 

Valencia  

Clausthal  
Bochum  
Kew. 

Greenwich  .  .  . 

!     Uccle  
Hermsdorf  
Beuthen  
Falmouth..    .    . 

Prague.  . 

Cracow  

Val  Toveux  ...    . 

Munich  
Kremsmiinster  
O'Gyalla  (Pesth)  
Odessa  
Pola 

Agincourt  (Toronto).  . 

Tiffis 

Capodimontc  
Ebro  (Tortosa)... 

Coimbra  .    .  . 

Baldwin  * 

Cheltenham..  . 

San  Fernando. 

Tokio.  . 

Tucson  

Lukiapang  **  . 
Dehra  Dun 

Helwan  

Barrackpore  t  
Hongkong  
Honolulu  

Toungoo  . 

Alibi,'.. 

Vieques  

Antipolo  .... 
Kodaikanal  \ 
Batavia-Buitenzorg.  .  . 
St.  Paul  de  Loanda.  .  . 
Samoa  (Apia)  
Tananarive  
Mauritius  
Pilar.  .  . 

•  i.-igo  
"Mchurch  
ar's  Island.... 
Orcadas  

^Baldwin  Obs'y  replaced  by  Tucson  Obs'y,  Oct.  1909;   mean  given  for  Jan  -Oct   '09 
"Replaced  Zi-ka-wei  ObsV,  1908.        f  Observations  discontinued  Apr    26    ioi< 
I  Provisumal  values  taken  for  position  ol  Port  Cork,  p.  298,  American  PracUcalNivigator,  1914  edition. 


SMITHSONIAN  TABLES. 


APPENDIX. 
DEFINITIONS  OF  UNITS. 

ACTIVITY.    Power  or  rate  of  doing  work;  unit,  the  watt. 

AMPERE.  Unit  of  electrical  current.  The  international  ampere,  "which  is  one-tenth 
of  the  unit  of  current  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  which 
is  represented  sufficiently  well  for  practical  use  by  the  unvarying  current  which, 
when  passed  through  a  solution  of  nitrate  of  silver  in  water,  and  in  accordance 
with  accompanying  specifications,  deposits  silver  at  the  rate  of  o.ooi  11800  of  a 
gram  per  second." 
The  ampere  =  i  coulomb  per  second  =  I  volt  through  I  ohm  =  IO-1  E.  M.  U.  =  3  X 

10 '  E.  S.  U.* 

Amperes  =  volts/ohms  =  watts/volts  =  (watts/ohms)*. 
Amperes  X  volts  =  amperes  2  X  ohms  =  watts. 
ANGSTROM.    Unit  of  wave-length  =  io-10  meter. 
ATMOSPHERE.    Unit  of  pressure. 

English  normal  =14.7  pounds  per  sq.  in.  ==29.929  in.  =  760.18  mm  Hg.  32°  F. 
French        "       =760  mm  of  Hg.  o°  0  =  29.922  in.  =  14.70  Ibs.  per  sq.  in. 
BAR.     A  pressure  of  one  dyne  per  cm.2  Meteorological  "  bar  "=  iott  dynes/cm2. 
BRITISH  THERMAL  UNIT.    Heat  required  to  raise  one  pound  of  water  at  its  tem- 
perature of  maximum  density,  i°   F.  =  252  gram-calories.    • 
CALORIE.      Small    calorie  =  gram-calorie  =  therm  =  quantity    of    heat    required    to 

raise  one  gram  of  water  at  its  maximum  density,  one  degree  Centigrade. 
Large  calorie  =  kilogram-calorie  =  1000  small  calories  =  one  kilogram  of  water  rrised 

one  degree  Centigrade  at  the  temperature  of  maximum  density. 
For  conversion  factors  see  page  197. 

CANDLE,  INTERNATIONAL.     The  international  unit  of  candlepower  maintained 

jointly  by  national  laboratories  of  England,  France  and  United  States  of  America. 

CARAT.     The   diamond   carat   standard   in   U.-S.  =  200  milligrams.     Old    standard 

=  205.3  milligrams  =  3.168  grains. 

The  gold  carat :   pure  gold  is  24  carats ;  a  carat  is  1/24  part. 
CIRCULAR  AREA.    The  square  of  the  diameter  =  1.2733  X  true  area. 

True  area  =  0.785398  X  circular  area. 

COULOMB.  Unit  of  quantity.  The  international  coulomb  is  the  quantity  of  electricity 
transferred  by  a  current  of  one  international  ampere  in  one  second.  =  icr1  E.  M.  U. 
=  3X  io9E.  S.  U. 

Coulombs  =  (volts-seconds) /ohms  =  amperes  X  seconds. 
CUBIT  =  18  inches. 
DAY.     Mean  solar  day  =1440  minutes  =  86400  seconds  =  1.0027379  sidereal  day. 

Sidereal  day  =  86164.10  mean  solar  seconds. 

DIGIT.    3/4  inch ;  1/12  the  apparent  diameter  of  the  sun  or  moon. 
DIOPTER.    Unit  of  "power"  of  a  lens.    The  number  of  diopters  =  the  reciprocal  of 

the  focal  length  in  meters. 

DYNE.    C.  G.  S.  unit  of  force  =  that  force  which  acting  for  one  second  on  one  gram 
produces  a  velocity  of  one  cm  per  sec.  =  ig  -4-  gravity  acceleration  in  cm/sec./sec. 
Dynes  =  wt.  in  g  X  acceleration  of  gravity  in  cm/sec./sec. 
ELECTROCHEMICAL  EQUIVALENT  is  the  ratio  of  the  mass  in  grams  deposited 

in  an  electrolytic  cell  by  an  electrical  current  to  the  quantity  of  electricity. 
ENERGY.    Sec  Erg. 
ERG.    C.  G.  S.  unit  of  work  and  energy  =  one  dyne  acting  through  one  centimeter. 

For  conversion  factors  see  page  197. 

FARAD.  Unit  of  electrical  capacity.  The  international  farad  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  coulomb 
of  electricity  =  io~*  E.  M.  U.  =  9  X  iou  E.  S.  U. 

The  one-millionth  part  of  a  farad  (microfarad)  is  more  commonly  used. 
Farads  =  coulombs/volts. 

*  E.  M.  U.=C.  G.  S.  electromagnetic  units.    E.  S.  TJ.=C.  G.  S.  electrostatic  units. 


APPENDIX. 

FOOT-POUND.    The  work  which  will  raise  one  pound  one  foot  high. 

For  conversion  factors  see  page  197. 
FOOT-POUNDALS.    The  English  unit  of  work  =  f oot-pounds/g. 

For  conversion  factors  see  page  197. 
g.    The  acceleration  produced  by  gravity. 

GAUSS.    A  unit  of  intensity  of  magnetic  field  =  I  E.  M.  U.  =  J  X  i<r10  E.  S.  U. 
GRAM.    See  page  6. 

GRAM-CENTIMETER.    The  gravitation  unit  of  work  =  g.  ergs. 
GRAM-MOLECULE  =  x  grams  where  x  =  molecular  weight  of  substance. 
GRAVITATION  CONSTANT  =  G  in  formula  G  ^-p8  =  666.07  X  icr10  cm.3/gr.  sec,1 

HEAT  OF  THE  ELECTRIC  CURRENT  generated  in  a  metallic  circuit  without  self- 
induction  is  proportional  to  the  quantity  of  electricity  which  has  passed  in  coulombs 
multiplied  by  the  fall  of  potential  in  volts,  or  is  equal  to  (coulombs  X  volts)/4.i8i  in 
small  calories. 

The  heat  in  small  or  gram-calories  per  second  =  (amperes2  X  ohms) /4.i8i  =  volts2/ 
(ohms  X  4-iSi)  =  (volts  X  amperes)/4.i8i  =  watts/4.i8i. 

HEAT.    Absolute  zero  of  heat  =  —  273.13°  C,  —459-6°  Fahrenheit,  —218.5°  Reaumur 

HEFNER  UNIT.    Photometric  standard;  see  page  260. 

HENRY.  Unit  of  induction.  It  is  "  the  induction  in  a  circuit  when  the  electromotive 
force  induced  in  this  circuit  is  one  international  volt,  while  the  inducing  current 
varies  at  the  rate  of  one  ampere  per  second."  =  io9  E.  M.  U.  =  1/9  X  icr11  E.  S.  U. 

HORSEPOWER.  The  English  and  American  horsepower  is  defined  by  some  authorities 
as  746  watts  and  by  others  as  550  foot-pounds  per  second.  The  continental  horse- 
power is  defined  by  some  authorities  as  736  watts  and  by  others  as  75  kilogram- 
meters  per  second.  See  page  197. 

JOULE.    Unit  of  work=  io7  ergs.    For  electrical  Joule  see  p.  xxxvii. 

Joules  =  (volts2  X  seconds) /ohms  =  watts  X  seconds  =  amperes2  X  ohms  X  sec. 
For  conversion  factors  see  page  197. 

JOULE'S  EQUIVALENT.  The  mechanical  equivalent  of  heat  =  4.i8s  X  IOT  ergs. 
See  page  197. 

KILODYNE.     looo  dynes.    About  I  gram. 

KINETIC  ENERGY  in  ergs  =  gramsX  (cm./sec.)2/2. 

LITER.    See  page  6. 

LUMEN.    Unit  of  flux  of  light-candles  divided  by  solid  angles. 

MEGABAR.     Unit  of  pressure  =  1000000  bars  =  0.987  atmospheres. 

MEGADYNE.    One  million  dynes.    About  one  kilogram 

METER.    See  page  6. 

METER  CANDLE.  The  intensity  of  lumination  due  to  standard  candle  distant  one 
meter. 

™S£'^The  Unit  of  electrical  conductivity.    It  is  the  reciprocal  of  the  ohm. 
11CRO.    A  prefix  indicating  the  millionth  part. 

MICROFARAD.  One-millionth  of  a  farad,  the  ordinary  measure  of  electrostatic 
capacity. 

MICRON,     (ft)  =  one-millionth  of  a  meter. 

MIL.    One-thousandth  of  an  inch. 

MILE.    See  pages  5,  6. 

MILE,  NAUTICAL  or  GEOGRAPHICAL  =  6080.204  feet. 

V1ILLI-.    A  prefix  denoting  the  thousandth  part. 

'H.    The  anomalistic  month  =  time  of  revolution  of  the  moon  from  one  perigee  to 
another  =  27.55460  days. 

The  nodical  month  =  draconitic  month  =  time  of  revolution  from  a  node  to  the  same 

node  again  =  27.2 1 222  days. 

The  sidereal  month  =  the  time  of  revolution  referred  to  the  stars  =27.32166  days 
value),  but  varies  by  about  three  hours  on  account  of  the  eccentricity  of  the 

orbit  and     perturbations." 
The  synodic  month  =  the  revolution  from  one  new  moon  to  another  =  29.5306  days 

(mean  value)  =the  ordinary  month.    It  varies  by  about  13  hours. 


APPENDIX. 


437 


OHM.  Unit  of  electrical  resistance.  The  international  ohm  is  based  upon  the  ohm 
equal  to  10"  units  of  resistance  of  the  C.  G.  S.  system  of  electromagnetic  units,  and 
"  is  represented  by  the  resistance  offered  to  an  unvarying  electric  current  by  a 
column  of  mercury,  at  the  temperature  of  melting  ice,  144521  grams  in  mass,  of  a 
constant  cross  section  and  of  the  length  of  106.3  centimeters."  =  10*  E.  M.  U. 
=  1/9  X  io-u  E.  S.  U. 

International  ohm  =  1.01367  B.  A.  ohms  =  1.06292  Siemens'  ohms. 
B.  A.  ohm  =  0.9865 1  international  ohms. 
Siemens'  ohm  =  0.94080  international  ohms. 
PENTANE  CANDLE.    Photometric  standard.    See  page  260. 
PI  =  TT  =  ratio  of  the  circumference  of  a  circle  to  the  diameter  =  3. 141 59265359. 
POUNDAL.    The  British  unit  of  force.    The  force  which  will  in  one  second  impart  a 

velocity  of  one  foot  per  second  to  a  mass  of  one  pound. 
RADIAN  =  i8o°A  =  57.295780  —  57°  i/  45"  =  206265". 
SECOHM.    A  unit  of  self-induction  =  I  second  X  I  ohm. 
THERM  =  small  calorie  =  (obsolete). 

THERMAL  UNIT,  BRITISH  =  the  quantity  of  heat  required  to  warm  one  pound  of 
water  at  its  temperature  of  maximum  density  one  degree  Fahrenheit  =  252  gram- 
calories. 

VOLT.  The  unit  of  electromotive  force  (E.  M.  R).  The  international  volt  is  "the 
electromotive  force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one 
international  ohm,  will  produce  a  current  of  one  international  ampere.  The  value 
of  the  E.  M.  F.  of  the  Weston  Normal  cell  is  taken  as  1.0183  international  volts  at 
20°  C.  =  io8  E.  M.  U.  =  1/300  E.  S.  U.  See  page  197. 
VOLT-AMPERE.  Equivalent  to  Watt/Power  factor. 

WATT.  The  unit  of  electrical  power  =  io7  units  of  power  in  the  C.  G.  S.  system.  It  is 
represented  sufficiently  well  for  practical  use  by  the  work  done  at  the  rate  of  one 
Joule  per  second. 

Watts  =  volts  X  amperes  =  amperes2  X  ohms  =  volts'/ohms  (direct  current  or  alter- 
nating current  with  no  phase  difference). 
For  conversion  factors  see  page  197. 
Watts  X  seconds  =  Joules. 

WEBER.    A  name  formerly  given  to  the  coulomb. 

WORK  in  ergs  =  dynes  X  cm.     Kinetic  energy  in  ergs  =  grams  X  (cm./sec.)  */2. 
YEAR.    See  page  414. 

Anomalistic  year  =  365  days,  6  hours,  13  minutes,  48  seconds. 
Sidereal  "    =365      "6  9  9-314 

Ordinary         "     =365       "     5       "      4»       "   46  + 
Tropical  ;    same  as  the  ordinary  year. 


43'S  APPENDIX. 

TABLE  58O. 
TEMPERATURE   MEASUREMENTS. 

The  ideal  standard  temperature  scale  (Kelvin's  thermodynamic  scale,  see  introduction,  p.  xxxiv)  is  in- 
dependent of  the  properties  of  ,nv  substance,  and  would  be  indicated  by  a  gas  thermometer  using  a  perfect 
gaT?he  scale  indlaLl  by  any  actual  .as  can  be  corrected  if  the  departure  of  that  gas  from  a  perfect  gas 
be  known  (see  Table  206,  p.  195,-  also  Buckingham,  Bull.  Bur.  Standards,  3,  237).  The  thermodynamic 
omoto  of  the  constant-pressure  scale  at  any  temperature  is  very  nearly  proportional  to  the  constant  pres- 
STeT^h  thegas  is  kept  and  that  for  the  const  ant-  volume  scale  is  approximately  proportional  to  the 
fdUal  pressure  at  the  ice-point.  The  gas  thermometer  has  been  earned  up  to  the  melting  point  of  palla- 
dium 1822°  K  (1549°  C)  (Day  and  Sosman,  Am.  J.  Sc.,  29,  p.  93.  iQio). 

A  proposed  international  agreement  divides  the  temperature  scale  into  three  intervals.  The  first  inter- 
val --40°  to  450°  C  uses  the  platinum  resistance  thermometer  calibrated  at  the  melting  point  of  ice,  o  C, 
at  saturated  steam,  100°  C,  and  sulphur  vapor,  444-6°  C,  all  under  standard  atmospheric  pressure.  Points 
on  the  temperature  scale  are  interpolated  by  the  Callendar  formula?: 


where  t  is  the  temperature,  R,  the  resistance,  Pt,  the  platinum  temperature,  and  5,  a  constant. 

Temperatures  in  the  second  interval  are  measured  by  a  standard  platinum-platinum-rhodium  couple  cal- 
ibrated say  at  the  freezing  points  of  zinc,  419-4°  C,  cadmium,  320.9°  C,  antimony,  630°  C,  and  copper  free 
from  oxide,  1083°  C.  These  points  furnish  constants  for  the  formula,  e  =a  +  bt  +  ct2  (see  Sosman,  Am.  J.  Sc., 
30,  p.  I,  1910). 

For  the  region  above  1100°  C  most  experimenters  base  their  results  upon  certain  radiation  laws. 
laws  all  apply  to  a  black  body  and  the  temperature  of  a  non-black  body  cannot  be  determined  directly  with- 
out correction  for  its  emissive  power.     For  standard  points  the  melting-  points  of  gold,  1336°  K  and  palla- 
dium 1822°  K,  are  convenient, 

Above  1336°  K  the  optical  pyrometer  is  generally  used  with  a  calibration  based  upon  Wien's  equation 


By  comparing  the  brightness  of  a  black  body  at  two  temperatures  and  applying  this  equation,  the  following 
formula  results: 

"»- 


where  R  is  the  ratio  of  the  brightnesses,  \,  the  wave-length  used,  TI  and  Ti,  the  two  temperatures,  and  C2 
=  14.250  n  deg.    Thus  if  R  is  measured  and  one  temperature  known,  the  other  can  be  calculated. 

A  table  of  the  standard  fixed  points  is  given  in  Table  207,  p.  195.  With  these  determined  there  comes  the 
difficulty  of  maintaining  this  temperature  scale  both  from  the  standpoint  of  the  standardizing  laboratory 
and  the  man  using  the  temperature  scale  in  the  practical  field.  In  the  region  of  the  platinum-resistance 
thermometer  and  the  thermocouple,  standards  of  either  can  be  obtained  from  the  standardizing  laboratories 
and  used  in  checking  up  the  secondary  instruments.  It  is  not  very  difficult  to  actually  check  up  a  resist- 
ance thermometer  at  any  one  of  the  standard  points  in  the  region  —40°  C  to  +450°  C.  It  is  a  little  more 
difficult  to  check  the  thermocouple  in  the  region  450°  C  to  1100°  C.  Most  of  the  standard  fixed  points  in 
this  region  are  given  by  melting  points  of  metals  that  must  be  melted  so  as  to  avoid  oxidation.  This  re- 
quires a  neutral  atmosphere,  or  that  the  saTnple  be  covered  with  some  flux  that  will  protect  it. 

Both  the  gold  and  the  palladium,  used  to  calibrate  the  scale  above  1300°  K,  can  be  successfully  melted  in 
a  platinum  wound  black  -body  furnace.  The  whole  operation  can  be  carried  out  in  the  open  air,  requiring 
neither  a  vacuum  nor  neutral  atmosphere  within  the  furnacs.  But  because  of  the  trouble  necessitated  by  a 
black-body  comparison,  much  time  can  be  saved  if  a  tungsten  lamp  with  filament  of  suitable  size  is  stand- 
ardized so  as  to  have  the  same  brightness  for  a  particular  part  of  the  filament,  when  observed  with  the 
optical  pyrometer,  as  the  standard  black-body  furnace  for  one  or  more  definite  temperatures.  With  such 
lamps  properly  calibrated,  any  one  may  maintain  his  own  temperature  scale  for  years,  if  the  calibration 
does  not  extend  higher  than  that  of  the  palladium  point  and  the  standard  lamp  is  not  accidentally  heated  to 
a  higher  temperature. 

(See  1919  Report  of  Standards  Committee  on  Pyrometry,  Forsythe,  J.  Opt.  Soc.  of  America,  4,  p.  205, 
i<)2o;  The  Measurement  of  High  Temperatures,  Burgess,  Le  Chatelier,  1912,  The  Disappearing  Filament 
Type  of  Optical  Pyrometer,  Forsythe,  Tr.  Faraday  Soc.,  1919.) 
SMITHSONIAN  TABLES. 


APPENDIX. 


439 


The  following  additional  adsorptio-  tables  (see  page  407,  Table  525)  may  be  of  use  in  the  "cleaning-up 
of  vacua."  See  Dushman,  General  Electric  Review,  24,  58, 1921,  Methods  for  the  Production  and  Meas- 
urement of  High  Vacua. 

TABLE  581.  —  Adsorption  of  H  and  He  by  Cocoanut  Charcoal  at  the  temperature  of  liquid  air. 

For  the  preparation  of  activated  charcoal  see  Dushman,  1.  c.  5  g  of  charcoal  at  the  temperature  of  liquid 
air  will  clean  up  the  residual  gases  in  a  volume  of  3000  cma  from  an  initial  pressure  of  i  bar  (bar  =  I  dyne/ cm3) 
to  less  than  0.0005  bars  at  the  temperature  of  liquid  air.  5  grams  cleaned  up  3000  cm8  of  H  from  an  initial 
pressure  at  room  temperature  of  o.oi  bar  to  a  final  pressure  at  liquid  air  temperature  of  less  than  0.0004  bar. 
The  clean-up  is  rapid  at  first  but  then  slower  taking  about  an  hour  to  reach  equilibrium.  The  figures 
of  the  following  table  are  from  Firth,  Z.  Phys.  Ch.  74, 129, 1910;  86,  294,  1913.  p  is  in  mm  of  Hg;  v  =  vol- 
ume adsorbed  per  g  of  charcoal  reduced  to  o°  C  and  76  cm  Hg. 


Hydrogen 

Helium 

P 

V 

p 

V 

P 

V 

9 

21.5 

QO 

59-3 

1  2O 

0-337 

17 

32.1 

126 

63.1 

171 

465 

3° 

46.5 

1  86 

69.2 

235 

.81 

5' 

53-3 

245 

76.0 

428 

I.I7 

59 

56.0 

705 

1.84 

TABLE  582.  —  Adsorption  by  Ch  rcoal  at  Low  Pressures  and  temperatures. 

Extrapolated  by  Dushman  from  Claude,  see  1.  c.,  and  C.R.  158,  861,  1914.  Amounts  occluded  in  terms 
of  volume  measured  at  i  bar,  o°  C.  e.g.  at  a  pressure  of  o.oi  bar,  i  g  charcoal  would  clean  up  130  cm3  hydro- 
gen or  18,000  cm3  nitrogen  from  a  pressure  of  i  bar  down  to  o.oi  bar. 


H,  T  -  77-6°  K 

N,  T  =  90.60  K 

p  =  8. 

v  =  106,000. 

P  =  5-3 

v  =  9,  500,000. 

I. 

i3'25° 

I. 

1,800,000 

O.I 

I»32S 

o.o 

180,000 

O.OI 

i33 

O.OI 

18,000 

O.OOI 

«3 

O.OOI 

i,  800 

TABLE  583.  —  Adsorption  of  Hydrogen  by  Palladium  Black. 

Palladium,  heated,  allows  hydrogen  to  pass  through  it  freely;  the  gas  is  first  adsorbed  and  then  diffuses 
through.  For  the  preparation  of  palladium  black,  see  reference  at  top  of  page  for  Dushman.  The  following 
data  are  from  Valentiner,  Verh.  Deutsch.  Phys.  Ges.,  3,  1003,  1911.  Different  samples  vary  greatly.  P  gives 
the  pressure  in  mm  of  Hg,  and  V  the  volume  at  standard  pressure  and  temperature  per  g  of  palladium  black. 


—  190°  C  :  P  =             .OOOC 
V=          2.05 

.001 
3.06 

.002 
33-° 

.005 
40.0 

.012 

47.2 

.025 
63.0 

+20°  C  :     P  =            .001 

.005 

•037 

.no 

•3T5 

.76 

V=     j     o.io 

0.26 

0.40 

0.52 

0.70 

0.92 

SMITHSONIAN  TABLES. 


INDEX. 


PAGE 

«  particles:  energy  of 396 

helium 394 

ions   produced 396,  398 

production    of 394 

range 396 

stopping  powers  of  substances  ....    395 

velocities,  initial 396 

Abbreviations 2 

Aberration  constant 4J4 

Absolute    units xxxvi,  311 

Absolute  zero  of  temperature 195,  408 

Absorption  coefficients:  see  transmission  coef. 

jS-rays    . 395 

T-rays 395 

X-rays        389 

Acceleration  of  gravity 424-426 

Accumulators,   voltage 3^3 

Actinium  group  of  radioactive  substances    ....   396 

Activity,   definition 435 

Adaptation,  rate  of  eye 257 

Adsorption,  by   charcoal 407 

by   fine   particles 407 

heat  of 407 

Aerodynamical   tables 150-153 

Agonic  line 433 

Air:  composition  of;  variation  with  alt.  and  lat.  .    .   421 

density  of  moist I33-I35 

densities  in   air,  reduction  to  vacuo    ....     73 

dielectric    strength 353 

humidity  relative,  via  v.   p.   and  dry    ....    187 

via  wet  and  dry 189 

index    of    refraction 292 

masses 4*9 

moist,  transparency,  short    X 419 

long   A 308 

transmission    coefficients    .    .   308, 418, 419 

resistance,   fluid 151—153 

sparkling  potentials  for 353-354 

thermal  conductivity,  high  temperatures   .    .    .   254 
thermometer,  comparison  with  59111     ....    193 

vapor  pressure  of  water  in 185-186 

viscosity ^4 

wave-lengths  in  air,  reduction  to  vacuo   .    .    .   293 

Albedos      417 

Altitudes  by    barometer 145 

by  boiling  points  of  water 144 

Alternating  current  resistances 344 

Aluminum:  mechanical    properties    .......    79-80 

resistivity   constants 334 

wire-tables,  English     units 342 

Metric   units 343 

Ammonia,  latent  and  specific  heats 228,  232 

Ampere  equivalents 311 

Ampere  turns xlvi 

Angstrom,  wave-length  unit 266 

Antennae,    resistances 364 

Antilogarithms,  std.  4-place,  p.  28;  .9  to  i.o   .    .     30 

Apothecaries    weights 7,8 

Arc,    iron,    lines    .    .    .    .    " 266-267 

Astronomical    data 411-420 

Atmosphere:  composition,  alt.  and  lat.  var 421 

density,   altitude  variation 421 

height  of 421 

homogeneous,   height   of 421 

pressure,  altitude  variation 421 

"  Atmosphere  ":  value  of  pressure  unit     .    .    .421,  435 

Atmospheric  water  vapor 185-186 

Atom:  Bohr 401 

Atom,  hydrogen:  mass,  mean  free  path 408 

radius,   mean   velocity 408 

Rutherford       401 


PAGE 

Atomic  heats,  elements  at  50°  K 226 

magnetic  field 401 

magnitudes 401,  408 

numbers 409 

volumes,    elements 226 

weights,  international 71 

/3-rays,  absorption  coefficients 395 

absorption    of 397 

ions  produced  by 398 

velocity 397 

Balmer  series  spectrum  formula 275 

Bar,  definition 435 

Barometer,  altitude,  variation  with 421 

heights,   determination  of  by     ....    145 

reduction  for    capillarity 143 

to  std.  gravity    ....    138-143 
to   std.    temperature    .    .    .    .    137 

Batteries,   composition,  voltages 312-313 

Baume  scale,  conversion  to  densities 109 

Bessel  functions,  ist,  2d  orders,  roots 66—68 

Biaxial  crystals,  formulae,  +  refractive    indices     .    .   286 
—  refractive    indices    .    .   287 

Black  absorbers,  long-\  transparencies 309 

Black-body:  brightness  (photometric)  of 261 

luminosity    of 261 

luminous  efficiency  of 261 

Planck's  constant 247 

radiation,  total,  for  various  temp.   .    .   247 
by  wave-lenths,  var.  temp.   .   248 

Stefan-Boltzmann   constant 247 

-temperature  for  C,  Pt  and  W  .    .    .    .   250 

Bohr    atom 275,401 

Boiling  points:  elements 199 

pressure  effect 200 

inorganic   compounds 201 

organic  compounds 203 

rise  of,  salts  in  H20 210 

water,-   pressure   variation    ....    144 

Boltzman  gas-constant  (entropy) 408 

Bougie   decimale 260 

Break-down   voltage,    dielectrics 304,  355 

Brightness  of  sky 419 

of  stars 413 

of    sun 260, 413 

temperature  of  C,  Pt  and  W 250 

of  various  illuminations 256 

of  various  light  sources 260-262 

Brinell    hardness 74 

British  thermal  unit 435 

IMtish    weights    and    measures 8-n 

Brownian  movement 406 

Buoyancy  correction:  of  densities      73 

weighings 73 

7-function      62 

7-rays:  absorption  coefficients 395 

absorption    of 397 

ions  produced  by 398 

Cadmium  line.  red.   X  of  intern,  prim,  std 266 

Calcite   grating   space 408 

Calibration  points  for  temperatures       195 

for  thermoelements 196 

Calorie,  definition 435 

Canal  rays 386 

Candle,  energy   from      260 

international  standard 260 

meter-candle,    foot-candle 259 

Capacity  of  wires  for  electrical  current 329 

Capacity,  specific  inductive:  crystals 361 

eases.  f(t,  p)   .    .  356-357 

liquids      357 

liq.    gases 359 

solids 360 

standard  solutions      .     360 


442 


INDEX. 


PAGE 

•  lority      173-174 

correction  to  barometer 143 

Cwxel    unit 260 

Cathode  rays: 386 

energy   of 386 

.:ion   depths 387 

generative   efficiency   for    .    .    387 

Cathodic  sputtering 387 

Is:  standard,  voltages 313 

:    normal xli 

portable xliii 

voltaic,    composition,    voltages     ....    312-313 

Contipoise       155 

Cbaract eristic    X-rays 387-392 

Charcoal,   adsorption   by 407 

Charge,   elementary   electrical 408 

Chemical    energy-    data 241-246 

Coals,  heats  of  combustion 242 

Collision   frequencies,    molecules 399 

Colloids 406-407 

Color:  eye  sensitiveness  to 256-258 

indices  of  various  stars 411 

lights,   of  various 261 

screens      306-307 

complimentary  colors 307 

temperature  of  (',  I't  and  \V 250 

Combination,    heats   of 245-246 

Combustion,  heats  of:  carbon  and  misc.  cpdj  .    .    .241 

explosives       243-244 

fuels       242 

Compressibility:  gases 104,128-132 

liquids 107 

solids       74  seq,  108 

Conductivity,  electrical:  see  resistivity    .    .    .    .322-332 

alloys 327-328 

electrolytic: 346-352 

equivalent 349 

ionic 352 

sp.  molecular 347 

limiting    values     .    .    .   348 

temp,    coefs 348 

Conductivity,  thermal:  alloys,   metals 213 

building    materials     .    .    .    .215 

earth      422 

gases 217 

high   temp 254 

insulators 214-216 

high  temp.    ...   214 

liquids       217 

metals,  high  temp 213 

salt   solutions 216 

water 216 

Cones,  number  and  distance  apart  in  eye 258 

Constants:  mathematical 14 

miscellaneous,  atomic,  etc 408 

radiation,  a,  Qlt  C2 247 

Contact  difference  of  potential      .    .    .    .   314  316  404 

Contrast,  eye  sensitiveness  to 

Convection,  cooling  by      251-255 

.  pressure   effect    .    .    .    .251-252 

sion  factors:  general  formulae,  see  introduction. 

Baumo  to  densities 109 

horse -power IQ7 

work-units   .  I0-: 

Cooling  of  bodies    ....  '  2-1-2?! 

Copper:  mechanical    properties      .    .'.'.'.'.'.    82-83 

wire,  alternating  current  resistance  '.  T.AA. 

wire  tables,   Knglish    units    .    .  ,$ 

metric    units    . 
Corpuscle    (Thomson) 

Corpuscular  radiation    (Z-rayi)    .'  '   ^87-188 

Cosines,  circular,  natural,    (", 

(radians)      .    '.    '.    \    \    37-40 

logarithmic,    (• ') ^-^ 

(vadians)        .    .    .    -57-40 
hyperbolic,  natural  logarithmic  ....   4i-47 
Cotangents,  circular,  natural,    r  ') 


212 
26l 


Critical  data  f 
Crova    wave-length     . 


PAGE 

Crystals:  diffracting    units,    X-rays 400 

elasticity 102-103 

refraction  indices:  alums,  quartz    .    .    .    .281 

fluorite,    spar    ....   280 

rock-salt,  silvine    .    .    .   279 

refr.  indices:  minerals,  isotropic    ....   282 

uniaxial 

(+-)     .    284,285 
biaxial 

(  +  -)    .   286,287 

miscel.  uniaxial 285 

biaxial 289 

Cubes  of  numbers 15 

Cubical  expansion  coefficients:  gases 222 

liquids       221 

solids     ....    222,  227 

Current  measures:  absolute   units xli 

equivalents 311 

Curie,  radium   standard 398 

point  and  constant,  magnetic     . 

Cutting-tool  lubricants i54 

Cylindrical  harmonics  (Bessel)  ist  and  2nd  deg.  .  66 
general  formulae  .  68 
roots  68 

Day,  length  of  sidereal .414 

Declination,  magnetic:  secular  change 428 

Degree  on  earth's  surface,  length  of 416 

Demagnetizing  factors  for  rods 374 

Densities  in  air,  reduction  to  vacuo  .    .    . 

Densities:  air  moist,  values  of  h/76o    .    .    .    .133-135 

alcohol  ethyl  aqueous 124 

methyl  aqueous J26 

alloys II4 

aqueous  solutions 122   159—161 

Baume  equivalents I09 

cane  sugar,  aqueous J26 

castor  oil      ... 

earth  ..::::::•;:::::  is 

elements   chemical IIO 

glycerol,    aqueous     .......  156 

inorganic   compounds 2oi 

insulators,  thermal 215216 

liquids       ,,. 

mercury,— 10°  to  +360°  C 121 

minerals „- 

organic   compounds    .    . 

Planets      ,   ,        \   ^ 

solids  various .113 

stars ]    '        [413 

sucrose,  aqueous   ........        '.156 

.sulphuric   add,  aqueous J26 

tin,  liquid;  tin-lead  eutectic 115 

water,  o°  to  41°  C,— 10°  to  250°  C.i  18, 120 

woods 95-98,  112 

Developers  and  resolving  power  of  photo,  plats   .       263 

Dtamagnetic  properties      36S 

Diamagnetic  susceptibility,  temperature 'effect   '.    '.    [372 


399 


Diameter  molecules 

^    some    organic    molecules    .  ,    400 

Dielectric  constant:   (sp.  inductive  capacity)    .   356-360 

crystals       361 

gases i  f(t,p) 356-357 

liquids 357 

liquefied  gases 359 

solids 36o 

standard  solutions      ...        .360 

cctric  strength   (see  sparking  potentials)    .   353-355 

Dielectrics,  volume  and  surface  resistances   .    .  331 

Differentials,  formulae      ...  „ 

Diffusion:  aqueous  solutions  into  water'.  166 

,Mscs 167,  168 

"twal      60 

>onic      40<; 

metals 


Dilution,'  beat  of  '(H2S64)    .'    .*  '   246 

Dimensional  formulae      ...  '*£  * 

Diopter      .  ?T.*   .'  '•    '•    '  ™ 

n!Pt  "I?*5"6*;'0'   '9 15  value,  secular  variation  .           430 

isK,  distribution  of  brightness  over  sun's  .               418 
Distance  earth  to  moon     . 

sim : . ; : : : :  414 


INDEX. 


443 


Distance  of  the  stars,  nebulae  and  clusters  .    .    .    .412 

Dyes,  transparency  of .?()I 

Dynamical  equivalent  of  thermal  unit 197 

e    (base  of  natural   logarithms) *4 

e   (elementary  electrical  charge) 400 

408 


e/rn 


•»,  and  th"ir  logarithms  x=o  to  10  . 
.c   fractional 


7T 


-o.i    to    5.0 


X—l      to     20 


55 


,.  , 

e  ~^x,  e~~    4  x=i   to  20      ...      55 

e'+e-*     e*~e~x  and  their  logarithms 41 

2  2 

Earth:   atmospheric  data 421 

conductivity,    thermal 422 

degrees  on,  length  of 410 

elements,  percentage  composition 423 

geochemical  data 423 

geodetical 424-427 

moments  of  inertia 427 

moon,  distance  of 4*4 

rigidity      427 

size  of,  shape  of 427 

spheroid  constants 427 

sun,   distance  of 4*4 

temperatures      420,  422 

viscosity 427 

Efficiency  of  various  lights 262 

Elastic  limit    (see  mechanical  properties)    ....      74 
Elastic  modulus  of  rigidity,   —temp,  variation   .    .    100 

Elasticity   (see  mechanical  data) 74 

crystals      102,  103 

Young's  modulus    (see   mechanical  prop.)     74 

Electrical   charge,  elementary 408 

Electrical  equivalents 3". 

Electrical  units:  international xxxyi 

standards   ....   xxxvm 

practical      xxxvi 

Electric  lights,  efficiency  of 262 

Electric,  triho-,  series   (frictional) 322 

Electrochemical  equivalents 345,  34» 

silver      345 

Electrolytic  conduction:  ammonium  acetate  .    .    .    .352 
equivalent  conductance  345~346 

hydrolysis 352 

ionic 352 

ionization  water      .    .    .    .352 

solutions       345-346 

spec,  molecular       .    .    .    .347 
limiting  value  (JL   .    .   348 

temp,    coef 348 

Electro-motive  force:  accumulators 3*3 

contact 314,316,404 

Peltier 321 

standard  cells      ......    313 

thermo-electric     ....   317—320 

pres.  effect      .    320 

voltaic  cells 312-313 

Weston  normal xli 

Weston   portable xliii 

Electromagnetic  system  of  units xxxi 

Electromagnetic/electrostatic    units =v      .    .    .   xxx,  xxxvi 

Electrons:  — ,    +      401 

affinity  of  elements 404 

e/m 404 

elementary  charge 404 

emission  from  hot  bodies 403 

ionization  potentials 403 

mass       408 

photo-electric  effect 403 

radius 408 

resonance  potentials 403 

work  required  to  remove 403 

Elements:  atomic  heats  at  50°  K 226 

atomic  numbers 409 

atomic  volumes 226 

atomic   weights    (international)     ....     71 

boiling   points 199 

compressibility 108 

conductivity  electrical    ......   323-326 

thermal      213 

densities no 

earth's  crust,  occurrence  in 423 


PAGE 

Elements:  evaporation  rate,  Mo,  W,  Pt 175 

expansion,  cubical    (gaseous) 222 

linear  (solid) 218 

hardness 73,  101 

isotopes      410 

latent  heat  of  evaporation 233 

melting  points 198 

meteorites,  occurrence  in 423 

Peltier  effect 317,  320—322 

periodic   system      409-410 

resistance,   electrical 323-326 

specific  heats 223,  225 

spectra       266-270 

thermal  conductivities 213 

expansion 128,  222 

thermo-electric  powers 317,319 

Thomson   effect 317,  320 

valencies 71 

vapor  pressures      175 

Elementary  electric  charge 408 

Elements,  magnetic,  at  various  observatories    .    .    .   434 

Elliptic  integrals 69 

Emanation    (radioactive) 398 

Emissivities,  radiation 249,  250 

Energy  kinetic,  definition      428 

of  molecule       408 

Energy,  minimum  visible  to  eye 261 

solar,  data  relating  to 418—420 

of  candle  radiation 260 

of  sound   waves 149 

Entropy  constant   (Boltzmann) 408 

Entropy  of  steam 234-240 

Equation  of  time 41.6 

Equilibrium   radioactive 394 

Equivalent,  electrochemical 345-346 

mechanical,  of  heat 197 


Erg 


435 


Erichson   values 73 

Errors,    probable 57~59 

Ettingshausen  effect 385 

Eutectic  mixtures,  melting  points 206,  207 

Evaporation  rate  of,  Mo,  Pt,  VV 175 

Expansion,  cubical:  gases      222 

liquids 221 

solids 220 

linear:  elements       218 

miscellaneous 219 

Explosives:  decomposition,   ignition  temp 244 

miscellaneous       243-244 

Exponential  functions :  see  index  under  e 41—55 

diffusion   integral 60 

gudermanians       41 

hyperbolic  functions  (nat)  .  41 
hyperbolic  functions  (logs)  .  41 
probability  integral  .  .  .  56-57 

Eye:  adaptation  rate 257 

color  sensitiveness 256-258 

contrast  sensibility 257 

Fechner's   law 258 

glare    sensibility 257 

heterochromatic   sensibility 257 

minimum  energy  visible 261 

miscellaneous    data 258 

persistence  of  vision 258 

pupil  size  for  various  intensities 258 

Purkinje    phenomenon 256 

sensitiveness  to  light 256-258 

small  dif.  of  color,  sensitiveness  to 258 

threshold  sensitiveness 256 

visibility  of  radiation,  relative 258 

Factorials:  y  function,  n=i  to  2 62 

n!,  n=i   to  20 47 

logs,  n=i  to  100 40 

Falling  bodies    (Stokes*   law) 150 

Farad 3 1 l 

Faraday      xliv,  311,  345 

Faraday  constant 408 

Fechner's   law 258 

Ferromagnetism       365 

Field,  magnetic:  earth's,  components    ....   428-434 
metals,  behavior  of  in   .    .    .    365-377 

resistance  of  metals  in 384 

rotation  of  plane  of  polarization  .    378 
thermo-galvanometric   effects      .    .   385 

Filaments,  heat  losses  from 255 

Flame  temperatures 244 

Fluidity     155 


444 


INDEX. 


PACE 

Foot  pound 436 

Fork,   tuning,  temperature  coefficient 149 

:ution,  heat  of,  for  elements 245,  246 

ule:  conversion .? 

dimensional,  see  introduction xxv 

least  squares 59 

Kraunhofer  lines,  solar,  wave-lengths jo? 

Free   path   of   molecules 399 

Free  zing  mixtures      211 

point,  lowering  of  for  salt  solutions  .    .    .   208 

point  of  water,  pressure  effect 200 

Frequencies,  corresponding  to  wave-lengths  ....   293 

in  air,  reduction  to  vacuo 293 

on,  mechanical       154 

internal  of  metals,  temp,  variation    .    .    .    101 

skin  (air  resistance) 152 

Frictional  electricity  series 322 

Functions:  Bessel   functions    (roots,    68)    ...   66-68 

cylindrical  harmonics 66-68 

elliptic 69 

exponential       48-56 

gamma 62 

hyperbolic 41 

probability       56-58 

trigonometric,  circular   (°  ') 32 

trigonometric,  circular  (radians)      ...     37 

zonal  harmonics 64 

Fundamental  frequency    (Rydberg) 408 

Fundamental  standards       xxxiii 

units xxiii 

Fusion  current  for  wires 329 

Fusion,  latent  heat  of 240 

Gages,  wire 333 

Galvano-magnetic  effects 385 

Gamma  function 62 

Gas  constant 408 

Gas  thermometry 192-194 

Gases:  absorption  of  by  liquids 172 

absorption  of  by  water 170-171 

absorption  coef:  long-wave  radiation      .    .    .   309 

X-rays       389 

compressibility 104 

conductivity,    thermal 217 

critical  data 212 

densities      127 

dielectric  constants 356-361 

strength       353~355 

diffusion      168 

ionic 405 

expansion    coefficients 222 

expansion    of      128-132 

flow  in  tubes 150 

ignition  temperatures  of  mixtures 244 

magnetic  susceptibility 377 

magnetic-optical  rotation 382 

refractive   indices 292 

Mnce    (aerodynamical) 150—153 

solubility  in   water 170-171 

sound,  velocity  of,  in 147 

specific  heats   (also  cp/c,) 230 

riscosity 164-165 

volume,  f  (t,  p) 104-106 

f(t),  1+0.00367,  logs  .    .    .    128-132 

x!v,  365 

•'•m  of  units xxxv 

Ceochemical  d;ita '    42^ 

MC  *,. .::::::: : : : : .;  ^ 

Clare  sensibility  of  eye ."257 

Chases:    refraction  indices,  American       277 

Orman,  temp.  var.    .    .    278 

•tance  electric,  temp,  var 332 

transparency  of 302-304,  306-307 

Glass  vessels,  volume  of 72 

(.'ram-molecule,    definition       43r, 

of  ralritc '.        4og 

•in     constant 427 

.  acceleration  of,  altitude  variation    .    .    !    .   424 
latitude  variation    ....    424 
.    .    425-420 
iipciftc,  see  densities. 

Gudermanians       ,, 

Gyration,  radii   of ..'.'.'.'    .'    ."    .'   70 

Hall  effect,  temperature  variation 3g- 


PAGE 

Hardness:  (sec  mechanical  properties) 74. 

Hrinell  test 74 

elements 101 

scleroscope    test 74 

Harmonics:  cylindrical   (Bessel) 66-68 

roots,  formulae   .    .     68 

zonal 64 

Heat:  adsorption  heats 407 

atomic  heats  of  elements 226 

combination 245-246 

combustion:  explosives 243-244 

fuels 242 

gases 242 

organic  compounds 241 

conductivity:  metals  (also  high  temp.)    .    .    .213 

gases       217,254 

liquids 217 

diffusivities 217 

dilution,   heat   of,   ILjSO* 246 

formation 245-246 

latent  heat  of  fusion ".   240 

vaporization,  elements      .    .    .233 

Nil, 232 

steam 234 

various    .    .    232-233 
pressure  variation,   NH3  liq.    .    .   232 

losses  from  incandescent  wires 255 

mechanical  equivalent  of 197 

neutralization,  H2SO,t 246 

solution 246 

specific:  alloys 227 

ammonia,   liq 228 

electricity       317 

elements 233 

gases      230 

liquids 227-228 

mercury      227 

minerals,  rocks 229 

silicates 229 

solids 227 

true   [elements,  f(t)] 225 

vapors 230 


water 


227 


total    [elements,  f(t)] 225 

treatment  of  steels 76 

Heating  effect,  radium  and  emanation  .  .    194 

Hefner  unit ,260 

Heights,  barometric  determination  of 145 

boiling  point  of  water  determination  of  .    .    144 

Helium,  production,  relation  to  radium 394 

Henry       xxxvii,  xliv,  311 

Heterochromatic  sensibility  of  eye 257 

Hertzen    wave-lengths 4O8 

High-frequency  electric  resistance  of  wires   ....   344 

Horizontal  intensity  earth's  field,   1915        .    .    .    .431 

secular    var.     .    .431 

Horse   power 197 

Humidity,  relative:  vapor-pressure  and  dry   ....    187 

wet  and  dry 189 

Hydrogen:  atomic  data,  mass,  radius,  etc 408 

series  spectra 275,  401 

thermometer      192—194 

Hydrolysis  of  ammonium  acetate 352 

Hydrostatic  pressures  of  Hg  and  HoO  columns  .  .136 
Hyperbolic  functions,  natural  and  logarithmic  .  .  41 
Hysteresis 365  et  seq,  375~376 

Ice,  allotropic  modifications      200 

freezing  point,  pressure  effects 200 

Ice-point,  thermodynamic  scale 195 

Ignition  temperatures  gaseous  mixtures 244 

Incandescent  filaments,  heat  losses 255 

Inclination  (dip)  of  magnetic  needle,  1915     ....   430 
secular  var.  .    .   430 

Index  of  refraction:  air 293 

alums 281 

crystals,  see  minerals,  etc. .  282-289 

fats 289 

fluorite,   f(t) 280 

gases  and  vapors 292 

glass  American 277 

German  f(t) 278 

Iceland  spar 280 

liquefied  gases 289 

liquids       290 

•  metals 296 

minerals,  isotropic 282 

uniaxial 284 

biaxial       286 


IXDKX. 


445 


PAGE 

Index  of  refraction:  miscellaneous,  isotropic       .    .      283 

uniaxial      .    .    .    285 

biaxial        .    .    .    289 

nitroso-dimthyl -aniline       .    .    .   280 

quartz 280 

rock-salt,   f(t)      279 

salt  solutions 291 

silvine       279 

solids,  biaxial       ....    286,  289 

isotropic    ....   282,  283 

uniaxial     ....   284, 285 

standard  media  for  microscope.    294 

vapors 292 

waxes 289 

Induction,  self 376 

Inductive  capacity,  specific:  crystals 361 

gases,  f(t.  i»)    .    .    356-357 

liquids       357 

liq.   gases 359 

solids 360 

standard  solutions    .    .360 

Inertia,  moments  of 70 

Inorganic  compounds:  boiling  points 201 

densities 201 

melting   points 201 

soluibilities 169 

Insulators:  break-down  potentials 364 

dielectric    properties    . 364 

resistance,  thermal 214-216 

electrical "...    331 

Integral:  diffusion 60 

elliptic 69 

formula 12 

gamma  function      62 

probability 56-57,60 

Intensity,  horizontal,  earth  field,  1915 431 

secular  var.   .    .    .   43 1 

Intensity,  total,  earth  field,   1915    .    .  • 432 

secular  var 432 

International    candle  standard 260 

electric  units xxxvi 

standards xxxvi  ii 

standard  radium 394,  398 

standard    wave-lengths    ....    266—267 


Intrinsic  brightness  of  various  lights  .  .  . 
Ionic  charge  

diffusion 

mobilities 

lonization  potentials 

Ions  produced  by  a,  /3,  •y  rays 

work  required  to  detach 

Ions,  conductance  of 

heat  of  formation 

Iron,  magnetic  properties  (steels)  .  .  . 

standard  wave-lengths,  international 

Isostacy 

Isotopes  


Joule      

Joule  magnetic  effect 


260 

401,  408 

•  •  405 

•  .  405 
. '.  403 
.  .  398 

403-404 
.  .  352 

.  .  246 

365-376 
266-267 
.  .  426 
.  .  410 


197 
365 


K  X-ray  spectrum  series 390 

Kerr's   constant,   magneto-optic 383 

Kinetic  energy 436 

molecular 408 

Kundt's  constant,  magneto-optic 383 

L  X-ray  series 39 r 

Lambert,   definition 256,  259 

Latent  heat  of  fusion 240 

Latent  heat  of  pressure  variation  liq.  ammonia  .    .    .  232 

Latent  heat  of  vaporization:  ammonia      .....  232 

formulse 232 

.  234 


steam  tables   . 
various     .    .    . 

Latitude  correction  to  barometer 

of  a  few  stations 

Least  squares:  formulse 

probability  integral,  arg,  hx 
x/r 
inverse 


Q.6745VV  (n—i) 


0.845  3  [i/Wn  — 


.    .   231 
139-142 

420, 434 

•  •      59 
.    .      56 

•  •      57 
.    .      60 

•  •      57 
.    .      58 
.    .      5S 

58 


Length,  standards  of xxxiv,  5 

Light:  eye,  sensitiveness  of  to 256-258 

flux,   definition 259 

intensities  on  various  days 256 

lambert,   definition      256 

least  visible  to  eye 261 

mechanical    equivalent 261 

photometric  standards 260 

units 259 

polarized,  reflection 295—297 

rotation  of  plane  by  substances  .    .310 
rotation  of  plane,  magnetic   .    378—383 

reflection  of:  formulae 297 

function  of  "  n  " 297 

reflecting  power:  metals 295-298 

pigments      299 

powders 300 

rough  surfaces     .    .    .    .    .   299 

scattered  light 300 

temperature  variation  .    .    .300 

sensitiveness  of  eye  to 256—258 

transparency  to:  crystals 305 

dyes 301 

glasses,   American    .    .   303—304 

Jena       302 

water 307 

velocity  of 408,  414 

wave-lengths:  cadmium  std.   line 266 

elements 269-271 

Fraunhofer  lines 265 

solar,  Rowland 272 

Std.  iron  lines     ....   266-267 

Lights,  brightness  of  various 260 

color  of  various 261 

efficiency  of  various  electric 262 

photographic  efficiency  of 264 

visibility  of  white  lights 260 

Light-year      414 

Limits  of  spectrum  series 276 

Linear  expansion  coefficients 218—219 

Liquids:  absorption  of  gases  by 172 

Baume  density  scale 109 

capillarity  of 173— 174 

combustion  heat,  fuels 242 

compressibilities 107 

conductivity,    thermal 217 

contact  emf 314-316 

densities 115-117 

mercury,  f(t)      121 

water,    f(t) 118-120 

dielectric  constant 357—360 

strength 355 

diffusion,  aqueous  solutions 166 

expansion    coefficients 221 

expansion  coefficients 221 

fuels,   combustion  heats 242 

magnetic  optic  rotation 380 

magnetic    susceptibility 377 

potential  dif.  with  substances   ....   314-316 

refractive  indices 289—291 

sound  velocity  in i47 

specific   heats 228 

surface   tensions 173—174 

thermal  conductivity      217 

expansion,,  cubical 221 

vapor  pressures 175-187 

viscosity,    absolute 157-159 

specific,    solutions 163 

Logarithms:  standard  4-place :     26 

1000  to  2000 24 

anti-,  standard  4-place 28 

.9000  to   i. oono 

Logarithmic   functions 40 

Longitudes  of  a  few  stations 420,  434 

Long-wave   transmissions 309 

Loschmidt's  number 408 

Lowering  of  freezing  points  by  salts 208 

Lubricants  for  cutting  tools 154 

Lumen 259 

Luminosity  of  black-body,   f(t) 261 

Lunar  parallax 414 

Lux 259 


0.45  3    in  —  i        ......      5« 

Leduc  thermomagnetic  effect     .........   385 

Legal  electrical  units     ...........    xxxvli 


M  X-ray    spectrum     .    . 
Mache    radioactivity    unit 
Maclauren's   theorem 


'  39o 

.  398 
.  13 


446 


1NDKX. 


ftic  field:  atomic 

bismuth,  resistance  in  ... 
Ettinghausen  effect  .... 
galvanometric  effects  .  .  . 

Hall    effect 

Joule  effect 

Leduc  effect 

Nernst   effect 

nickel,  resistance  in  .... 
optical  rotation  polarization  .  378 

resistance  (if  metals  in 

thermo-magnctic  effects 

Villari    effect 

Wiedemann  effect 

Magnetic  observatories,  magnetic  elements    .    .    .    . 
Magnetic  properties:  cobalt,  o°  to  100°  C.    .    .    . 

Curie  constant 

Curie  point 

definitions 

demagnetizing  factor  for  rods  . 
diamagnctism,  f(t)  .  .  365 

ferro-cobalt   alloy 

ferromagnetism 

hystersis       375 

iron: 367 

cast,   intense   fields 

pure 

soft,  o  and  100°  C.   .    . 
very  weak  fields  .... 

wrought       

magnetite,  o°,  100°  C.  .  . 
magneto-strict ive  effects  .  . 

magnet   steel 

maxwell 311 

nickel,  o°,   100°  C 

paramagnetism,  f(t)    .    .    365 

permeability 365 

saturation  values  for  steels   . 

steel: 367 

energy  losses  .  . 
magnet  steel  .  . 
manganese  steel 
saturation  values  . 
temperature  effect  . 
tool  steel  .... 
transformer  steel  .  371 

weak    fields 

Steinmetz  constant  .... 
susceptibility  .  .  365,  372 
temperature  effects  .  .371 

Magnetism  terrestrial:  agonic   line 

declination     .    .    . 

dip 

inclination 

intensity,  horizontal      .    .    . 

total      

magnetic  character  yearly  .    . 
observatories,  elements  at     . 

Magneto-optic  rotation,  gases 

Kerr    constant 

Kundt  constant 

liquids 

solids 

solutions       

Verdet's  constant    .    .    378 

Magnitudes,  absolute  stellar 415 

stellar 415 

sun 

Mass:. electronic,  f(velocity) 401 

fundamental  standard 

hydrogen    atom 

absorption  coefficient  for  X-rays   '. 

stellar 

Mathematical  constants .   .   . 

physical 

Maxwell xlv,  311 

Mean  free   path,   H  molecule    .... 

Telocity  H  molecule 

Measures,  weights:  customary— metric       

English — metric      

'•al  equivalent  of  heat    .    .    . 

light      .... 

Mechanical  properties:  definitions       

elastic   limit      .    . 
Krichson   value    . 
hardness    .    .    .    . 
moduli     .    . 


VAGE 
.  403 
.  384 
,  385 
•  385 
.  385 
,  365 
.  385 
,  385 
.  384 
-383 
384 
385 
365 
365 
434 
373 
37-2 
372 
365 
374 
3/2 
370 
365 
-376 
-376 
368 
369 
37i 
370 
373 
373 
365 
370 
,365 
373 
.  372 
,  37i 

•  373 
-376 

376 
370 
373 
373 

-372 
373 

,376 
370 
375 
377 

-373 
425 
420 
422 
422 
423 
424 
425 
426 
382 
383 
383 
380 
379 
38i 

-383 
412 
412 
415 
408 
xxxiv 
408 
389 
404 
H 
408 

,365 
408 
408 
-10 
5-7 
197 
261 
74 
74 

•  74 
74 

•  74 


PAGE 

il  properties:  definitions:  modulus  of  rupture     74 

proportional   limit.  '  74 

scleroscope     .    .    . 

ultimate     strength, 

eompr. 

tension 

yield  point    .    .    . 

alloys:  aluminum 

brasses 

bronzes 

copper 

iron 

miscel. 

steel 

white    metal    . 


74 

74 
74 
74 
8l 


83-85 
83-85 
75-79 
88-89 
•  77 
.89 


aluminum:       80-8 1 


alloys 
brick  and  brick  piers  ....     93 

cement go 

cement  mortars 90 

clay    products 93 

concrete      91 

copper: ..."     82 

brasses  and  bronzes  83—85 

wire 82-83 

heat  treatment  for  steels   .    .     76 

iron: 75 

alloys 75 

leather  belting 94 

p-ratio   extension/contraction.    101 
rigidity  moduli  f(t)    .    .    .    .    100 

rope,  manila 95 

steel-wire 79 

rubber,   sheet  .     94 

steel: 76 

alloys 77 

heat  treatment  for   .    .     76 

semi- 78 

wire      78 

wire-rope 79 

stone  products 92 

terra-cotta  piers 93 

tungsten      89 

white  metal 89 

woods:  conifers:  English    unit     99 

metric  unit  .      97 

hard:  English   unit     .     98 

metric  unit  .    .     96 

Melting  points:  alloys 206 

elements 198 

eutectics       207 

inorganic  compounds 201 

lime-alumina-silica  compounds     .    .    207 

organic    compounds 203 

paraffins 203 

pressure  effect 200 

water-ice,  pressure  effect     ....   200 

Meniscus,  volume  of  mercury 143 

Mercury:  density  and  volume,   — 10°  to  360"  C.     .    121 

conductivity  thermal,  high  temp 254 

electric  resistance   standard xxxviii 

meniscus,  volume  of 143 

pressure  hydrostatic  of  columns 136 

specific  heat 227 

thermometer 190-194 

vapor    pressure 180 

Metals:  conductivity,  thermal 213 

diffusion 168 

potential    differences,    Volta    ....   316,404 

reflection  of  light  by 295-296,  298 

refraction  indices 295-296 

optical  constants 295-298 

resistivity,  temperature  coefficient    ....   323 

pressure   effect 326 

Volta   emf 316,404 

weight  sheet  metal 116 

Metallic    reflection 295-296,  298 

Meteors,  chemical  composition 423 

Meter-candle      256,  259 

Metric  weights  and  measures,  equivalents  .    .    .       5-10 
Mho 436 


INDEX. 


447 


PAGE 

Micron,  fi 7,  436 

Milky  way,  pole  of 4'4 

Minerals:  densities 115 

refractive  indices:  biaxial      286 

isotropic 282 

uniaxial 284 

specific    heats 229 

Minimum  energy  for  light  sensation 261 

Mixtures  freezing 211 

Mobilities,   ionic 405 

Moduli,  — see  mechanical  properties 74-i«3 

Mogendorf  series  formula 275 

Moist  air,  density   of I33-I35 

maintenance    of 135 

transparency  to  radiation,  .36    to    1.711.   411 
to  2o/ti  .    .    .    308 

Molecular   collision    frequencies 399 

conductivities:  equivalent      ....   349-352 

specific 346-348 

crystal  units 400 

diameters      399,  400 

free    paths 399 

heats  of  adsorption       407 

liquefaction 407 

kinetic  energy 408 

magnitudes 399~4oo,  408 

number  in  cm3,  76  cm,  o°  C 4°8 

gram -molecule 408 

velocities       399 

weights  of  colloids 406 

Moments  of  inertia:  earth 427 

formulae     .........      70 

Month 4i4,  436 

Moon:  albedo 41 7 

distance  from  earth,  parallax 4T4 

radiation  compared  with  sun's 407 

Musical  scale 148 

tone    quality 149 

Mutual  induction 37& 

Nernst  thermomagnetic  potential  difference   ....   385 

Neutral  points,  thermoelectric 3*7 

Neutralization,  heat  of 246 

Nickel,  Kerr's    constants    for 383 

magnetic  properties,  o  to  100° 373 

resistance  in  magnetic  field 384 

Nitrogen   thermometer 192 

Nitroso-dimethyl-aniline,  refractive  index 280 

Nuclear  charge,  atomic 393,  4°i 

Number  of  stars 417 

Numbers  atomic 409 

X-ray  spectra  and     ....   390-393 

Numbers:  magnetic   character 433 

sun-spot '....415 

Nutation 4*4 

Observatories,  magnetic  elements  at 434 

Ohm:       xxxvii,  xxxviii,  311 

electrical  equivalents 311 

Oersted xlvi 

Oils,  viscosity  of 156,  157 

Optical  constants  of  metals 295 

Optical  rotation  magnetic 378—383 

Optical  thermometry 250 

Organ  pipes,  pitch 149 

Organic  compounds:  boiling  points 203 

densities 203 

melting  points 203 

Organic  salts,  solubilities 170 

Oscillation  constants  wireless  telegraphy       ....   362 

times  of  wires,  temperature  variation  .    .    101 

Overtones 149 

Tf  pi 14,  436 

P-limit  (proportional  limit) 74  et  seq. 

Parsec 414 

Parallax,  solar,  lunar 414 

stellar       412,  415 

Paramagnetism 365 

Partials   (sound) 149 

Particle,  smallest  visible 406 

Peltier  effect: 317,  321 

pressure   effect 320 


Pendulum,  second:  formula;  latitude  variation    .    .  42? 

Penetration  cathode  rays 3°7 

high  speed  molecules 387 

Pentane  candle      260 

thermometer 194 

Periodic  system:  Hackh 410 

Mendelejeff 409 

Permeability,  magnetic 365  et  seq. 

Persistence  of  vision 258 

Petrol-ether  thermometer 194 

Phosphorescence  (radio-active  excitation)      ....   394 

Phot 259 

Photoelectricity      403 

Photographic  data:  intensification 264 

lights,  efficiencies 264 

plate  characteristics 263 

resolving  power 263 

speeds  various   materials    .    .    .   263 

Photometric  definitions,  units 259 

standards 260 

Physiological  constants  of  the  eye 258 

Pi    (ir) 14,436 

Pigments,  reflecting  powers  f(X) 299 

Pipes,  organ:  pitch 149 

Pitch: 148 

organ  pipes 149 

voice,  limits 149 

Planck's  "  h"      408 

radiation  formulae,  Ci  Co 247 

Plane,   air  resistance  to 150-152 

Planetary  data 416 

Platinum  resistance  thermometer 195 

thermoelectric  thermometer 196 

thermoelectric  powers  against 319 

Poisson's  ratio 101 

Polonium  radioactive  series 398 

Polarized  light:  reflection  by 295-296,  297 

rotation  of   plane 310 

magnetic 378-383 

Porcelain,  resistance,   f(t) 332 

Positive    rays 386 

Potential   (emf ) :  accumulators      313 

cells  voltaic 312-313 

contact      314,316,404 

ionizing      403 

Peltier 321 

sparking,  kerosene      355 

various        .    .    .    .    353-355 

resonance 403 

standard   cells 313 

thermo-electric       317-320 

pressure  effect   .    .   320 

Weston  normal xli 

portable xliii 

Poundal      436 

Precession       414 

Pressure:  air,   on   moving  surfaces 150-152 

barometric,  reductions,  capillarity  .  .  .  143 
gravity  .  .  138-143 
temperature  .  .  137 

boiling  water 144 

critical,   gases 212 

mercury  columns 136 

volume  relations,  gases 104 

water  columns 136 

Pressure  effect  on  boiling   points      200 

melting    points 200 

resistance    electrical 326 

thermoelectric  powers 320 

Pressure  vapor:  alcohol,  methyl  and  ethyl   ....    178 
aqueous    (steam  tables  234)    .    183-186 

elements 175 

mercury 180 

salt  solutions 181 

water  vapor  (steam  tables  234)  183—186 

various      176-181 

Probable   errors      56-50 

Probability  integral 56-57 

inverse      60 

Proportional  limit  (P-limit) 74  et  seq. 

Pupil    diameter 258 

Purkinje    phenomenon 256 


Quality,    tone 

Quartz:  refraction    indices     .    .    .    . 
transmission  of  radiation  by 


149 
280 
30$ 


448 


INDEX. 


PAGE 

R,  gas  constant 408 

p,  I'oisson's  ratio I0' 

.ui 430 

circular  functions  in  terms  of 37 

Radiation:  black-hody.   formula? 247 

f(X,T)       -'47,^48 

total,   f(t) 247 

candle      26° 

constants,  <r,   Ci,  ('« 247 

cooling  by,  across  airspaces      .      ...   253 

high    temperatures    ....    254 

ordinary  temperatures  .    .    .   253 

-    pressure   effect      .    .    .   251-252 

emissivities       249,250 

eye  sensitiveness  to      256-258 

f(\) 256,258 

moon's  compared  to  sun's 4*5 

Planck's    formula 247 

a,   Stefan's   formula 247 

solar  constant  of 4i° 

variation  with  latitude 420 

month 420 

Stefan's  formula 247 

sun's  to  earth 4*8 

sun's   compared  to   moon 4*5 

temperature  as  function  of 250 

transmissibility  of  by  air,  moist     .   308,  419 

alum 305 

atmosphere  .  308,  419 
crystals,  f(\)  .  .  305 
dyes,  f(  )  .  .  .  301 
fluorite,  f(X)  .  .  305 
glass,  f(X)  .302-304 
ice-land  spar  .  .305 
lamp-black  .  .  .  309 
long-wave,  f(\)  .  309 
quartz,  f(X)  .  .  305 
rock-salt,  f(X)  .  305 
water,  f(X)  .  .  307 

visibility  of  by  eye 256,  258 

Radii  of  gyration 70 

Radio-activity 394-39$ 

o  rays:  helium 394 

ions  produced 398 

kinetic  energy 396 

number    produced 396 

production  of 394 

range 396 

stopping  powers  for     ....    395 

velocity,  initial 396 

actinium    group 396 

/Jrays:  absorption  coefficients  .   395,397 

ions  produced 398 

velocities      397 

7  rays:  absorption  coefficients   .   395,  397 

ions   produced 398 

constants,   various 396—397 

Curie    unit 398 

emanation 398 

general  characteristics 394 

heating  effects 394 

helium,  Production   of 394 

ions  produced  by  a,  @  and  y  rays     .    398 

isotopes 410 

Mache  unit 398 

phosphorescence 394 

radium   group 396 

spectra      398 

standard,  international 394 

thorium    group       396 

transformations 396,410 

transformation  constants 396 

vapor  pressure  of  emanation     .    .    .398 

ll*<flwm  emanation,    vapor-pressure 398 

Kroup 396 

spectra      398 

Radius  hydrogen  atom 408 

Reciprocals !j 

Reflection  of  light:  formulae      .297 

long-wave 309 

metals 295-298 

miscellaneous 298 

f(n,i) 297 

pigments  dry,  f(X) 299 

polarization  by 297 

rough  surfaces    .    .    .  200 

stelUte 296 

variation  with  angle      ....   300 
temperature    .    .300 


.       PAGE 

Refraction  index,  air,  f(X) 293 

alum       281 

crystals,  see  minerals   .    .    .   279-289 

fats 289 

fluorite,  f(t)      280 

gases      292 

glasses,  American,   f(X)    ....   277 

Jena,   f(X,  t) 278 

Iceland-spar 280 

liquids 290 

liquefied  gases 289 

microscopic  determination  media  .   294 

minerals,  biaxial,  positive     .    .    .   286 

negative     ...   287 

isotropic 282 

uniaxial,   positive   .    .    .   284 
negative  .    .    .   284 

miscellaneous,  biaxial 289 

isotropio     ....   283 

uniaxial       ....    285 

nitroso-dimethyl    aniline    ....   280 

oils 289 

quartz 280 

rock-salt,    f(t)       279 

salt    solutions 291 

silvine 279 

vapors 292 

waxes 289 

Relative  humidity,  vapor  pressure  and  dry    ....    187 

wet  and  dry 189 

Resistance,  air   (aerodynamical) 151-153 

planes 151 

angle  factor 152 

aspect  factor 152 

shape  factor 153 

size   factor 153 

skin  friction 152 

speed  factor 153 

Resistance,  resistivity   electrical    (see   conductivity). 

alloys,  f(t) 323,  327-328 

aluminum 334 

wire  tables 342,  343 

alternating  current  values 344 

antenna?    (wireless)      364 

copper,  f(t) 334,  335 

reduction  to  standard  temperature  335 

wire-tables,  English  units   .    .    .   336 

metric    units    .    .    .    339 

dielectrics,  volume,  surface 331 

electrolytic,  see  conductivity  .    .    .   345-352 

equivalents 311 

glass,  f(t) 332 

high  frequency  values 344 

high  temperature  values 330 

low  temperature  values 330 

magnetic   field,    effect  of 384 

mercury  resistance  standards  ....     xxxvili 

metals,   f(t) 323 

porcelain,   f(t) 332 

pressure    effect 3-26 

standards,  mercury xxxviii 

surface,  of  dielectrics 331 

thermometer,  platinum  resistance    .    .    .    195 

volume,  of  dielectrics 331 

wire,   auxiliary  table  for  computing   .    .   322 

wire  tables,  aluminum,  common   units    .   342 

metric     ....   343 

copper,  common  units      .    .   336 

metric 339 

Resolving  power  photographic  plate 263 

Resonance   potentials    (spectra) 403 

Retina,   physiological   data 258 

sensitiveness  to  light  and  colors  .    .    .   256-258 

RlKidity  of  earth "  .    427 

Rigidity  moduli,  f(t) 100 

Ritz  spectrum  series  formula 275 

Rocks,  specific  heats  of 229 

Rock-salt,  index  of  refraction 279 

Rods  in  retina  of  eye 258 

Rontgen  rays: 383-393 

absorption  'coefficients    (mass)    .    .    .    389 
atomic  numbers  and  spectra     .    .    390-393 

cathode  efficiencies 387 

corpuscular  radiation 387-388 

characteristic  radiations 387 

energy  relations 387 

general   radiations 387 


INDEX. 


449 


PAGE 

Rontgen  rays:  heterogeneous   radiations      387 

homogeneous  radiations 387 

independent  radiations 387 

intensity       388 

ionization 388 

K  series  of  radiations 39<> 

L  series  of  radiations 39 1 

M  series  of  radiations 392 

monochromatic   radiations 387 

secondary  radiations 387 

spectra:  absorption      393 

K  series 390 

L  series      391 

M  series 392 

tungsten 392 

wave-length  and  cathode  fall  ....  387 

Roots  of  Bessel  functions,   ist  and  2nd  orders    .    .  68 

Roots  square 15 

Rope,  manilla,  mechanical  properties 95 

steel  wire,  mechanical  properties 79 

Rotation  of  polarized  light       310 

magnetic    ....   378-382 

Rough  surfaces,  reflecting  power 299 

Rowland  solar  wave-lengths 272 

Rupture,  moduli  of 74  et  seq 

Rutherford   atom 401 

Kydherg  constant 408 

Rydberg  series  formula  (spectrum) 275 

a,  Stefan-Boltzmann 247 

Salt  solutions:  boiling   point   raising 210 

conductivity    thermal 216 

freezing  point  lowering 208 

vapor  pressure .    .    .    181 

Scales,   musical 148 

Scleroscope    (hardness  test) 74 

Screens,   color 306—307 

Second  pendulum,  formula 419 

sea-level  values,  f(0) 419 

Secohm xliv 

Secondary  batteries 313 

X-rays 387 

Self  induction 376 

Sensation,  Minimum  energy  of  light  for 261 

Sensitiveness  of  eye  to  light  and  radiation  .    .   256-258 

Series,    mathematical 13 

Series  spectra:  Balmer  formula 401,  275 

first  terms 276 

limits   of 276 

Morgendorff  formula 275 

Ritz  formula 275 

Rydberg   formula 275 

vibration  differences 276 

Sheet  metal,  weight  of 116 

Silver,  electrochemical  equivalent 345 

Silver  voltameter xl 

Silvine,   refractive   index 279 

Sines,  natural  and  logarithmic,  circular 32 

hyperbolic    ....     41 

Sky  brightness 419 

Skin  friction,  air  resistance 152 

Soap  films 174 

Solids:  compressibility 108 

contact  potentials 314,316,404 

densities 113 

dielectric  constants 360 

expansion  coefficients,  cubical 227 

linear     ....   218-220 

hardness 74  et  seq,  101 

magneto-optic  rotation 379 

refractive  indices 277-289 

resistance,  electrical 323-344 

velocity  of  sound 146 

Verdet's  constant 379 

Solubility:  gases  in  water 170 

pressure  effect   .      ...    171 
salts  in  water,  inorganic,  f(t)    .    .    .    .    169 

organic,  f(t) 170 

Solutions:  boiling  point  raise  by  salts  in    ....   210 

conductivity  electrolytic 346-352 

thermal 216 

densities   of   aqueous 122 

diffusion   of    aqueous 166 

dielectric  constant,  calibration  stds.  .  .  360 
freezing  points  lowering  by  salts  in  ...  208 
magneto-optic  rotation  by 381 


PAGE 

Solutions:  refractive  indices 291 

specific  heats 228 

surface  tensions 173 

vapor  pressures 181 

Verdet's  constant 381 

viscosities,  specific 1 59,  163 

Sound,  velocity  of:  gases       147 

liquids 147 

solids 147 

waves,   energy  of 149 

Sparking  potentials:  air,  alternating  potentials  .  .  353 
large  spark-gaps,  f(p)  .  .  354 
steady  potentials  .  .  .  .353 

dielectrics 355 

kerosene 355 

Specific  heat  of  electricity 317 

Specific  heats:  ammonia,   sat.   liq 228 

elements 223,  225,  226 

gases,  also  cp  /cr 230 

liquids 228 

mercury      227 

minerals  and  rocks 229 

rocks      229 

silicates 229 

solids 227 

vapors 230 

water 227 

Specific  gravities  (see  densities) 109—135 

conversion  of  Baume 109 

Specific  inductive  capacities:  crystals 361 

gases,  f(t,p)   .    .   356-357 
liquids,    f(t)       .    357~359 

solids      360 

std.  solutions     .    .    .   360 

Specific    molecular   conductivity 347-348 

Specific  resistance,  see  resistivity 323-326 

Specific  viscosity: 159,  163 

Spectrum:  black-body  intensities 247,  248 

elements,  international  units    .    .    .   267,  270 

eye  sensitiveness,   f(X) 256—258 

iron  standards,  international  units  .   266,  267 

radium      398 

series,  limits,   first  terms,  etc 276 

solar:  intensities  of  energy 418 

Rowland   wave-lengths 272 

cor.  to  intern,  scale  .    .   272 
standard  wave-lengths,  intern,  units.    266—267 

stellar 403 

wave-lengths  standards 266,  267 

reduction   to   std.   pressure.   268 

X-ray:  absorption 393 

atomic  numbers 390—393 

K  series 390 

L  series 391 

M  series 392 

tungsten      392 

Speed  of  corpuscles 401 

Spherical  harmonics 64 

Sputtering,     cathodic     ..." 386 

Squares  of  numbers 15 

Square  roots  of  numbers 15 

Squares,  least,  —  formulae  and  tables 56-59 

Standard  cells,  emf  of 313 

radium,    international 394 

refractive  media  for  microscope 294 

resistance,    mercury xxxviii 

temperature  calibration  points 195 

wave-lengths:  primary  (international)  .  266 
secondary  (international)  .  266 
tertiary  (international)  .  .  267 
reduction  to  std.  pressure  .  268 

Standards:  electrical,   international xxxviii 

fundamental xxxiii 

photometric 260 

Stars:  brightness 413 

densities 413 

distances 412 

equivalent  ist  magnitude 4*7 

first  magnitude  data   (positions,  etc.)    .    .    .415 

Harvard  classification 4" 

light,    total 417 

magnitudes,  apparent  and  absolute 413 

masses 413 

motions 412 

number  of 417 

parallax 415 


45° 


INDEX. 


FACE 

Stars:  size 4'3 

spectra 4" 

temperatures,    surface 411 

velocities    .   .   .   .' 41*.  4*5 

Steam  tables *34 

Steel:  ma&netic   properties 367-376 

mechanical    properties 76—79 

Stefan-Boltzmunn  constant,  and  formula 247 

Steinmetz  magnetic  constant 375 

Stcllite.  reflecting  powers 150 

Stem  correction  for  thermometers 190-191 

Stokes  law  for  falling  bodies 150 

Stone,  mechajiical  properties 92 

Storage  batteries 3 '3 

Strengths — see   mechanical  properties 74~99 

Sucrose,  viscosities  of  solutions,  f(t) 156 

Sugar  cane,  densities  aqueous  solutions 126 

Sulphuric  acid,  densities  aqueous  solutions  ....  126 

Sun:  apex  of  solar  motion 4" 

brightness       260 

disk  brightness  distribution 418 

distance  to  earth 4*4 

Fraunhofer   lines 265 

magnitude,    stellar 4*3 

motion 4" 

numbers.  Wolf's  sun-spot 4*5 

parallax      4*4 

radiation  compared  to  moon 4*4 

constant  (solar  constant) 41° 

variation  with  month  and  latitude  .    .  420 

spectrum:  energy  intensities 4T^ 

Fraunhofer   lines 265 

Rowland's    wave-lengths 272 

spot  numbers,    Wolf's 41 5 

temperature 418 

velocity      41 1 

wave-lengths:  Fraunhofer  lines      265 

Rowland's 272 

Sunshine,  duration  of  f  (month,  latitude) 417 

Surface  resistivities,  solid  dielectrics 331 

Surface    tensiens 173,  174 

Susceptibility  magnetic,  definition 365 

elements,    etc 377 

Tangents  circular,  nat.  and  log.,  f(°,  ')      ....  32 

f  (radians)     ...  37 

hyperbolic,  nat.  and  log 41 

Taylor's  series 13 

Telegraphy,    wireless: 362,  364 

Temperature,  black -body  scale  for  W 250 

brightness  black  body  as  function  of.  261 

brightness  scale  for  C 250 

color  scale  for  W 250 

critical  gas  constants 212 

earth:  f  (altitude) 421 

f(latitude) 422 

monthly  and  yearly  means   .    .  420 

variation  below  surface     .    .    .  422 

flame  temperatures 244 

ignition,  gaseous  mixtures 244 

standards xxxiv 

stellar      411 

sun's 418 

thermodynamic 195 

zero  absolute       195 

Tensile  strengths,  see  mechanical  properties  .    .    .   74-99 

Tension,    surface 173,  174 

Tensions,  vapor,  see  vapor  pressures 175-186 

Terrestrial  magnetism:  agonic  line 425 

declination 420 

dip 422 

inclination 422 

intensity,  horizontal     .    .    .  423 

total 424 

magnetic  character,  yearly    .  425 

observatories,   elements  at    .  426 

Thermal  unit,  British 435 

standard  calorie 435 

Thermal  conductivity:  alloys,   metals 213 

building  materials      .  215 

earth      422 

gases      217 

high  temperature  254 


PAGE 

Thermal  conductivity:  insulators 214-216 

high  temp.   214 

liquids 217 

metals,    high    temper- 
ature        213 

salt  solutions     .    .    .   216 

water 216 

Thermal  diffusivities 217 

Thermal  expansion:  cubical:  gases 222 

liquids      221 

solids 220 

linear:  elements 218 

miscellaneous      ....   219 

Thermal  unit:  British 435 

calorie 435 

dynamical   equivalents    ...    197 

Thermo-chemistry:  heat  of  combustion:  carbon  cpds    .   241 

coals       .    .    .    242 

cokes      .    .    .    242 

gases      .    .    .   242 

liquid   fuels      .242 

miscellaneous    .  24 1 

peats       .    .    .    242 

heat  of  dilution,  H2S04     ....   246 

formation       245 

ions 246 

neutralization       ....   246 

Thermodynamical  scale  of  temperature,  ice-point  .    .    195 
Thermoelectrical  properties:   (emf)   alloys     ....   318 

platinum  319 
elements  .  .  .  317 
Peltier  .  .  317,  321 
pressure  effects  .  320 
Thomson  .  317,  320 

Thermoelements,  calibration  of ^96 

Thermogalvanometric   effect 385 

Thermomagnetic   effects 385 

Thermometry:  absolute  zero       195 

air—  i6Hl  o°  to  300°  C  ....  193 

59in>  100°  to  200°  C  ...  193 

59*11,  high    temperature    ...    194 

calibration  points,  standard    .    .    .    .    195 

gas-mercury,  formulae,  comparisons  192-194 

hydrogen— 1 6Hi,  o°  to  100°  C  .    .    192 

i6in,     59  _5°     to 

—  35°  C 192 

various 194 

ice   point 195 

Kelvin    scale 193 

mercury  cf  with  gas 190-194 

platinum  resistance 195 

resistance   electrical 195 

stem  corrections 190-191 

thermodynamic  scale,  ice-point   ...    195 
thermo-electric,  Cu-Constantan    ...    196 

Pt-PtRh 196 

Thomson  thermo-electric  effect 317,320 

Thorium  radio-active  group,  constants  of 396 

Threshold  sensitiveness  of  eye ^  .    .    .   256 

Timber,  strength  of 96-99 

Timbre    (sound) 149 

Time,  equation  of 416 

Time,  solar,  sidereal 414 

Time  standards xxxiv 

Transformation  constants  of  radio-active  substances.   396 

Transformation  points  of  minerals 207 

Transmissibility  to  radiation:  air,  moist  .  .  .  308,419 
atmospheric  .  .  .  .418 
crystals,  various  .  .  .  306 

dyes 301 

glass,  American   .   303,  304 
Jena       ....   302 

water 307 

water-vapor       .    .    308,  419 

Trigonometric  functions :  circular,    (° ')    nat.,   log.    .     32 

(radians),  log   .    .     37 

hyperbolic,  nat.,  log.   ...     41 

Tribo-electric  series 322 

Tubes,  flow  of  gas  through 150 

Tuning  forks,  temperature  coefficients 149 

Ultimate  strengths  of  materials,  see  Mechanical. 

properties 74~99 


INDEX. 


451 


Ynits  of  measurements,  see  Introduction     ... 

electrical,  absolute  .    .    . 

international    . 

legal      .    .    . 

practical      .    . 

fundamental 

photometric 

radioactive 

work,  transformation  factors 
Uranium  group  of  radio-active  substances  .... 


PAGE 

.  xxiii 
.  xxxv  i 
.  xxxvi 
xxxvii 
.  xxxvi 
xxiii 
.  260 
.  394 
197 
•  396 


T,  ratio  electro-magnetic  to  —static  units  .    .   xxx,  xxxvi 

Vacuo,  reduction  of  densities  to 73 

weighings  to 73 

Valencies  of  the  elements 71 

Van  der  Waal's   constants 212 

Vaporization,  latent  heat  Of: 231 

ammonia 232 

elements,  theoretical  .   233 

formula      232 

steam  tables  .    .    .    .234 

Vapor  pressure:  alcohol  ethyl 178 

methyl       178 

aqueous  (see  water  below)  .    .    183,  234 

carbon    disulphide i79 

elements      *75 

mercury 180 

radium   emanation    .......   398 

salt  solutions 181 

various 179—180 

water:  atmospheric  via  wet  and  dry 

sea-level    .    .    .    186 
other  altitudes  .    185 

saturated       183 

steam    tables 234 

Vapor,  water;  weight  per  m3  and  ft3 185 

Vapors:  densities 127,  234 

diffusion  of 167,  168 

heats  of  vaporization 231-239 

heats  specific 230 

pressures,  see  vapor  pressures  ....    175—186 

refractive  indices 292 

specific  heats 230 

viscosities      164 

water,  transparency  to  radiation  .    .    .   308,  419 

Velocity  of  light 408,  414 

molecules 399 

sound,  in  gases       147 

liquids 147 

solids      146 

stars 4H»  412 

sun      411 

Verdet's  constant   (magneto- optic) 378-382 

gases 382 

liquids       380 

solids 379 

solutions,    aqueous 381 

Vessels,  volume  of  glass,  via  Hg 72 

Villari  magnetic  effect 365 

Viscosity:  air 164 

alcohol  ethyl,  f(t,  dilution) 155 

castor  oil,  f(t) 156 

centipoise,    definition 155 

definition       155 

earth 427 

gases,  temperature  and  pressure  var.   164-165 

glycerol,  dilution  variation 156 

liquids,    f(t) 157-158 

specific:  solutions,  f(dens.,  t)      ....    159 

atom.  cone.  25°  C.     .    163 

sucrose  solutions,  f(t,  dilution)    ....    156 

vapors,  f  (p,  t) 164-165 

water,  f(t) 155 

Visibility  of  radiation       256-258 

relative  of  various  colors 256-258 

white  lights • 260 

Vision,  distinct      258 

persistence   of 258 

Voice,  pitch  limits  of 149 

Voltages:  accumulators       313 

contact      314,  316,  404 

Peltier 321 

standard   cells 313 

thermoelectric      317-320 

pressure   effect 320 

voltaic  cells 312-313 

Weston  normal xli 

Weston   portable .  xliii 


PAGE 

Voltaic  cells;    comp.,  emf:  double  fluid 312 

secondary 313 

single  fluid 313 

standard 313 

storage 313 

Voltameter,   silver xl 

Volts,  electrical  equivalents 311 

Volts,  legal,  international xli,  3 1 1 

Volume  atomic,  50°  K 226 

critical  for  gases 212 

glass  vessels,  determination  of 72 

gases,  f  (p) 104-106 

f(t) 128-132 

mercury,  — 10°  to  +360°  C 121 

resistance  of  dielectrics 331 

specific  of  elements 225 

water,  o°  to  40°  C 119 

—  10°  to  250°  C 120 

Vowels,  tone  characteristics 149 

Waal's   (van  der)  constants 212 

Water:  boiling  point,  f(p) 144 

density,f  (t)  o°  to  4i°C,—  10°  to  25o°C  118-120 

solutions,  ethyl  alcohol      124 

glycerol      156 

methyl  alcohol 126 

sucrose       156 

sugar    (cane) 126 

sulphuric  acid 126 

various      .    .    .    122,  159-163 

freezing  point,   f( pressure) 200 

ionization   of 352 

melting  point,  f(p) 200 

pressure   (hydrostatic)   of  columns  of   ...    136 

solutions:  boiling  points 210 

densities,  see  water,  density  solu- 
tions    .    .    118-126,  156,  159-163 

diffusion 166 

electrolytic  conduction      .    .   346-352 

freezing   points 208 

viscosities 156,  159-163 

specific   heat      227 

thermal  conductivity      : 216 

transparency  to  radiation 307 

vapor  pressure 234—239,  183—184 

vapor  pressure  of  in  atmosphere     .    .    .    185—189 

viscosity,  f(t) 155 

volume,  o°  to  40°  C,  — 10°  to  250°  C.  119,  120 
Water-vapor,  determination   in    atmosphere,   via   wet 

and  dry  sea-level      186 

various    altitudes    .    .    .    .    185 

relative  humidity  via  wet  and  dry  .    .    189 

dry  and  v.p.  .    .    187 

in  atmosphere,  f  (altitude) 421 

transparency 308, 419 

weight  saturated  per  m3  and  ft3  .    .    .    185 

Watt      xxxvii,  xlv,  311 

Wave-lengths:  Angstrom,  definition 266 

cadmium  red  line 266 

Crova       261 

elements,  international  scale  .    .   267,  270 

Fraunhofer  solar  lines '  265 

iron  arc  standards 266—267 

neon,  international  scale    .    .    .  •  .    .   266 

pipes    (sound) 149 

limits.  Hertz,  X,  visible,  etc.   ...   408 

Rontgen       390-393 

Rowland   solar 272 

corrections  to  Intern   X  272 

solar,  Fraunhofer  lines 265 

Rowland 272 

standard  pressure,  correction  to  ...   268 

standards:  international  primary     .    .   266 

secondary  266-267 

tertiary      .    .   267 

vacuo,  reduction  to 293 

wireless 362-364 

X-ray      390-393 

Waves,  energy  of  sound 149 

Weighings,  reduction  to  vacuo 73 

Weight  sheet  metal 116 

Weights,    atomic 71 

Weights  and  Measures:  customary  to  metric  ...  5 
metric  to  customary  ...  6 
metric  to  imperial  ....  8 
imperial  to  metric  ....  10 
miscellaneous 7 


452 


INDEX. 


PAGE 

Weston  normal  cell xli 

Weston  portable  cell xlili 

Wiedemaiui  magnetic  effect 365 

Wind   pressures      150-153 

Wire  gages,  comparison 333 

Wire,  mechanical  properties:  copper 82-83 

steel 78 

sifi'l  rope  and  cable     .      79 

Wire  resistance,  auxiliary  table  for  computing  .    .    .   322 

Wire  tables:  aluminum,  English  measures     ....   342 

metric    measures      ....   343 

see  also 334 

copper,  English    measures 336 

metric  measures 339 

see  also 334 

temperature  coefficients      .334,335 
reduc.  to  std.  .   .335 

Wires,  alternating-current  resistance 344 

carrying  capacity  of 329 

high-frequency  resistance 344 

V.ires.  .beat  losses  from  incandescent,  bright  Pt.    .    255 
Pt  sponge     .   255 

Wireless  telegraphy:  antennae  resistances      ....   364 
wave-lengths,  frequencies,  oscil- 
lation constants 362 

Wolf  sun-spot  numbers,  1750  to  1917 415 

Woods:  densities 96-99,  112 

mechanical  properties:  conifers,  Eng.  units.     99 

metric  units     97 

hard  wds,  Eng.  units     98 

metric  units    96 

Work,  conversion  factors  ,  , 197 


PAGE 

X-rays:      383-393 

absorption  coefficients    (mass)      389 

atomic  numbers  and  spectra     .    .  " .    .   390-393 

calcite  grating  space 408 

cathode  efficiencies 387 

characteristic  radiations 387 

corpuscular  radiation 387-388 

crystals,  diffraction  with 401 

energy  relations 387 

general    radiations 387 

heterogeneous  radiations 387 

homogeneous    radiations 387 

independent  radiations 387 

intensity 388 

ionization      388 

K  series  of  radiations 390 

L  series  of  radiations 391 

M  series  of  radiations 392 

monochromatic  radiations 387 

secondary  radiations 387 

spectra:  absorption 393 

K  series 390 

L  series 391 

M  series 392 

tungsten      392 

wave-lengths 390-393 

wave-lengths  and  cathode  fall 387 

Years 414, 437 

\  early  temperature  means 420 

Young's  modulus,  definition       74 

values 74-103 

Yield  point  (mechanical  property) 74-103 

Zero,  absolute,   thermodynamic  scale 195 

Zonal   harmonics 64. 


£bc  fctoettfi&e  press 

CAMBRIDGE   .    MASSACHUSETTS 
U  .  S  .  A 


DATE    DUE    SLIP 

OL    I.I1IKAKV 

THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


Ql'i     7-     | 

SEP  2  5  1942 
US 


2  ii  1946 


1949 


OGT  25  195" 


rtt 


Iiibrary  of  the 
University  of  California  Medical 


